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You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org" }, "file": "books/boyden-first-book-in-algebra-1895.json" }, "chapters": [ { "id": "boyden-first-book-in-algebra-1895/ch-preface", "number": "PREFACE", "title": "PREFACE", "name": "Boyden 1895, PREFACE", "pages": null, "concepts": [ "concept/arithmetic" ], "excerpts": [ "boyden-first-book-in-algebra-1895/x-ba155aca8b", "boyden-first-book-in-algebra-1895/x-424354f563", "boyden-first-book-in-algebra-1895/x-2ac6747809", "boyden-first-book-in-algebra-1895/x-682fc91098", "boyden-first-book-in-algebra-1895/x-741ec4980f" ], "equations": [], "exercise_sets": [ "boyden-first-book-in-algebra-1895/ex-1", "boyden-first-book-in-algebra-1895/ex-2", "boyden-first-book-in-algebra-1895/ex-3", "boyden-first-book-in-algebra-1895/ex-4", "boyden-first-book-in-algebra-1895/ex-5", "boyden-first-book-in-algebra-1895/ex-6", 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"boyden-first-book-in-algebra-1895/x-d04db172ac" ], "equations": [], "exercise_sets": [ "boyden-first-book-in-algebra-1895/ex-15" ] }, { "id": "boyden-first-book-in-algebra-1895/ch-subtraction", "number": "SUBTRACTION", "title": "SUBTRACTION", "name": "Boyden 1895, SUBTRACTION", "pages": null, "concepts": [ "concept/difference", "concept/minuend", "concept/negative-number", "concept/number-line", "concept/parenthesis", "concept/polynomial", "concept/remainder", "concept/subtrahend", "method/addition", "method/subtraction", "theorem/removing-parentheses-preceded-by-minus", "theorem/removing-parentheses-preceded-by-plus" ], "excerpts": [ "boyden-first-book-in-algebra-1895/x-5a03958014", "boyden-first-book-in-algebra-1895/x-14994bf130", "boyden-first-book-in-algebra-1895/x-1880333ab4", "boyden-first-book-in-algebra-1895/x-6db5540ae4", "boyden-first-book-in-algebra-1895/x-6416c9abd4" ], "equations": [ "boyden-first-book-in-algebra-1895/eq-eac7109220", 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"concepts": [ "concept/coefficient", "concept/complete-divisor", "concept/dividend", "concept/divisibility", "concept/divisor", "concept/exponent", "concept/monomial", "concept/polynomial", "concept/quotient", "concept/radical-sign", "concept/remainder", "concept/root", "concept/trial-divisor", "method/dividing-a-monomial-by-a-monomial", "method/dividing-a-polynomial-by-a-monomial", "method/dividing-a-polynomial-by-a-polynomial", "method/division", "method/extracting-the-cube-root", "method/extracting-the-root-of-a-fraction", "method/extracting-the-root-of-a-monomial", "method/extracting-the-square-root", "method/multiplication", "method/multiplying-a-compound-expression", "theorem/cube-of-a-sum", "theorem/index-law-in-division", "theorem/law-of-signs-in-division", "theorem/law-of-signs-in-multiplication", "theorem/square-of-a-sum" ], "excerpts": [ "boyden-first-book-in-algebra-1895/x-603e62820e", "boyden-first-book-in-algebra-1895/x-b0a424718b", 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"boyden-first-book-in-algebra-1895/eq-31aeee1cab", "boyden-first-book-in-algebra-1895/eq-efe3242df1", "boyden-first-book-in-algebra-1895/eq-f8c037cebf", "boyden-first-book-in-algebra-1895/eq-f0e694f3da", "boyden-first-book-in-algebra-1895/eq-0b11f67dc0", "boyden-first-book-in-algebra-1895/eq-aaa1990315" ], "exercise_sets": [ "boyden-first-book-in-algebra-1895/ex-31", "boyden-first-book-in-algebra-1895/ex-32", "boyden-first-book-in-algebra-1895/ex-33", "boyden-first-book-in-algebra-1895/ex-34", "boyden-first-book-in-algebra-1895/ex-35", "boyden-first-book-in-algebra-1895/ex-36", "boyden-first-book-in-algebra-1895/ex-37", "boyden-first-book-in-algebra-1895/ex-38" ] }, { "id": "boyden-first-book-in-algebra-1895/ch-greatest-common-factor", "number": "GREATEST COMMON FACTOR", "title": "GREATEST COMMON FACTOR", "name": "Boyden 1895, GREATEST COMMON FACTOR", "pages": null, "concepts": [ "concept/common-factor", "concept/factor", "concept/highest-common-factor", "concept/prime-factor", "method/finding-the-highest-common-factor" ], "excerpts": [ "boyden-first-book-in-algebra-1895/x-17cd022a74", "boyden-first-book-in-algebra-1895/x-a12f96a6c4", "boyden-first-book-in-algebra-1895/x-e270c330fa", "boyden-first-book-in-algebra-1895/x-a30b6fbde1" ], "equations": [ "boyden-first-book-in-algebra-1895/eq-6b7c844c53", "boyden-first-book-in-algebra-1895/eq-4852306701", "boyden-first-book-in-algebra-1895/eq-70f6a00386" ], "exercise_sets": [ "boyden-first-book-in-algebra-1895/ex-39" ] }, { "id": "boyden-first-book-in-algebra-1895/ch-least-common-multiple", "number": "LEAST COMMON MULTIPLE", "title": "LEAST COMMON MULTIPLE", "name": "Boyden 1895, LEAST COMMON MULTIPLE", "pages": null, "concepts": [ "concept/common-multiple", "concept/equivalent-fractions", "concept/factor", "concept/lowest-common-denominator", "concept/lowest-common-multiple", "concept/lowest-terms", "concept/mixed-number", "concept/prime-factor", "method/adding-fractions", "method/dividing-by-a-fraction", "method/factoring", "method/finding-the-lowest-common-multiple", "method/multiplying-fractions", "method/reducing-a-fraction-to-lowest-terms", "method/reducing-fractions-to-lowest-common-denominator", "method/simplifying-a-complex-fraction" ], "excerpts": [ "boyden-first-book-in-algebra-1895/x-5885b6a06a", "boyden-first-book-in-algebra-1895/x-8e99a01aef", "boyden-first-book-in-algebra-1895/x-f629da5e05" ], "equations": [], "exercise_sets": [ "boyden-first-book-in-algebra-1895/ex-40", "boyden-first-book-in-algebra-1895/ex-41" ] }, { "id": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "number": "REDUCTION OF FRACTIONS", "title": "REDUCTION OF FRACTIONS", "name": "Boyden 1895, REDUCTION OF FRACTIONS", "pages": null, "concepts": [ "concept/algebraic-fraction", "concept/equivalent-fractions", "concept/highest-common-factor", "concept/lowest-common-denominator", "concept/lowest-common-multiple", "concept/lowest-terms", "concept/mixed-number", "method/factoring", "method/reducing-a-fraction-to-an-integral-or-mixed-expression", "method/reducing-a-fraction-to-lowest-terms", "method/reducing-a-mixed-expression-to-a-fraction", "method/reducing-fractions-to-lowest-common-denominator" ], "excerpts": [ "boyden-first-book-in-algebra-1895/x-9b2757713a", "boyden-first-book-in-algebra-1895/x-03fca7add8", "boyden-first-book-in-algebra-1895/x-d2961ca779", "boyden-first-book-in-algebra-1895/x-ef6f872f0a", "boyden-first-book-in-algebra-1895/x-de60a748c3" ], "equations": [ "boyden-first-book-in-algebra-1895/eq-641bd3efa5", "boyden-first-book-in-algebra-1895/eq-03fca7add8", "boyden-first-book-in-algebra-1895/eq-ef6f872f0a", "boyden-first-book-in-algebra-1895/eq-3a9b5f53a1", "boyden-first-book-in-algebra-1895/eq-4ba2a5499f" ], "exercise_sets": [ "boyden-first-book-in-algebra-1895/ex-42", "boyden-first-book-in-algebra-1895/ex-43" ] }, { "id": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "number": "OPERATIONS UPON FRACTIONS", "title": "OPERATIONS UPON FRACTIONS", "name": "Boyden 1895, OPERATIONS UPON FRACTIONS", "pages": null, "concepts": [ "concept/algebraic-fraction", "concept/equivalent-fractions", "concept/lowest-common-denominator", "concept/lowest-terms", "method/adding-fractions", "method/dividing-a-fraction-by-an-expression", "method/dividing-by-a-fraction", "method/extracting-the-root-of-a-fraction", "method/factoring", "method/multiplying-a-fraction-by-an-expression", "method/multiplying-fractions", "method/raising-a-fraction-to-a-power", "method/writing-by-inspection", "theorem/difference-of-two-cubes", "theorem/difference-of-two-squares", "theorem/fundamental-principle-of-fractions", "theorem/sum-of-two-cubes" ], "excerpts": [ "boyden-first-book-in-algebra-1895/x-79a4e44dc9", "boyden-first-book-in-algebra-1895/x-ebebf6dceb", "boyden-first-book-in-algebra-1895/x-7a92af1474", "boyden-first-book-in-algebra-1895/x-bf66e18b0d", "boyden-first-book-in-algebra-1895/x-a549763b75" ], "equations": [ "boyden-first-book-in-algebra-1895/eq-abfdb69264", "boyden-first-book-in-algebra-1895/eq-4db100aa7c", "boyden-first-book-in-algebra-1895/eq-c78fd82121", "boyden-first-book-in-algebra-1895/eq-02f247f875", "boyden-first-book-in-algebra-1895/eq-a2d7b7babd", "boyden-first-book-in-algebra-1895/eq-22083ef9c6", "boyden-first-book-in-algebra-1895/eq-7e92e07c3b" ], "exercise_sets": [ "boyden-first-book-in-algebra-1895/ex-44", "boyden-first-book-in-algebra-1895/ex-45", "boyden-first-book-in-algebra-1895/ex-46", "boyden-first-book-in-algebra-1895/ex-47", "boyden-first-book-in-algebra-1895/ex-48", "boyden-first-book-in-algebra-1895/ex-49", "boyden-first-book-in-algebra-1895/ex-50" ] }, { "id": "boyden-first-book-in-algebra-1895/ch-complex-fractions", "number": "COMPLEX FRACTIONS", "title": "COMPLEX FRACTIONS", "name": "Boyden 1895, COMPLEX FRACTIONS", "pages": null, "concepts": [ "concept/algebraic-fraction", "concept/complex-fraction", "concept/highest-common-factor", "concept/lowest-common-multiple", "concept/lowest-terms", "method/adding-fractions", "method/dividing-a-polynomial-by-a-polynomial", "method/dividing-by-a-fraction", "method/factoring", "method/multiplying-fractions", "method/simplifying-a-complex-fraction" ], "excerpts": [ "boyden-first-book-in-algebra-1895/x-2847ff79e7", "boyden-first-book-in-algebra-1895/x-afae468ec3", "boyden-first-book-in-algebra-1895/x-5e5eba6d11" ], "equations": [ "boyden-first-book-in-algebra-1895/eq-235658c1c5", "boyden-first-book-in-algebra-1895/eq-0085d942b5" ], "exercise_sets": [ "boyden-first-book-in-algebra-1895/ex-51", "boyden-first-book-in-algebra-1895/ex-52" ] }, { "id": "boyden-first-book-in-algebra-1895/ch-equations", "number": "EQUATIONS", "title": "EQUATIONS", "name": "Boyden 1895, EQUATIONS", "pages": null, "concepts": [ "concept/coefficient", "concept/equality", "concept/equation", "concept/fractional-equation", "concept/lowest-common-multiple", "concept/member", "concept/unknown", "method/clearing-an-equation-of-fractions", "method/collecting-like-terms", "method/solving-an-equation", "method/stating-a-problem-as-an-equation", "method/transposing-the-terms", "theorem/transposition-rule" ], "excerpts": [ "boyden-first-book-in-algebra-1895/x-a7cffd08e4", "boyden-first-book-in-algebra-1895/x-3ae284b38a", "boyden-first-book-in-algebra-1895/x-f1f64de1fa", "boyden-first-book-in-algebra-1895/x-fb23e82ee0", "boyden-first-book-in-algebra-1895/x-c28859238f", "boyden-first-book-in-algebra-1895/x-15f1024802" ], "equations": [ "boyden-first-book-in-algebra-1895/eq-f9a831ae41", "boyden-first-book-in-algebra-1895/eq-455e6e9296" ], "exercise_sets": [ "boyden-first-book-in-algebra-1895/ex-53", "boyden-first-book-in-algebra-1895/ex-54" ] }, { "id": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "number": "SIMULTANEOUS EQUATIONS", "title": "SIMULTANEOUS EQUATIONS", "name": "Boyden 1895, SIMULTANEOUS EQUATIONS", "pages": null, "concepts": [ "concept/affected-quadratic-equation", "concept/algebra", "concept/equation", "concept/fractional-equation", "concept/linear-equation", "concept/pure-quadratic-equation", "concept/quadratic-equation", "concept/simultaneous-equations", "concept/unknown", "method/clearing-an-equation-of-fractions", "method/dividing-a-polynomial-by-a-polynomial", "method/elimination", "method/extracting-the-square-root", "method/factoring", "method/finding-the-highest-common-factor", "method/solving-an-equation", "method/stating-a-problem-as-an-equation", "method/substitution" ], "excerpts": [ "boyden-first-book-in-algebra-1895/x-e2dad0784e", "boyden-first-book-in-algebra-1895/x-cd46195fd8", "boyden-first-book-in-algebra-1895/x-f69596531a", "boyden-first-book-in-algebra-1895/x-e3a409b57e", "boyden-first-book-in-algebra-1895/x-4bc99a8834", "boyden-first-book-in-algebra-1895/x-40bac1cb12", "boyden-first-book-in-algebra-1895/x-00802aaf15", "boyden-first-book-in-algebra-1895/x-76171e5269", "boyden-first-book-in-algebra-1895/x-4927fc4e85" ], "equations": [ "boyden-first-book-in-algebra-1895/eq-680896f600", "boyden-first-book-in-algebra-1895/eq-a7d5314152" ], "exercise_sets": [ "boyden-first-book-in-algebra-1895/ex-55", "boyden-first-book-in-algebra-1895/ex-56", "boyden-first-book-in-algebra-1895/ex-57", "boyden-first-book-in-algebra-1895/ex-58" ] } ], "excerpts": [ { "id": "boyden-first-book-in-algebra-1895/x-ba155aca8b", "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "PREFACE", "latex": "The study of algebra is a continuation of what the pupil has been doing for years, but it is expected that this new work will result in a knowledge of \\textit{ general truths} about numbers, and an increased power of clear thinking.", "markdown": "The study of algebra is a continuation of what the pupil has been doing for years, but it is expected that this new work will result in a knowledge of *general truths* about numbers, and an increased power of clear thinking.", "why": "It tells the learner that algebra builds on arithmetic and aims at general truths rather than only computation.", "use": [ "lesson", "website" ], "concepts": [ "concept/algebra", "concept/arithmetic" ] }, { "id": "boyden-first-book-in-algebra-1895/x-424354f563", "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "PREFACE", "latex": "All the differences between this work and that pursued in arithmetic may be traced to the introduction of two new elements, namely, negative numbers and the representation of numbers by letters.", "markdown": "All the differences between this work and that pursued in arithmetic may be traced to the introduction of two new elements, namely, negative numbers and the representation of numbers by letters.", "why": "It names the two new ideas, negative numbers and letters for numbers, that separate algebra from arithmetic.", "use": [ "lesson" ], "concepts": [ "concept/arithmetic", "concept/negative-number", "concept/variable" ] }, { "id": "boyden-first-book-in-algebra-1895/x-2ac6747809", "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "PREFACE", "latex": "One of these is the use of \\textit{ letters to represent numbers}, and you will see in the following exercises that this change makes the solution of problems much easier.", "markdown": "One of these is the use of *letters to represent numbers*, and you will see in the following exercises that this change makes the solution of problems much easier.", "why": "It introduces the letter as a stand-in for an unknown number and promises that this makes problems easier to solve.", "use": [ "lesson" ], "concepts": [ "concept/variable" ] }, { "id": "boyden-first-book-in-algebra-1895/x-682fc91098", "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "PREFACE", "latex": "Where in arithmetic did you learn the principle applied in transposing the 8?", "markdown": "Where in arithmetic did you learn the principle applied in transposing the 8?", "why": "It asks the learner to recall the arithmetic principle behind moving a term to the other side of an equation.", "use": [ "lesson" ], "concepts": [ "method/solving-an-equation", "method/transposing-the-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/x-741ec4980f", "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "PREFACE", "latex": "instead of making a statement of what the child is to see in the illustrative example, questions are asked which shall lead him to find for himself that which he is to learn from the example.", "markdown": "instead of making a statement of what the child is to see in the illustrative example, questions are asked which shall lead him to find for himself that which he is to learn from the example.", "why": "It describes the book's method of guiding the learner to discover each rule through questions rather than being told it.", "use": [ "lesson", "website" ], "concepts": [] }, { "id": "boyden-first-book-in-algebra-1895/x-bb1fbb97c1", "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MODES OF REPRESENTING THE OPERATIONS", "latex": "The sum of $y$ + $y$ + $y$ + etc. written seven times is 7$y$.", "markdown": "The sum of $y$ + $y$ + $y$ + etc. written seven times is 7$y$.", "why": "It shows a learner that a repeated sum is written compactly as a coefficient times the number.", "use": [ "lesson" ], "concepts": [ "concept/coefficient", "method/addition" ] }, { "id": "boyden-first-book-in-algebra-1895/x-47b409efcc", "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MODES OF REPRESENTING THE OPERATIONS", "latex": "The 7 and $x$ are called the coefficients of the number following.", "markdown": "The 7 and $x$ are called the coefficients of the number following.", "why": "It gives the term coefficient in the same breath as the example that motivates it.", "use": [ "lesson" ], "concepts": [ "concept/coefficient" ] }, { "id": "boyden-first-book-in-algebra-1895/x-ea4c31ee57", "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MODES OF REPRESENTING THE OPERATIONS", "latex": "We find a difficulty in solving this last example, because we do not know just how large $x, b, m, y$, and $z$ are with reference to each other.", "markdown": "We find a difficulty in solving this last example, because we do not know just how large $x, b, m, y$, and $z$ are with reference to each other.", "why": "It shows why a problem with opposite directions cannot be solved with letters alone, which motivates signed numbers.", "use": [ "lesson" ], "concepts": [ "concept/algebraic-number", "concept/negative-number" ] }, { "id": "boyden-first-book-in-algebra-1895/x-071789ec8b", "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MODES OF REPRESENTING THE OPERATIONS", "latex": "In algebra, therefore, numbers are considered as increasing from zero in opposite directions. Those in one direction are called Positive Numbers (or + numbers); those in the other direction Negative Numbers (or - numbers).", "markdown": "In algebra, therefore, numbers are considered as increasing from zero in opposite directions. Those in one direction are called Positive Numbers (or + numbers); those in the other direction Negative Numbers (or - numbers).", "why": "It introduces positive and negative numbers as two opposite directions from zero, a picture a learner can hold onto.", "use": [ "lesson", "history" ], "concepts": [ "concept/algebraic-number", "concept/negative-number", "concept/positive-number" ] }, { "id": "boyden-first-book-in-algebra-1895/x-ffcfaee34b", "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MODES OF REPRESENTING THE OPERATIONS", "latex": "Negative numbers are usually spoken of as less than zero, because they are used to represent losses. To illustrate: suppose a man's money affairs be such that his debts just equal his assets, we say that he is worth nothing.", "markdown": "Negative numbers are usually spoken of as less than zero, because they are used to represent losses. To illustrate: suppose a man’s money affairs be such that his debts just equal his assets, we say that he is worth nothing.", "why": "A concrete debt example makes the idea that a negative number can be less than zero intuitive for a learner.", "use": [ "lesson", "website" ], "concepts": [ "concept/negative-number" ] }, { "id": "boyden-first-book-in-algebra-1895/x-f7acf6d369", "chapter": "boyden-first-book-in-algebra-1895/ch-algebraic-expressions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ALGEBRAIC EXPRESSIONS", "latex": "An \\textbf{ algebraic expression} is any representation of a number by algebraic notation.", "markdown": "An **algebraic expression** is any representation of a number by algebraic notation.", "why": "Gives the learner the umbrella idea that every polynomial, term and monomial in the chapter sits under.", "use": [ "lesson", "website" ], "concepts": [ "concept/algebraic-expression" ] }, { "id": "boyden-first-book-in-algebra-1895/x-b02adc4e18", "chapter": "boyden-first-book-in-algebra-1895/ch-algebraic-expressions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ALGEBRAIC EXPRESSIONS", "latex": "A \\textbf{ term} is an algebraic expression not connected with any other by the sign plus or minus, or one of the parts of an algebraic expression with its own sign plus or minus. If no sign is written, the plus sign is understood.", "markdown": "A **term** is an algebraic expression not connected with any other by the sign plus or minus, or one of the parts of an algebraic expression with its own sign plus or minus. If no sign is written, the plus sign is understood.", "why": "Shows that a term is decided by the signs that separate it, and that an unwritten sign counts as plus.", "use": [ "lesson" ], "concepts": [ "concept/term" ] }, { "id": "boyden-first-book-in-algebra-1895/x-ba356b9bc9", "chapter": "boyden-first-book-in-algebra-1895/ch-algebraic-expressions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ALGEBRAIC EXPRESSIONS", "latex": "\\textbf{ Similar terms} are terms having the same letters affected by the same exponents. \\textbf{ Dissimilar terms} are terms which differ in letters or exponents, or both.", "markdown": "**Similar terms** are terms having the same letters affected by the same exponents. **Dissimilar terms** are terms which differ in letters or exponents, or both.", "why": "Gives the exact test for whether two terms can be combined, which learners need before collecting like terms.", "use": [ "lesson" ], "concepts": [ "concept/like-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/x-0b0523d71a", "chapter": "boyden-first-book-in-algebra-1895/ch-algebraic-expressions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ALGEBRAIC EXPRESSIONS", "latex": "A \\textbf{monomial} is an algebraic expression of one term. A \\textbf{polynomial} is an algebraic expression of more than one term. A polynomial of two terms is called a \\textbf{binomial}, and one of three terms is called a \\textbf{trinomial}.", "markdown": "A **monomial** is an algebraic expression of one term. A **polynomial** is an algebraic expression of more than one term. A polynomial of two terms is called a **binomial**, and one of three terms is called a **trinomial**.", "why": "Names the family of expressions by counting terms, so learners can classify any expression they meet.", "use": [ "lesson" ], "concepts": [ "concept/binomial", "concept/monomial", "concept/polynomial", "concept/trinomial" ] }, { "id": "boyden-first-book-in-algebra-1895/x-a2a54dcd8c", "chapter": "boyden-first-book-in-algebra-1895/ch-algebraic-expressions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ALGEBRAIC EXPRESSIONS", "latex": "How do these terms compare with reference to degree? They are called \\textit{homogeneous} terms.", "markdown": "How do these terms compare with reference to degree? They are called *homogeneous* terms.", "why": "Ties homogeneity to equal degree, the idea behind the exercise on homogeneous trinomials.", "use": [ "lesson" ], "concepts": [ "concept/degree", "concept/homogeneous-polynomial" ] }, { "id": "boyden-first-book-in-algebra-1895/x-1d10f26d96", "chapter": "boyden-first-book-in-algebra-1895/ch-algebraic-expressions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ALGEBRAIC EXPRESSIONS", "latex": "Henry bought some apples at 3 cents apiece, and twice as many pears at 4 cents apiece, paying for the whole 66 cents. How many of each did he buy?", "markdown": "Henry bought some apples at 3 cents apiece, and twice as many pears at 4 cents apiece, paying for the whole 66 cents. How many of each did he buy?", "why": "A worked-style word problem that shows how a stated relation between two unknowns becomes an equation.", "use": [ "lesson" ], "concepts": [ "method/stating-a-problem-as-an-equation" ] }, { "id": "boyden-first-book-in-algebra-1895/x-4ce6477d92", "chapter": "boyden-first-book-in-algebra-1895/ch-algebraic-expressions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ALGEBRAIC EXPRESSIONS", "latex": "The \\textbf{degree of an algebraic expression} is the same as the degree of its highest term.", "markdown": "The **degree of an algebraic expression** is the same as the degree of its highest term.", "why": "Explains why a polynomial's degree is set by its highest-degree term, so learners can name any polynomial's degree at a glance.", "use": [ "lesson", "website" ], "concepts": [ "concept/degree", "concept/polynomial" ] }, { "id": "boyden-first-book-in-algebra-1895/x-b4eafd9be4", "chapter": "boyden-first-book-in-algebra-1895/ch-addition", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ADDITION", "latex": "In combining numbers in algebra it must always be borne in mind that negative numbers are the opposite of positive numbers in their tendency.", "markdown": "In combining numbers in algebra it must always be borne in mind that negative numbers are the opposite of positive numbers in their tendency.", "why": "It gives the learner the guiding idea that signs pull in opposite directions before any rule is applied.", "use": [ "lesson", "website" ], "concepts": [ "concept/negative-number", "concept/positive-number" ] }, { "id": "boyden-first-book-in-algebra-1895/x-9f88067f32", "chapter": "boyden-first-book-in-algebra-1895/ch-addition", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ADDITION", "latex": "To add similar terms with like signs, add the coefficients, annex the common letters, and prefix the common sign.", "markdown": "To add similar terms with like signs, add the coefficients, annex the common letters, and prefix the common sign.", "why": "It states the simplest case of combining like terms in one clear rule.", "use": [ "lesson" ], "concepts": [ "concept/coefficient", "concept/like-terms", "method/addition" ] }, { "id": "boyden-first-book-in-algebra-1895/x-f21e72dbc7", "chapter": "boyden-first-book-in-algebra-1895/ch-addition", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ADDITION", "latex": "To add similar terms with unlike signs, add the coefficients of the plus terms, add the coefficients of the minus terms, to the difference of these sums annex the common letters, and prefix the sign of the greater sum.", "markdown": "To add similar terms with unlike signs, add the coefficients of the plus terms, add the coefficients of the minus terms, to the difference of these sums annex the common letters, and prefix the sign of the greater sum.", "why": "It shows a learner how to handle opposite signs by separating positive and negative parts before subtracting.", "use": [ "lesson" ], "concepts": [ "concept/algebraic-sum", "concept/like-terms", "method/addition" ] }, { "id": "boyden-first-book-in-algebra-1895/x-eb8c3b19bc", "chapter": "boyden-first-book-in-algebra-1895/ch-addition", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ADDITION", "latex": "To add dissimilar terms, write the terms successively, each with its own sign", "markdown": "To add dissimilar terms, write the terms successively, each with its own sign", "why": "It tells the learner that unlike terms are not combined and are simply written side by side with their signs.", "use": [ "lesson" ], "concepts": [ "concept/term", "method/addition" ] }, { "id": "boyden-first-book-in-algebra-1895/x-d04db172ac", "chapter": "boyden-first-book-in-algebra-1895/ch-addition", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "ADDITION", "latex": "A man travels $a$ miles north, then $x$ miles south, then 5 miles further south, and then $y$ miles north. How far is he from his starting point?", "markdown": "A man travels $a$ miles north, then $x$ miles south, then 5 miles further south, and then $y$ miles north. How far is he from his starting point?", "why": "A journey north and south makes signed addition concrete, and it is the same picture the chapter closes with.", "use": [ "lesson", "website" ], "concepts": [ "concept/algebraic-sum", "concept/negative-number" ] }, { "id": "boyden-first-book-in-algebra-1895/x-5a03958014", "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SUBTRACTION", "latex": "The principle is clear; namely, \\textbf{ \\textit{The subtraction of any number gives the same result as the addition of that number with the opposite sign.}}", "markdown": "The principle is clear; namely, ***The subtraction of any number gives the same result as the addition of that number with the opposite sign.***", "why": "It states the core idea that subtracting a number is the same as adding its opposite, which underlies every later step.", "use": [ "lesson", "website" ], "concepts": [ "method/addition", "method/subtraction" ] }, { "id": "boyden-first-book-in-algebra-1895/x-14994bf130", "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SUBTRACTION", "latex": "\\textit{To subtract one number from another, consider the sign of the subtrahend changed and add.}", "markdown": "*To subtract one number from another, consider the sign of the subtrahend changed and add.*", "why": "It gives the working rule a learner applies to each subtraction problem: change the sign of the subtrahend, then add.", "use": [ "lesson" ], "concepts": [ "concept/subtrahend", "method/subtraction" ] }, { "id": "boyden-first-book-in-algebra-1895/x-1880333ab4", "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SUBTRACTION", "latex": "The parenthesis indicates that the numbers enclosed are considered as one number.", "markdown": "The parenthesis indicates that the numbers enclosed are considered as one number.", "why": "It explains that a parenthesis groups terms into a single quantity, which is why its contents can be treated as one unit.", "use": [ "lesson" ], "concepts": [ "concept/parenthesis" ] }, { "id": "boyden-first-book-in-algebra-1895/x-6db5540ae4", "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SUBTRACTION", "latex": "\\textbf{\\textit{Any number of terms may be removed from a parenthesis preceded by the minus sign by changing the sign of each term}.}", "markdown": "***Any number of terms may be removed from a parenthesis preceded by the minus sign by changing the sign of each term*.**", "why": "It gives the sign-changing rule for dropping a parenthesis after a minus sign, the step most often done wrong.", "use": [ "lesson" ], "concepts": [ "concept/parenthesis", "theorem/removing-parentheses-preceded-by-minus", "theorem/removing-parentheses-preceded-by-plus" ] }, { "id": "boyden-first-book-in-algebra-1895/x-6416c9abd4", "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SUBTRACTION", "latex": "\\textbf{\\textit{Any number of terms may be enclosed in a parenthesis preceded by the minus sign by changing the sign of each term}.}", "markdown": "***Any number of terms may be enclosed in a parenthesis preceded by the minus sign by changing the sign of each term*.**", "why": "It states the converse, so a learner can see how to group terms after a minus sign and check the result by removing the parenthesis again.", "use": [ "lesson" ], "concepts": [ "concept/parenthesis", "theorem/removing-parentheses-preceded-by-minus" ] }, { "id": "boyden-first-book-in-algebra-1895/x-125cbcba2f", "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MULTIPLICATION", "latex": "In arithmetic you learned that multiplication is the addition of equal numbers, that the multiplicand expresses one of those equal numbers, and the multiplier the number of them.", "markdown": "In arithmetic you learned that multiplication is the addition of equal numbers, that the multiplicand expresses one of those equal numbers, and the multiplier the number of them.", "why": "It ties the new algebraic product to the arithmetic a learner already knows, before negative numbers complicate it.", "use": [ "lesson" ], "concepts": [ "concept/multiplier", "method/multiplication" ] }, { "id": "boyden-first-book-in-algebra-1895/x-1c8ef5d308", "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MULTIPLICATION", "latex": "This must mean the opposite of what $+4$ meant as a multiplier. Plus four meant add, minus four must mean subtract.", "markdown": "This must mean the opposite of what $+4$ meant as a multiplier. Plus four meant add, minus four must mean subtract.", "why": "It gives the reason a negative multiplier reverses the operation, so the sign rule is understood rather than memorised.", "use": [ "lesson" ], "concepts": [ "concept/negative-number", "theorem/law-of-signs-in-multiplication" ] }, { "id": "boyden-first-book-in-algebra-1895/x-6d7658455f", "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MULTIPLICATION", "latex": "\\textit{To multiply a monomial by a monomial, multiply the coefficients together for the coefficient of the product, add the exponents of like letters for the exponent of the same letter in the product, and give the product of two numbers having like signs the plus sign, having unlike signs the minus sign.}", "markdown": "*To multiply a monomial by a monomial, multiply the coefficients together for the coefficient of the product, add the exponents of like letters for the exponent of the same letter in the product, and give the product of two numbers having like signs the plus sign, having unlike signs the minus sign.*", "why": "It states the complete procedure for multiplying monomials in one place, with the sign rule included.", "use": [ "lesson", "website" ], "concepts": [ "concept/coefficient", "concept/exponent", "method/multiplying-a-monomial-by-a-monomial" ] }, { "id": "boyden-first-book-in-algebra-1895/x-632ef37543", "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MULTIPLICATION", "latex": "To multiply a polynomial by a polynomial, multiply the multiplicand by each term of the multiplier, and add the products.", "markdown": "To multiply a polynomial by a polynomial, multiply the multiplicand by each term of the multiplier, and add the products.", "why": "It gives the general pattern that every later expansion of a product of sums follows.", "use": [ "lesson" ], "concepts": [ "concept/polynomial", "method/multiplying-a-compound-expression" ] }, { "id": "boyden-first-book-in-algebra-1895/x-73df8487f8", "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MULTIPLICATION", "latex": "It is intended that the answers in the following exercise shall be written directly without going through the multiplication.", "markdown": "It is intended that the answers in the following exercise shall be written directly without going through the multiplication.", "why": "It tells the learner that the expansions are meant to be recognised from the pattern, which is the skill the exercise builds.", "use": [ "lesson" ], "concepts": [ "theorem/binomial-theorem" ] }, { "id": "boyden-first-book-in-algebra-1895/x-603e62820e", "chapter": "boyden-first-book-in-algebra-1895/ch-division", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "DIVISION", "latex": "\\textbf{Division} is the process by which, when a product is given and one factor known, the other factor is found.", "markdown": "**Division** is the process by which, when a product is given and one factor known, the other factor is found.", "why": "Gives the learner the defining idea of division as the reverse of multiplication before any procedure is used.", "use": [ "lesson" ], "concepts": [ "method/division" ] }, { "id": "boyden-first-book-in-algebra-1895/x-b0a424718b", "chapter": "boyden-first-book-in-algebra-1895/ch-division", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "DIVISION", "latex": "What is the relation of the dividend to the divisor and quotient? What factors must the dividend contain? What factors must the quotient contain?", "markdown": "What is the relation of the dividend to the divisor and quotient? What factors must the dividend contain? What factors must the quotient contain?", "why": "Asks the learner to see how the three parts of a division depend on one another, before any rule is given.", "use": [ "lesson" ], "concepts": [ "concept/dividend", "concept/divisor", "concept/quotient" ] }, { "id": "boyden-first-book-in-algebra-1895/x-25c94716ee", "chapter": "boyden-first-book-in-algebra-1895/ch-division", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "DIVISION", "latex": "Why stop the work at the point given? What is the complete quotient? Is the dividend exactly divisible by the divisor? When is one number exactly divisible by another?", "markdown": "Why stop the work at the point given? What is the complete quotient? Is the dividend exactly divisible by the divisor? When is one number exactly divisible by another?", "why": "Prompts the learner to decide when a polynomial division is finished and what exact divisibility means.", "use": [ "lesson" ], "concepts": [ "concept/divisibility", "concept/quotient", "concept/remainder" ] }, { "id": "boyden-first-book-in-algebra-1895/x-d370abbce5", "chapter": "boyden-first-book-in-algebra-1895/ch-division", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "DIVISION", "latex": "To divide a polynomial by a monomial, divide each term of the dividend by the divisor, and add the quotients.", "markdown": "To divide a polynomial by a monomial, divide each term of the dividend by the divisor, and add the quotients.", "why": "States the rule in one plain sentence that a learner can apply term by term.", "use": [ "lesson" ], "concepts": [ "method/dividing-a-polynomial-by-a-monomial" ] }, { "id": "boyden-first-book-in-algebra-1895/x-71db7ea47e", "chapter": "boyden-first-book-in-algebra-1895/ch-division", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "DIVISION", "latex": "To divide a polynomial by a polynomial, arrange the terms of the dividend, and divisor similarly, divide the first term of the dividend by the first term of the divisor for the first term of the quotient, multiply the divisor by the quotient and subtract the product from the dividend; divide the first term of the remainder by the first term of the divisor for the next term of the quotient, multiply and subtract as before; continue this work of dividing, multiplying, and subtracting until there is no remainder or until the first term of the remainder is not divisible by the first term of the divisor.", "markdown": "To divide a polynomial by a polynomial, arrange the terms of the dividend, and divisor similarly, divide the first term of the dividend by the first term of the divisor for the first term of the quotient, multiply the divisor by the quotient and subtract the product from the dividend; divide the first term of the remainder by the first term of the divisor for the next term of the quotient, multiply and subtract as before; continue this work of dividing, multiplying, and subtracting until there is no remainder or until the first term of the remainder is not divisible by the first term of the divisor.", "why": "Lays out the full long-division procedure as a repeating cycle of divide, multiply, subtract that a learner can follow step by step.", "use": [ "lesson" ], "concepts": [ "concept/divisibility", "concept/remainder", "method/dividing-a-polynomial-by-a-polynomial" ] }, { "id": "boyden-first-book-in-algebra-1895/x-d210fa94a0", "chapter": "boyden-first-book-in-algebra-1895/ch-division", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "DIVISION", "latex": "Since division is the reverse of multiplication, let us consider an example in the multiplication of polynomials.", "markdown": "Since division is the reverse of multiplication, let us consider an example in the multiplication of polynomials.", "why": "Shows the learner that the division procedure is built on a product they already know how to form.", "use": [ "lesson" ], "concepts": [ "method/division", "method/multiplying-a-compound-expression" ] }, { "id": "boyden-first-book-in-algebra-1895/x-bc069eab44", "chapter": "boyden-first-book-in-algebra-1895/ch-division", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "DIVISION", "latex": "is indicated by the radical sign and index. When no index is expressed, \\textit{two} is understood.", "markdown": "is indicated by the radical sign and index. When no index is expressed, *two* is understood.", "why": "Explains the notation of roots and the convention that an unmarked radical means the square root.", "use": [ "lesson" ], "concepts": [ "concept/radical-sign", "concept/root" ] }, { "id": "boyden-first-book-in-algebra-1895/x-ffaf10fb76", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "When we divide a number into two numbers, which multiplied together will give a product equal to the given number, we have found the factors of that number. This process is called \\textbf{factoring}.", "markdown": "When we divide a number into two numbers, which multiplied together will give a product equal to the given number, we have found the factors of that number. This process is called **factoring**.", "why": "It gives the learner the definition of a factor and of factoring from the ground up, before any polynomial appears.", "use": [ "lesson", "website" ], "concepts": [ "concept/factor", "method/factoring" ] }, { "id": "boyden-first-book-in-algebra-1895/x-527bac9e54", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "Sometimes a polynomial in the form given has no factor common to all its terms, but has factors common to several terms. It may be possible then to group the terms in parentheses so that there will be a binomial or trinomial factor common to all the terms of the polynomial in its new form.", "markdown": "Sometimes a polynomial in the form given has no factor common to all its terms, but has factors common to several terms. It may be possible then to group the terms in parentheses so that there will be a binomial or trinomial factor common to all the terms of the polynomial in its new form.", "why": "It tells the learner what to try when no single factor divides every term, which is the step that grouping needs.", "use": [ "lesson" ], "concepts": [ "concept/common-factor", "method/factoring-by-grouping" ] }, { "id": "boyden-first-book-in-algebra-1895/x-5d3fa2f0af", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "Write two factors, of which one is the sum and the other the difference of the square roots of the terms.", "markdown": "Write two factors, of which one is the sum and the other the difference of the square roots of the terms.", "why": "It turns the difference of two squares into a one-line recipe that a learner can check by multiplying the factors back.", "use": [ "lesson" ], "concepts": [ "concept/root", "theorem/difference-of-two-squares" ] }, { "id": "boyden-first-book-in-algebra-1895/x-08a02029e7", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "This is the reverse of the case under Multiplication given in Art. 14.", "markdown": "This is the reverse of the case under Multiplication given in Art. 14.", "why": "It ties factoring a trinomial to the multiplication it undoes, so a learner sees factoring as running the product backwards.", "use": [ "lesson" ], "concepts": [ "method/factoring-a-trinomial-of-the-form-x-2-ax-b", "method/multiplying-two-binomials" ] }, { "id": "boyden-first-book-in-algebra-1895/x-00f15fc0da", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "That the quotient is the square of the first term of the divisor, minus the product of the first term by the second, plus the square of the second.", "markdown": "That the quotient is the square of the first term of the divisor, minus the product of the first term by the second, plus the square of the second.", "why": "It names the pattern a learner must recognise in the quotient of a sum of cubes, which is where the sign errors usually happen.", "use": [ "lesson" ], "concepts": [ "theorem/sum-of-two-cubes" ] }, { "id": "boyden-first-book-in-algebra-1895/x-17cd022a74", "chapter": "boyden-first-book-in-algebra-1895/ch-greatest-common-factor", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "GREATEST COMMON FACTOR", "latex": "This number is called their \\textit{Greatest Common Factor}.", "markdown": "This number is called their *Greatest Common Factor*.", "why": "It gives the learner the defining name for the largest common factor, tied to the question just asked.", "use": [ "lesson" ], "concepts": [ "concept/highest-common-factor" ] }, { "id": "boyden-first-book-in-algebra-1895/x-a12f96a6c4", "chapter": "boyden-first-book-in-algebra-1895/ch-greatest-common-factor", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "GREATEST COMMON FACTOR", "latex": "\\textit{To find the G.C.F. of two or more numbers, find the prime factors of each of the numbers and take the product of the common factors}.", "markdown": "*To find the G.C.F. of two or more numbers, find the prime factors of each of the numbers and take the product of the common factors*.", "why": "It states the procedure for the highest common factor in a form a learner can follow step by step.", "use": [ "lesson" ], "concepts": [ "concept/common-factor", "concept/prime-factor", "method/finding-the-highest-common-factor" ] }, { "id": "boyden-first-book-in-algebra-1895/x-e270c330fa", "chapter": "boyden-first-book-in-algebra-1895/ch-greatest-common-factor", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "GREATEST COMMON FACTOR", "latex": "What is the value of a number, one of whose factors is zero?", "markdown": "What is the value of a number, one of whose factors is zero?", "why": "It prompts the learner to see that any product with a zero factor is zero, a useful check before dividing by factors.", "use": [ "lesson" ], "concepts": [ "concept/factor" ] }, { "id": "boyden-first-book-in-algebra-1895/x-a30b6fbde1", "chapter": "boyden-first-book-in-algebra-1895/ch-greatest-common-factor", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "GREATEST COMMON FACTOR", "latex": "If a man bought a horse for $x$ dollars and sold him so as to gain $5 \\%$, what will represent the number of dollars he gained?", "markdown": "If a man bought a horse for $x$ dollars and sold him so as to gain $5 \\%$, what will represent the number of dollars he gained?", "why": "It shows how a simple sale is turned into an algebraic expression, a habit the learner needs for word problems.", "use": [ "lesson" ], "concepts": [ "concept/algebraic-expression" ] }, { "id": "boyden-first-book-in-algebra-1895/x-5885b6a06a", "chapter": "boyden-first-book-in-algebra-1895/ch-least-common-multiple", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "LEAST COMMON MULTIPLE", "latex": "To find the L.C.M. of two or more numbers, find the prime factors of each number, take the product of the different factors, using each the greatest number of times it is found in any of the numbers", "markdown": "To find the L.C.M. of two or more numbers, find the prime factors of each number, take the product of the different factors, using each the greatest number of times it is found in any of the numbers", "why": "It gives the whole procedure for the lowest common multiple in one sentence a learner can apply to any list of numbers or expressions.", "use": [ "lesson" ], "concepts": [ "concept/lowest-common-multiple", "concept/prime-factor", "method/finding-the-lowest-common-multiple" ] }, { "id": "boyden-first-book-in-algebra-1895/x-8e99a01aef", "chapter": "boyden-first-book-in-algebra-1895/ch-least-common-multiple", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "LEAST COMMON MULTIPLE", "latex": "$12 a^{2} b^{3}$ is the least common multiple of $3 a^{2} b$ and $4 a b^{3}$. How many of the factors of $3 a^{2} b$ are found in the L.C.M.?", "markdown": "$12 a^{2} b^{3}$ is the least common multiple of $3 a^{2} b$ and $4 a b^{3}$. How many of the factors of $3 a^{2} b$ are found in the L.C.M.?", "why": "It asks the learner to see that a least common multiple keeps each factor as many times as the largest power in which it appears, which makes the rule concrete.", "use": [ "lesson" ], "concepts": [ "concept/factor", "concept/lowest-common-multiple" ] }, { "id": "boyden-first-book-in-algebra-1895/x-f629da5e05", "chapter": "boyden-first-book-in-algebra-1895/ch-least-common-multiple", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "LEAST COMMON MULTIPLE", "latex": "This exercise should be conducted orally, and if, at any point, the students do not readily recall the method, the examples of that class should be duplicated till the principle is clear.", "markdown": "This exercise should be conducted orally, and if, at any point, the students do not readily recall the method, the examples of that class should be duplicated till the principle is clear.", "why": "It is the book's own teaching advice for the fraction drill: repeat the worked class of examples until the principle is secure.", "use": [ "lesson" ], "concepts": [ "concept/equivalent-fractions", "concept/lowest-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/x-9b2757713a", "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "REDUCTION OF FRACTIONS", "latex": "To reduce a fraction to its lowest terms, divide the terms of the fraction by their greatest common factor.", "markdown": "To reduce a fraction to its lowest terms, divide the terms of the fraction by their greatest common factor.", "why": "It states the rule for reducing a fraction in one sentence that a learner can apply to any of the exercises.", "use": [ "lesson" ], "concepts": [ "concept/highest-common-factor", "concept/lowest-terms", "method/reducing-a-fraction-to-lowest-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/x-03fca7add8", "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "REDUCTION OF FRACTIONS", "latex": "\\frac{a^2bx-b^3x}{a^2bx-ab^2x} = \\frac{bx(a^2-b^2) \\div bx(a-b)}{abx(a-b) \\div bx(a-b)} = \\frac{a+b}{a}", "markdown": "a^2bx-b^3xa^2bx-ab^2x = bx(a^2-b^2) ÷bx(a-b)abx(a-b) ÷bx(a-b) = a+ba", "why": "It shows the method in action: factor numerator and denominator first, then divide out the common factor bx(a-b).", "use": [ "lesson" ], "concepts": [ "concept/highest-common-factor", "method/factoring", "method/reducing-a-fraction-to-lowest-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/x-d2961ca779", "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "REDUCTION OF FRACTIONS", "latex": "To find an entire or mixed number equivalent to a given fraction, divide the numerator by the denominator.", "markdown": "To find an entire or mixed number equivalent to a given fraction, divide the numerator by the denominator.", "why": "It gives the learner the procedure for turning a fraction with a polynomial numerator into an entire or mixed expression.", "use": [ "lesson" ], "concepts": [ "concept/mixed-number", "method/reducing-a-fraction-to-an-integral-or-mixed-expression" ] }, { "id": "boyden-first-book-in-algebra-1895/x-ef6f872f0a", "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "REDUCTION OF FRACTIONS", "latex": "\\frac{ac-bc-d}{c} = a - b -\\frac{d}{c}", "markdown": "ac-bc-dc = a - b -dc", "why": "It is a short worked case where dividing each term of the numerator by c gives an entire part and a remainder fraction.", "use": [ "lesson" ], "concepts": [ "concept/mixed-number", "method/reducing-a-fraction-to-an-integral-or-mixed-expression" ] }, { "id": "boyden-first-book-in-algebra-1895/x-de60a748c3", "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "REDUCTION OF FRACTIONS", "latex": "To change fractions to equivalent fractions having a common denominator, multiply the terms of each fraction by such a number as will make its denominator equal to the L.C.M. of the given denominators.", "markdown": "To change fractions to equivalent fractions having a common denominator, multiply the terms of each fraction by such a number as will make its denominator equal to the L.C.M. of the given denominators.", "why": "It states the rule for finding a common denominator, which is the step learners most often need to check before adding fractions.", "use": [ "lesson" ], "concepts": [ "concept/equivalent-fractions", "concept/lowest-common-multiple", "method/reducing-fractions-to-lowest-common-denominator" ] }, { "id": "boyden-first-book-in-algebra-1895/x-79a4e44dc9", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "To add fractions, find equivalent fractions having a common denominator, add their numerators, write the sum over the common denominator, and reduce to lowest terms.", "markdown": "To add fractions, find equivalent fractions having a common denominator, add their numerators, write the sum over the common denominator, and reduce to lowest terms.", "why": "It gives the complete procedure for adding fractions in one sentence a learner can follow step by step.", "use": [ "lesson" ], "concepts": [ "concept/equivalent-fractions", "concept/lowest-terms", "method/adding-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/x-ebebf6dceb", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "\\frac{a-2b}{a}-\\frac{a-4b}{a-2b}=\\frac{a^2-4ab+4b^2}{a(a-2b)}-\\frac{a^2-4ab}{a(a-2b)}=\\frac{4b^2}{a(a-2b)}", "markdown": "a-2ba-a-4ba-2b=a^2-4ab+4b^2a(a-2b)-a^2-4aba(a-2b)=4b^2a(a-2b)", "why": "It shows subtraction of fractions worked out over a common denominator, with each step visible.", "use": [ "lesson" ], "concepts": [ "method/adding-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/x-7a92af1474", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "In case the terms of the fraction are polynomials, notice that the change in sign affects every term of the numerator or denominator.", "markdown": "In case the terms of the fraction are polynomials, notice that the change in sign affects every term of the numerator or denominator.", "why": "It warns learners that a sign change in a polynomial fraction must be applied to every term, a common source of error.", "use": [ "lesson" ], "concepts": [ "concept/algebraic-fraction", "theorem/fundamental-principle-of-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/x-bf66e18b0d", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "To multiply one fraction by another, multiply the numerators together for the numerator of the product and the denominators for its denominator, and reduce to lowest terms.", "markdown": "To multiply one fraction by another, multiply the numerators together for the numerator of the product and the denominators for its denominator, and reduce to lowest terms.", "why": "It states the rule for multiplying fractions and reminds learners to cancel common factors at the end.", "use": [ "lesson" ], "concepts": [ "concept/lowest-terms", "method/multiplying-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/x-a549763b75", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "To divide one fraction by another, invert the divisor and proceed as in multiplication", "markdown": "To divide one fraction by another, invert the divisor and proceed as in multiplication", "why": "It reduces division of fractions to multiplication by the reciprocal, which is the key idea a learner must carry forward.", "use": [ "lesson" ], "concepts": [ "method/dividing-by-a-fraction", "method/multiplying-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/x-2847ff79e7", "chapter": "boyden-first-book-in-algebra-1895/ch-complex-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "COMPLEX FRACTIONS", "latex": "A \\textbf{ complex fraction} is one which has a fraction in one or both of its terms.", "markdown": "A **complex fraction** is one which has a fraction in one or both of its terms.", "why": "Gives the learner the defining feature of a complex fraction in one sentence, before any work begins.", "use": [ "lesson", "website" ], "concepts": [ "concept/complex-fraction" ] }, { "id": "boyden-first-book-in-algebra-1895/x-afae468ec3", "chapter": "boyden-first-book-in-algebra-1895/ch-complex-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "COMPLEX FRACTIONS", "latex": "\\textit{To simplify a complex fraction, multiply each term of the complex fraction by the L.C.M. of the denominators of the fractions in the terms, and reduce.}", "markdown": "*To simplify a complex fraction, multiply each term of the complex fraction by the L.C.M. of the denominators of the fractions in the terms, and reduce.*", "why": "States the procedure for simplifying a complex fraction as a single rule the learner can apply to each exercise.", "use": [ "lesson" ], "concepts": [ "concept/lowest-common-multiple", "method/simplifying-a-complex-fraction" ] }, { "id": "boyden-first-book-in-algebra-1895/x-5e5eba6d11", "chapter": "boyden-first-book-in-algebra-1895/ch-complex-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "COMPLEX FRACTIONS", "latex": "What is a simple fraction? What is the effect of multiplying a simple fraction by its denominator or by any multiple of its denominator?", "markdown": "What is a simple fraction? What is the effect of multiplying a simple fraction by its denominator or by any multiple of its denominator?", "why": "Asks the learner to recall why multiplying by a denominator clears fractions, which is the idea the whole chapter rests on.", "use": [ "lesson" ], "concepts": [ "concept/algebraic-fraction", "concept/complex-fraction" ] }, { "id": "boyden-first-book-in-algebra-1895/x-a7cffd08e4", "chapter": "boyden-first-book-in-algebra-1895/ch-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "EQUATIONS", "latex": "An \\textbf{equation} is an expression of the equality of two numbers. The parts of the expression separated by the sign of equality are called the \\textbf{members} of the equation.", "markdown": "An **equation** is an expression of the equality of two numbers. The parts of the expression separated by the sign of equality are called the **members** of the equation.", "why": "Gives the learner the basic definition of an equation and names its two members.", "use": [ "lesson" ], "concepts": [ "concept/equation", "concept/member" ] }, { "id": "boyden-first-book-in-algebra-1895/x-3ae284b38a", "chapter": "boyden-first-book-in-algebra-1895/ch-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "EQUATIONS", "latex": "In each of these illustrations $b$ has been transposed (changed over) from the first to the second member, and in each case its sign has been changed.", "markdown": "In each of these illustrations $b$ has been transposed (changed over) from the first to the second member, and in each case its sign has been changed.", "why": "Shows concretely what happens to a term's sign when it is moved across the equals sign, before the general rule is stated.", "use": [ "lesson" ], "concepts": [ "method/transposing-the-terms", "theorem/transposition-rule" ] }, { "id": "boyden-first-book-in-algebra-1895/x-f1f64de1fa", "chapter": "boyden-first-book-in-algebra-1895/ch-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "EQUATIONS", "latex": "\\textbf{\\textit{Any term may be transposed from one member of an equation to the other provided its sign be changed.}}", "markdown": "***Any term may be transposed from one member of an equation to the other provided its sign be changed.***", "why": "States the transposition rule that lets a learner move unknown and known terms to opposite sides.", "use": [ "lesson" ], "concepts": [ "method/transposing-the-terms", "theorem/transposition-rule" ] }, { "id": "boyden-first-book-in-algebra-1895/x-fb23e82ee0", "chapter": "boyden-first-book-in-algebra-1895/ch-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "EQUATIONS", "latex": "\\textit{To clear an equation of fractions, multiply each member of the equation by the L.C.M. of the denominators of the fractional terms.}", "markdown": "*To clear an equation of fractions, multiply each member of the equation by the L.C.M. of the denominators of the fractional terms.*", "why": "Gives the procedure for removing fractions from an equation, which learners need before solving fractional equations.", "use": [ "lesson" ], "concepts": [ "concept/lowest-common-multiple", "method/clearing-an-equation-of-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/x-c28859238f", "chapter": "boyden-first-book-in-algebra-1895/ch-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "EQUATIONS", "latex": "\\textbf{\\textit{Any changes may be made in an equation which do not destroy the equality of the members.}}", "markdown": "***Any changes may be made in an equation which do not destroy the equality of the members.***", "why": "Tells the learner that an equation can be transformed freely so long as both members stay equal, which is the idea behind every solving step.", "use": [ "lesson", "website" ], "concepts": [ "concept/equality", "concept/equation" ] }, { "id": "boyden-first-book-in-algebra-1895/x-15f1024802", "chapter": "boyden-first-book-in-algebra-1895/ch-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "EQUATIONS", "latex": "\\textit{ To solve an equation, clear of fractions if necessary, transpose the terms containing the unknown number to one member and the known terms to the other, unite the terms, and divide both members by the coefficient of the unknown number}.", "markdown": "*To solve an equation, clear of fractions if necessary, transpose the terms containing the unknown number to one member and the known terms to the other, unite the terms, and divide both members by the coefficient of the unknown number*.", "why": "Lays out the full solving procedure in order, giving learners a checklist for linear equations.", "use": [ "lesson" ], "concepts": [ "concept/coefficient", "method/clearing-an-equation-of-fractions", "method/collecting-like-terms", "method/solving-an-equation", "method/transposing-the-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/x-e2dad0784e", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "\\textbf{Simultaneous equations} are equations in which the same unknown numbers have the same value.", "markdown": "**Simultaneous equations** are equations in which the same unknown numbers have the same value.", "why": "It gives the learner the defining idea that one set of unknown values must satisfy every equation at once.", "use": [ "lesson", "website" ], "concepts": [ "concept/simultaneous-equations", "concept/unknown" ] }, { "id": "boyden-first-book-in-algebra-1895/x-cd46195fd8", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "One equation containing more than one unknown number cannot be solved. There must be as many simultaneous equations as there are unknown numbers.", "markdown": "One equation containing more than one unknown number cannot be solved. There must be as many simultaneous equations as there are unknown numbers.", "why": "It warns that one equation cannot fix two unknowns, so a second independent equation is always needed.", "use": [ "lesson" ], "concepts": [ "concept/simultaneous-equations" ] }, { "id": "boyden-first-book-in-algebra-1895/x-f69596531a", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "\\textit{Multiply one or both of the equations by such a number that one of the unknown numbers shall have like coefficients. If the signs of the terms having like coefficients are alike, subtract one equation from the other; if unlike, add the equations}.", "markdown": "*Multiply one or both of the equations by such a number that one of the unknown numbers shall have like coefficients. If the signs of the terms having like coefficients are alike, subtract one equation from the other; if unlike, add the equations*.", "why": "It states the elimination rule in one sentence, including when to subtract and when to add.", "use": [ "lesson" ], "concepts": [ "concept/simultaneous-equations", "method/elimination" ] }, { "id": "boyden-first-book-in-algebra-1895/x-e3a409b57e", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "To find the value of $x$, substitute the value of $y$ in the second equation:", "markdown": "To find the value of $x$, substitute the value of $y$ in the second equation:", "why": "It shows the step after elimination, where one found value is put back into an equation to find the other.", "use": [ "lesson" ], "concepts": [ "concept/simultaneous-equations", "method/substitution" ] }, { "id": "boyden-first-book-in-algebra-1895/x-4bc99a8834", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "\\textit{ To solve a pure quadratic equation, reduce to the form $x^2 = a$ and take the square root of each member}.", "markdown": "*To solve a pure quadratic equation, reduce to the form $x^2 = a$ and take the square root of each member*.", "why": "It gives the short procedure for equations with only an x-squared term.", "use": [ "lesson" ], "concepts": [ "concept/pure-quadratic-equation", "method/extracting-the-square-root" ] }, { "id": "boyden-first-book-in-algebra-1895/x-40bac1cb12", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "\\textit{ To solve an affected quadratic equation, reduce the equation to the form $x^2 + bx + c = O$, factor the first member, place each factor in turn equal to zero, and solve the simple equations thus formed.}", "markdown": "*To solve an affected quadratic equation, reduce the equation to the form $x^2 + bx + c = O$, factor the first member, place each factor in turn equal to zero, and solve the simple equations thus formed.*", "why": "It lays out the factoring route for quadratics as a sequence of steps a learner can follow.", "use": [ "lesson" ], "concepts": [ "concept/affected-quadratic-equation", "method/factoring" ] }, { "id": "boyden-first-book-in-algebra-1895/x-00802aaf15", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "This equation will be satisfied if either factor is equal to zero.", "markdown": "This equation will be satisfied if either factor is equal to zero.", "why": "It explains why setting each factor to zero gives the solutions of a factored quadratic.", "use": [ "lesson" ], "concepts": [ "concept/affected-quadratic-equation" ] }, { "id": "boyden-first-book-in-algebra-1895/x-76171e5269", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "The above method of solving affected quadratic equations is the simplest of three methods commonly used, and will not solve all possible cases; the method given for solving simultaneous equations is only one of three known methods; the cases in factoring are less than half of those usually taken.", "markdown": "The above method of solving affected quadratic equations is the simplest of three methods commonly used, and will not solve all possible cases; the method given for solving simultaneous equations is only one of three known methods; the cases in factoring are less than half of those usually taken.", "why": "It is an honest note that the methods taught here are partial, which helps a learner judge what the chapter does and does not cover.", "use": [ "history" ], "concepts": [ "concept/affected-quadratic-equation", "concept/simultaneous-equations", "method/factoring" ] }, { "id": "boyden-first-book-in-algebra-1895/x-4927fc4e85", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "Algebra is the knowledge which has for its object general truths about numbers.", "markdown": "Algebra is the knowledge which has for its object general truths about numbers.", "why": "It is the book's own old definition of algebra and shows how the subject was framed in 1895.", "use": [ "history" ], "concepts": [ "concept/algebra" ] } ], "equations": [ { "id": "boyden-first-book-in-algebra-1895/eq-11fe4d7c70", "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MODES OF REPRESENTING THE OPERATIONS", "latex": "m - y", "name": null, "statement": "A farmer who sold a sheep for m dollars and gained y dollars paid m - y dollars for it.", "kind": "result", "symbols": [ { "unit": "dollar", "symbol": "m", "meaning": "price for which the sheep was sold" }, { "unit": "dollar", "symbol": "y", "meaning": "amount gained on the sheep" } ], "sympy": null, "physics": false, "states": [], "concepts": [ "concept/difference", "concept/negative-number", "method/subtraction" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-7924acabcd", "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MODES OF REPRESENTING THE OPERATIONS", "latex": "x - b + m + y - z", "name": null, "statement": "Taking east as positive and combining the separate eastward and westward distances gives the man's net distance from his starting point as x - b + m + y - z.", "kind": "result", "symbols": [ { "unit": "mile", "symbol": "x", "meaning": "miles traveled east (first leg)" }, { "unit": "mile", "symbol": "b", "meaning": "miles traveled west (second leg)" }, { "unit": "mile", "symbol": "m", "meaning": "miles traveled east (third leg)" }, { "unit": "mile", "symbol": "y", "meaning": "miles traveled east (fourth leg)" }, { "unit": "mile", "symbol": "z", "meaning": "miles traveled west (fifth leg)" } ], "sympy": null, "physics": false, "states": [], "concepts": [ "concept/algebraic-sum", "concept/negative-number", "concept/positive-number", "concept/real-number" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-8e65cfdb09", "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MODES OF REPRESENTING THE OPERATIONS", "latex": "x \\cdot x = xx = x^2", "name": null, "statement": "The product of x with itself, written xx, is the second power of x, written x^2.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "x", "meaning": "the factor taken twice" } ], "sympy": "Eq(x*x, x**2)", "physics": false, "states": [], "concepts": [ "concept/exponent", "concept/perfect-square", "concept/power", "concept/square", "method/multiplication" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-1b147006ff", "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MODES OF REPRESENTING THE OPERATIONS", "latex": "x \\cdot x \\cdot x = xxx = x^3", "name": null, "statement": "The product of three factors each equal to x, written xxx, is the third power of x, written x^3.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "x", "meaning": "the factor taken three times" } ], "sympy": "Eq(x*x*x, x**3)", "physics": false, "states": [], "concepts": [ "concept/exponent", "concept/hexahedron", "concept/power", "method/multiplication" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-eac7109220", "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SUBTRACTION", "latex": "a + (b - c - x) = a + b - c - x", "name": null, "statement": "Removing the parenthesis preceded by a plus sign leaves the terms inside it unchanged, so a plus-preceded parenthesis can simply be dropped.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "b", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "c", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "x", "meaning": "a number or general algebraic quantity" } ], "sympy": "Eq(a + (b - c - x), a + b - c - x)", "physics": false, "states": [], "concepts": [ "concept/parenthesis", "method/addition", "theorem/removing-parentheses-preceded-by-plus" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-17f167238d", "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SUBTRACTION", "latex": "a + c - d + e = a + (c - d + e)", "name": null, "statement": "Terms may be enclosed in a parenthesis preceded by a plus sign without changing their signs, which is the converse of removing such a parenthesis.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "c", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "d", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "e", "meaning": "a number or general algebraic quantity" } ], "sympy": "Eq(a + c - d + e, a + (c - d + e))", "physics": false, "states": [], "concepts": [ "concept/parenthesis", "method/addition", "theorem/removing-parentheses-preceded-by-plus" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-d23e379903", "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SUBTRACTION", "latex": "x - (y + z - c) = x - y - z + c", "name": null, "statement": "Removing a parenthesis preceded by a minus sign changes the sign of each term inside it, so subtracting the bracketed sum gives the same result as subtracting each term.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "x", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "y", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "z", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "c", "meaning": "a number or general algebraic quantity" } ], "sympy": "Eq(x - (y + z - c), x - y - z + c)", "physics": false, "states": [], "concepts": [ "concept/parenthesis", "method/subtraction", "theorem/removing-parentheses-preceded-by-minus" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-5c412b5885", "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SUBTRACTION", "latex": "a - b - c + d = a - (b + c - d)", "name": null, "statement": "Enclosing terms in a parenthesis preceded by a minus sign requires changing the sign of each enclosed term, which is the converse of removing such a parenthesis.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "b", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "c", "meaning": "a number or general algebraic quantity" }, { "unit": null, "symbol": "d", "meaning": "a number or general algebraic quantity" } ], "sympy": "Eq(a - b - c + d, a - (b + c - d))", "physics": false, "states": [], "concepts": [ "concept/parenthesis", "method/subtraction", "theorem/removing-parentheses-preceded-by-minus" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-8a3bb4d944", "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MULTIPLICATION", "latex": "a^3 = a \\cdot a \\cdot a", "name": null, "statement": "The third power of a is a times a times a.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "a", "meaning": "the base, a number or expression" } ], "sympy": "Eq(a**3, a*a*a)", "physics": false, "states": [], "concepts": [ "concept/exponent", "concept/hexahedron", "concept/power" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-f00a950ee4", "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MULTIPLICATION", "latex": "(x-y)^4=x^4-4x^3y+6x^2y^2-4xy^3+y^4", "name": null, "statement": "The fourth power of x minus y expands to x^4 - 4x^3y + 6x^2y^2 - 4xy^3 + y^4, written directly without multiplying out.", "kind": "result", "symbols": [ { "unit": null, "symbol": "x", "meaning": "a number or algebraic expression" }, { "unit": null, "symbol": "y", "meaning": "a number or algebraic expression" } ], "sympy": "Eq((x-y)**4, x**4-4*x**3*y+6*x**2*y**2-4*x*y**3+y**4)", "physics": false, "states": [], "concepts": [ "concept/binomial", "concept/exponent", "concept/power", "theorem/binomial-theorem" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-a27e4bc9ae", "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "MULTIPLICATION", "latex": "(x-1)^3=x^3-3x^2+3x-1", "name": null, "statement": "The cube of x minus 1 expands to x^3 - 3x^2 + 3x - 1.", "kind": "result", "symbols": [ { "unit": null, "symbol": "x", "meaning": "a number or algebraic expression" } ], "sympy": "Eq((x-1)**3, x**3-3*x**2+3*x-1)", "physics": false, "states": [], "concepts": [ "concept/binomial", "concept/hexahedron", "concept/power", "theorem/binomial-theorem" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-16cf008035", "chapter": "boyden-first-book-in-algebra-1895/ch-division", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "DIVISION", "latex": "(a + b)^{2} = a^{2} + 2ab + b^{2} = a^{2} + (2a + b)b", "name": "square of a sum", "statement": "The square of a sum of two quantities equals the square of the first, plus twice their product, plus the square of the second.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "first term of the binomial (a general number)" }, { "unit": null, "symbol": "b", "meaning": "second term of the binomial (a general number)" } ], "sympy": "Eq((a + b)**2, a**2 + 2*a*b + b**2)", "physics": false, "states": [ "theorem/square-of-a-sum" ], "concepts": [ "concept/binomial", "concept/identity" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-cefd196911", "chapter": "boyden-first-book-in-algebra-1895/ch-division", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "DIVISION", "latex": "(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} = a^{3} + (3 a^{2} + 3 a b + b^{2}) b", "name": "cube of a sum", "statement": "The cube of a sum of two quantities expands to the cube of the first, plus three times the square of the first times the second, plus three times the first times the square of the second, plus the cube of the second.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "first term of the binomial (a general number)" }, { "unit": null, "symbol": "b", "meaning": "second term of the binomial (a general number)" } ], "sympy": "Eq((a + b)**3, a**3 + 3*a**2*b + 3*a*b**2 + b**3)", "physics": false, "states": [ "theorem/cube-of-a-sum" ], "concepts": [ "concept/binomial", "concept/identity" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-15eb597cb6", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "2 a b + 6 a c + 4 a d = 2 a \\left(b + 3 c + 2 d \\right)", "name": null, "statement": "Taking out the common factor 2a from each term of 2ab + 6ac + 4ad leaves the factored form 2a(b + 3c + 2d).", "kind": "result", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a letter standing for a number (general symbol)" }, { "unit": null, "symbol": "b", "meaning": "a letter standing for a number (general symbol)" }, { "unit": null, "symbol": "c", "meaning": "a letter standing for a number (general symbol)" }, { "unit": null, "symbol": "d", "meaning": "a letter standing for a number (general symbol)" } ], "sympy": "Eq(2*a*b + 6*a*c + 4*a*d, 2*a*(b + 3*c + 2*d))", "physics": false, "states": [], "concepts": [ "concept/factor", "concept/polynomial", "method/factoring-by-taking-out-a-common-factor" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-9ff5c9ec8a", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "2am+2ax+bm+bx=(m+x)(2a+b).", "name": null, "statement": "The four-term polynomial 2am + 2ax + bm + bx factors as (m + x)(2a + b) after grouping terms.", "kind": "result", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a letter standing for a number (general symbol)" }, { "unit": null, "symbol": "b", "meaning": "a letter standing for a number (general symbol)" }, { "unit": null, "symbol": "m", "meaning": "a letter standing for a number (general symbol)" }, { "unit": null, "symbol": "x", "meaning": "a letter standing for a number (general symbol)" } ], "sympy": "Eq(2*a*m + 2*a*x + b*m + b*x, (m + x)*(2*a + b))", "physics": false, "states": [], "concepts": [ "concept/binomial", "concept/factor", "concept/polynomial", "method/factoring-by-grouping" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-31aeee1cab", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "a^8+a^6-a^5-a^3+a^2+1=(a^2+1)(a^6-a^3+1).", "name": null, "statement": "The polynomial a^8 + a^6 - a^5 - a^3 + a^2 + 1 factors as (a^2 + 1)(a^6 - a^3 + 1).", "kind": "result", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a letter standing for a number (general symbol)" } ], "sympy": "Eq(a**8 + a**6 - a**5 - a**3 + a**2 + 1, (a**2 + 1)*(a**6 - a**3 + 1))", "physics": false, "states": [], "concepts": [ "concept/factor", "concept/polynomial", "method/factoring-by-grouping" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-efe3242df1", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "a^2-b^2=(a+b)(a-b)", "name": "difference of two squares", "statement": "The difference of the squares of two numbers equals the sum of the numbers times their difference.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a letter standing for a number (general symbol)" }, { "unit": null, "symbol": "b", "meaning": "a letter standing for a number (general symbol)" } ], "sympy": "Eq(a**2 - b**2, (a + b)*(a - b))", "physics": false, "states": [ "theorem/difference-of-two-squares" ], "concepts": [ "concept/binomial", "concept/factor", "concept/perfect-square" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-f8c037cebf", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "x^2 + 14x + 45 = (x + 9)(x + 5)", "name": null, "statement": "The trinomial x^2 + 14x + 45 factors as (x + 9)(x + 5), since 9 and 5 have sum 14 and product 45.", "kind": "result", "symbols": [ { "unit": null, "symbol": "x", "meaning": "a letter standing for a number (general symbol)" } ], "sympy": "Eq(x**2 + 14*x + 45, (x + 9)*(x + 5))", "physics": false, "states": [], "concepts": [ "concept/binomial", "concept/factor", "concept/trinomial", "method/factoring-a-trinomial-of-the-form-x-2-ax-b" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-f0e694f3da", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "x^2 - 6x + 5 = (x - 5)(x - 1)", "name": null, "statement": "The trinomial x^2 - 6x + 5 factors as (x - 5)(x - 1), since -5 and -1 have sum -6 and product 5.", "kind": "result", "symbols": [ { "unit": null, "symbol": "x", "meaning": "a letter standing for a number (general symbol)" } ], "sympy": "Eq(x**2 - 6*x + 5, (x - 5)*(x - 1))", "physics": false, "states": [], "concepts": [ "concept/binomial", "concept/factor", "concept/trinomial", "method/factoring-a-trinomial-of-the-form-x-2-ax-b" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-0b11f67dc0", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "x^2 + 2x - 3 = (x + 3)(x - 1)", "name": null, "statement": "The trinomial x^2 + 2x - 3 factors as (x + 3)(x - 1), since 3 and -1 have sum 2 and product -3.", "kind": "result", "symbols": [ { "unit": null, "symbol": "x", "meaning": "a letter standing for a number (general symbol)" } ], "sympy": "Eq(x**2 + 2*x - 3, (x + 3)*(x - 1))", "physics": false, "states": [], "concepts": [ "concept/binomial", "concept/factor", "concept/trinomial", "method/factoring-a-trinomial-of-the-form-x-2-ax-b" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-aaa1990315", "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "FACTORING", "latex": "x^2 - 8x - 20 = (x - 10)(x + 2)", "name": null, "statement": "The trinomial x^2 - 8x - 20 factors as (x - 10)(x + 2), since -10 and 2 have sum -8 and product -20.", "kind": "result", "symbols": [ { "unit": null, "symbol": "x", "meaning": "a letter standing for a number (general symbol)" } ], "sympy": "Eq(x**2 - 8*x - 20, (x - 10)*(x + 2))", "physics": false, "states": [], "concepts": [ "concept/binomial", "concept/factor", "concept/trinomial", "method/factoring-a-trinomial-of-the-form-x-2-ax-b" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-6b7c844c53", "chapter": "boyden-first-book-in-algebra-1895/ch-greatest-common-factor", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "GREATEST COMMON FACTOR", "latex": "3ac+3bc & = & 3c(a+b)", "name": null, "statement": "The first expression in the illustration factored by taking out the common factor 3c.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "letter (algebraic quantity)" }, { "unit": null, "symbol": "b", "meaning": "letter (algebraic quantity)" }, { "unit": null, "symbol": "c", "meaning": "letter (algebraic quantity)" } ], "sympy": "Eq(3*a*c + 3*b*c, 3*c*(a+b))", "physics": false, "states": [], "concepts": [ "concept/factor", "method/factoring-by-taking-out-a-common-factor" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-4852306701", "chapter": "boyden-first-book-in-algebra-1895/ch-greatest-common-factor", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "GREATEST COMMON FACTOR", "latex": "6a^2x+12abx+6b^2x & = & 6x(a+b)(a+b)", "name": null, "statement": "The second expression in the illustration factored as 6x times the square of (a+b).", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "letter (algebraic quantity)" }, { "unit": null, "symbol": "b", "meaning": "letter (algebraic quantity)" }, { "unit": null, "symbol": "x", "meaning": "letter (algebraic quantity)" } ], "sympy": "Eq(6*a**2*x + 12*a*b*x + 6*b**2*x, 6*x*(a+b)*(a+b))", "physics": false, "states": [], "concepts": [ "concept/factor", "concept/perfect-square", "method/factoring-by-taking-out-a-common-factor" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-70f6a00386", "chapter": "boyden-first-book-in-algebra-1895/ch-greatest-common-factor", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "GREATEST COMMON FACTOR", "latex": "3(a+b)=3a+3b", "name": null, "statement": "The greatest common factor of the two illustrated expressions is 3(a+b), which expands to 3a+3b.", "kind": "result", "symbols": [ { "unit": null, "symbol": "a", "meaning": "letter (algebraic quantity)" }, { "unit": null, "symbol": "b", "meaning": "letter (algebraic quantity)" } ], "sympy": "Eq(3*(a+b), 3*a+3*b)", "physics": false, "states": [], "concepts": [ "concept/highest-common-factor", "law/distributive-law", "method/factoring-by-taking-out-a-common-factor" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-641bd3efa5", "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "REDUCTION OF FRACTIONS", "latex": "\\frac{5a^2b \\div 5ab}{10ab^2 \\div 5ab} = \\frac{a}{2b}", "name": null, "statement": "Dividing the numerator and denominator of 5a^2b/(10ab^2) by their common factor 5ab gives the lowest-terms form a/(2b).", "kind": "result", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a letter standing for a number" }, { "unit": null, "symbol": "b", "meaning": "a letter standing for a number" } ], "sympy": "Eq((5*a**2*b)/(10*a*b**2), a/(2*b))", "physics": false, "states": [], "concepts": [ "concept/lowest-terms", "concept/rational-number", "method/factoring-by-taking-out-a-common-factor", "method/reducing-a-fraction-to-lowest-terms", "theorem/fundamental-principle-of-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-03fca7add8", "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "REDUCTION OF FRACTIONS", "latex": "\\frac{a^2bx-b^3x}{a^2bx-ab^2x} = \\frac{bx(a^2-b^2) \\div bx(a-b)}{abx(a-b) \\div bx(a-b)} = \\frac{a+b}{a}", "name": null, "statement": "The fraction (a^2bx - b^3x)/(a^2bx - ab^2x) reduces to (a+b)/a after removing the common factor bx(a-b) from numerator and denominator.", "kind": "result", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a letter standing for a number" }, { "unit": null, "symbol": "b", "meaning": "a letter standing for a number" }, { "unit": null, "symbol": "x", "meaning": "a letter standing for a number" } ], "sympy": "Eq((a**2*b*x - b**3*x)/(a**2*b*x - a*b**2*x), (a+b)/a)", "physics": false, "states": [], "concepts": [ "concept/highest-common-factor", "concept/lowest-terms", "concept/rational-number", "method/factoring-by-taking-out-a-common-factor", "method/reducing-a-fraction-to-lowest-terms", "theorem/fundamental-principle-of-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-ef6f872f0a", "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "REDUCTION OF FRACTIONS", "latex": "\\frac{ac-bc-d}{c} = a - b -\\frac{d}{c}", "name": null, "statement": "A fraction whose numerator is divided by its denominator equals a mixed expression: the whole part a - b plus the remaining fraction -d/c.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a letter standing for a number" }, { "unit": null, "symbol": "b", "meaning": "a letter standing for a number" }, { "unit": null, "symbol": "c", "meaning": "a letter standing for a number (the denominator)" }, { "unit": null, "symbol": "d", "meaning": "a letter standing for a number" } ], "sympy": "Eq((a*c - b*c - d)/c, a - b - d/c)", "physics": false, "states": [], "concepts": [ "concept/entire-number", "concept/method-reducing-a-fraction-to-an-integral-or-mixed-expression", "concept/mixed-number", "concept/rational-number" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-3a9b5f53a1", "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "REDUCTION OF FRACTIONS", "latex": "b + \\frac{a}{c} = \\frac{bc + a}{c}", "name": null, "statement": "An entire expression b plus a fraction equals a single fraction with denominator c, obtained by multiplying b by c and adding a.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a letter standing for a number" }, { "unit": null, "symbol": "b", "meaning": "a letter standing for a number" }, { "unit": null, "symbol": "c", "meaning": "a letter standing for a number (the denominator)" } ], "sympy": "Eq(b + a/c, (b*c + a)/c)", "physics": false, "states": [], "concepts": [ "concept/equivalent-fractions", "concept/method-reducing-a-mixed-expression-to-a-fraction", "concept/mixed-number", "concept/rational-number" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-4ba2a5499f", "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "REDUCTION OF FRACTIONS", "latex": "b - \\frac{a - x}{c} = \\frac{bc - a + x}{c}", "name": null, "statement": "An entire expression b minus a fraction equals a single fraction with denominator c, obtained by multiplying b by c and subtracting a - x.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a letter standing for a number" }, { "unit": null, "symbol": "b", "meaning": "a letter standing for a number" }, { "unit": null, "symbol": "c", "meaning": "a letter standing for a number (the denominator)" }, { "unit": null, "symbol": "x", "meaning": "a letter standing for a number" } ], "sympy": "Eq(b - (a - x)/c, (b*c - a + x)/c)", "physics": false, "states": [], "concepts": [ "concept/equivalent-fractions", "concept/method-reducing-a-mixed-expression-to-a-fraction", "concept/mixed-number", "concept/rational-number" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-abfdb69264", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "\\frac{a}{b}=\\frac{-a}{-b}=-\\frac{-a}{b}=-\\frac{a}{-b}", "name": null, "statement": "Changing the sign of both numerator and denominator, or of one of them, leaves the value of a fraction unchanged.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "numerator term" }, { "unit": null, "symbol": "b", "meaning": "denominator term" } ], "sympy": "Eq(a/b, (-a)/(-b))", "physics": false, "states": [], "concepts": [ "concept/algebraic-fraction", "concept/zodiacal-sign" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-4db100aa7c", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "\\frac{a-b}{x-y}=\\frac{b-a}{y-x}=-\\frac{b-a}{x-y}=-\\frac{a-b}{y-x}", "name": null, "statement": "When both terms of a polynomial fraction are polynomials, reversing the sign of every term in the numerator and in the denominator leaves the fraction's value unchanged.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "letter in the numerator polynomial" }, { "unit": null, "symbol": "b", "meaning": "letter in the numerator polynomial" }, { "unit": null, "symbol": "x", "meaning": "letter in the denominator polynomial" }, { "unit": null, "symbol": "y", "meaning": "letter in the denominator polynomial" } ], "sympy": "Eq((a-b)/(x-y), (b-a)/(y-x))", "physics": false, "states": [], "concepts": [ "concept/algebraic-fraction", "concept/equivalent-fractions", "concept/polynomial", "theorem/fundamental-principle-of-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-c78fd82121", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "\\frac{a-b+c}{x+y+z}=\\frac{b-c-a}{-x-y-z}=-\\frac{b-c-a}{x+y+z}=-\\frac{a-b+c}{-x-y-z}", "name": null, "statement": "For a trinomial numerator and denominator, changing the signs of all terms in either or both gives a fraction equal in value to the original.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "letter in the numerator" }, { "unit": null, "symbol": "b", "meaning": "letter in the numerator" }, { "unit": null, "symbol": "c", "meaning": "letter in the numerator" }, { "unit": null, "symbol": "x", "meaning": "letter in the denominator" }, { "unit": null, "symbol": "y", "meaning": "letter in the denominator" }, { "unit": null, "symbol": "z", "meaning": "letter in the denominator" } ], "sympy": "Eq((a-b+c)/(x+y+z), (b-c-a)/(-x-y-z))", "physics": false, "states": [], "concepts": [ "concept/algebraic-fraction", "concept/equivalent-fractions", "concept/trinomial", "theorem/fundamental-principle-of-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-02f247f875", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "\\frac{b}{c}\\div \\frac{x}{y}=\\frac{b}{c}\\times\\frac{y}{x}=\\frac{by}{cx}", "name": null, "statement": "Dividing one fraction by another gives the same result as multiplying by the reciprocal of the divisor.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "b", "meaning": "numerator of the dividend" }, { "unit": null, "symbol": "c", "meaning": "denominator of the dividend" }, { "unit": null, "symbol": "x", "meaning": "numerator of the divisor" }, { "unit": null, "symbol": "y", "meaning": "denominator of the divisor" } ], "sympy": "Eq((b/c)/(x/y), b*y/(c*x))", "physics": false, "states": [], "concepts": [ "concept/algebraic-fraction", "concept/method-dividing-by-a-fraction", "concept/reciprocal" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-a2d7b7babd", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "\\left(\\frac{a}{b}\\right)^2 = \\frac{a}{b} \\times \\frac{a}{b} = \\frac{a^2}{b^2}", "name": null, "statement": "The square of a fraction is found by squaring its numerator and its denominator separately.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "a", "meaning": "numerator of the fraction" }, { "unit": null, "symbol": "b", "meaning": "denominator of the fraction" } ], "sympy": "Eq((a/b)**2, a**2/b**2)", "physics": false, "states": [], "concepts": [ "concept/algebraic-fraction", "concept/method-raising-a-fraction-to-a-power", "concept/power" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-22083ef9c6", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "\\frac{b^4}{a^4} - \\frac{y^4}{x^4} = \\left(\\frac{b^2}{a^2} + \\frac{y^2}{x^2}\\right) \\left(\\frac{b}{a} + \\frac{y}{x}\\right) \\left( \\frac{b}{a} - \\frac{y}{x}\\right)", "name": null, "statement": "The difference of two fourth powers of fractions factors into the product of a sum and two differences, as a difference of squares applied twice.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "a", "meaning": "denominator of the first fraction" }, { "unit": null, "symbol": "b", "meaning": "numerator of the first fraction" }, { "unit": null, "symbol": "x", "meaning": "denominator of the second fraction" }, { "unit": null, "symbol": "y", "meaning": "numerator of the second fraction" } ], "sympy": "Eq(b**4/a**4 - y**4/x**4, (b**2/a**2 + y**2/x**2)*(b/a + y/x)*(b/a - y/x))", "physics": false, "states": [], "concepts": [ "concept/factor", "concept/method-factoring", "concept/theorem-difference-of-two-squares" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-7e92e07c3b", "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "OPERATIONS UPON FRACTIONS", "latex": "x^4 + x^2 + \\frac{1}{4} = \\left(x^2 + \\frac{1}{2}\\right)^2", "name": null, "statement": "The expression x^4 + x^2 + 1/4 is a perfect square, equal to (x^2 + 1/2) squared; note the illustration's heading reads x^4 + x^3 + 1/4, which does not match this displayed equation, so the heading appears to be a misprint.", "kind": "identity", "symbols": [ { "unit": null, "symbol": "x", "meaning": "variable" } ], "sympy": "Eq(x**4 + x**2 + Rational(1, 4), (x**2 + Rational(1, 2))**2)", "physics": false, "states": [], "concepts": [ "concept/factor", "concept/method-factoring-a-perfect-square-trinomial", "concept/perfect-square" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-235658c1c5", "chapter": "boyden-first-book-in-algebra-1895/ch-complex-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "COMPLEX FRACTIONS", "latex": "\\begin{array}{ccccc} a &+& \\frac{ax}{b} & \\times & abd \\\\ \\cline{1-3} \\frac{c}{d} &+& \\frac{x}{ab} & \\times & abd \\end{array} = \\frac{ a^2bd + a^2dx }{ abc + dx }", "name": null, "statement": "Multiplying the numerator and the denominator of the complex fraction (a + ax/b)/(c/d + x/(ab)) by abd clears the inner fractions and gives (a^2bd + a^2dx)/(abc + dx).", "kind": "result", "symbols": [ { "unit": null, "symbol": "a", "meaning": "a general number (letter) in the illustration" }, { "unit": null, "symbol": "b", "meaning": "a general number (letter) in the illustration" }, { "unit": null, "symbol": "c", "meaning": "a general number (letter) in the illustration" }, { "unit": null, "symbol": "d", "meaning": "a general number (letter) in the illustration" }, { "unit": null, "symbol": "x", "meaning": "a general number (letter) in the illustration" } ], "sympy": "Eq((a + a*x/b)/(c/d + x/(a*b)), (a**2*b*d + a**2*d*x)/(a*b*c + d*x))", "physics": false, "states": [], "concepts": [ "concept/algebraic-fraction", "concept/complex-fraction", "concept/lowest-common-denominator", "method/simplifying-a-complex-fraction", "theorem/fundamental-principle-of-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-0085d942b5", "chapter": "boyden-first-book-in-algebra-1895/ch-complex-fractions", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "COMPLEX FRACTIONS", "latex": "\\begin{array}{ccccc} \\frac{1}{1-x} &-& \\frac{1}{1+x} & \\times & (1-x)(1+x) \\\\ \\cline{1-3} \\frac{1}{1-x} &+& \\frac{1}{1+x} & \\times & (1-x)(1+x) \\end{array} = \\frac{1 + x - 1 + x}{1 + x + 1 - x} = \\frac{2x}{2} = x", "name": null, "statement": "Multiplying the numerator and the denominator of the complex fraction by (1-x)(1+x) clears the inner fractions, and the simplified value is x.", "kind": "result", "symbols": [ { "unit": null, "symbol": "x", "meaning": "a general number (letter) in the illustration" } ], "sympy": "Eq((1/(1-x) - 1/(1+x))/(1/(1-x) + 1/(1+x)), x)", "physics": false, "states": [], "concepts": [ "concept/algebraic-fraction", "concept/complex-fraction", "concept/lowest-common-denominator", "method/simplifying-a-complex-fraction", "theorem/fundamental-principle-of-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-f9a831ae41", "chapter": "boyden-first-book-in-algebra-1895/ch-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "EQUATIONS", "latex": "x = a - b", "name": null, "statement": "Subtracting b from each member of x + b = a gives x equal to a minus b, so b has been transposed with its sign changed.", "kind": "result", "symbols": [ { "unit": null, "symbol": "x", "meaning": "unknown number" }, { "unit": null, "symbol": "a", "meaning": "known number" }, { "unit": null, "symbol": "b", "meaning": "known number" } ], "sympy": "Eq(x, a - b)", "physics": false, "states": [], "concepts": [ "concept/equation", "concept/member", "concept/unknown", "method/subtraction", "method/transposing-the-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-455e6e9296", "chapter": "boyden-first-book-in-algebra-1895/ch-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "EQUATIONS", "latex": "x = c + b", "name": null, "statement": "Adding b to each member of x - b = c gives x equal to c plus b, so b has been transposed with its sign changed.", "kind": "result", "symbols": [ { "unit": null, "symbol": "x", "meaning": "unknown number" }, { "unit": null, "symbol": "c", "meaning": "known number" }, { "unit": null, "symbol": "b", "meaning": "known number" } ], "sympy": "Eq(x, c + b)", "physics": false, "states": [], "concepts": [ "concept/equation", "concept/member", "concept/unknown", "method/addition", "method/transposing-the-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-680896f600", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "x^2 = a", "name": null, "statement": "A pure quadratic equation is reduced to this form, and then the square root of each member is taken to solve it.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "x", "meaning": "the unknown number" }, { "unit": null, "symbol": "a", "meaning": "the constant that the square of the unknown equals" } ], "sympy": "Eq(x**2, a)", "physics": false, "states": [], "concepts": [ "concept/method-extracting-the-square-root", "concept/pure-quadratic-equation", "concept/quadratic-equation", "concept/root", "concept/unknown" ] }, { "id": "boyden-first-book-in-algebra-1895/eq-a7d5314152", "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "SIMULTANEOUS EQUATIONS", "latex": "x^2 + bx + c = O", "name": null, "statement": "An affected quadratic equation is reduced to this form (with zero on the right), its first member is factored, each factor is set equal to zero, and the resulting simple equations are solved. The book prints the letter O where zero is meant.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "x", "meaning": "the unknown number" }, { "unit": null, "symbol": "b", "meaning": "the coefficient of the first power of the unknown" }, { "unit": null, "symbol": "c", "meaning": "the constant term" } ], "sympy": "Eq(x**2 + b*x + c, 0)", "physics": false, "states": [], "concepts": [ "concept/affected-quadratic-equation", "concept/coefficient", "concept/constant-term", "concept/factor", "concept/method-factoring", "concept/quadratic-equation", "concept/unknown", "concept/zero" ] } ], "exercise_sets": [ { "id": "boyden-first-book-in-algebra-1895/ex-1", "set": "1", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "practices": [ "concept/linear-equation", "method/addition", "method/division", "method/multiplication", "method/solving-an-equation", "method/stating-a-problem-as-an-equation", "method/subtraction" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-2", "set": "2", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "practices": [ "concept/linear-equation", "method/addition", "method/collecting-like-terms", "method/multiplication", "method/solving-an-equation", "method/stating-a-problem-as-an-equation" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-3", "set": "3", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "practices": [ "method/addition", "method/collecting-like-terms", "method/solving-an-equation", "method/stating-a-problem-as-an-equation", "method/subtraction", "method/transposing-the-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-4", "set": "4", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "practices": [ "method/addition", "method/collecting-like-terms", "method/multiplication", "method/solving-an-equation", "method/stating-a-problem-as-an-equation", "method/transposing-the-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-5", "set": "5", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "practices": [ "concept/linear-equation", "method/addition", "method/collecting-like-terms", "method/multiplication", "method/solving-an-equation", "method/stating-a-problem-as-an-equation" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-6", "set": "6", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "practices": [ "concept/linear-equation", "method/collecting-like-terms", "method/solving-an-equation", "method/stating-a-problem-as-an-equation", "method/transposing-the-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7", "set": "7", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "practices": [ "concept/algebraic-fraction", "method/division", "method/multiplication", "method/solving-an-equation", "method/stating-a-problem-as-an-equation" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8", "set": "8", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "practices": [ "concept/algebraic-fraction", "method/addition", "method/collecting-like-terms", "method/solving-an-equation", "method/stating-a-problem-as-an-equation" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-9", "set": "9", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-preface", "practices": [ "concept/algebraic-fraction", "method/division", "method/multiplication", "method/solving-an-equation", "method/stating-a-problem-as-an-equation" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-10", "set": "10", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "practices": [ "method/addition" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-12", "set": "12", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "practices": [ "concept/cube", "concept/exponent", "concept/power", "method/multiplication" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-13", "set": "13", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-modes-of-representing-the-operations", "practices": [ "method/division" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-14", "set": "14", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-algebraic-expressions", "practices": [ "concept/algebraic-expression", "concept/arrangement", "concept/binomial", "concept/degree", "concept/exponent", "concept/homogeneous-polynomial", "concept/like-terms", "concept/monomial", "concept/numerical-value", "concept/polynomial", "concept/term", "concept/trinomial", "method/stating-a-problem-as-an-equation", "method/substitution" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-15", "set": "15", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-addition", "practices": [ "concept/algebraic-expression", "concept/algebraic-sum", "concept/coefficient", "concept/like-terms", "concept/negative-number", "concept/polynomial", "concept/positive-number", "concept/term", "method/addition", "method/collecting-like-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-16", "set": "16", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "practices": [ "concept/algebraic-fraction", "concept/algebraic-sum", "concept/difference", "concept/like-terms", "concept/minuend", "concept/negative-number", "concept/polynomial", "concept/remainder", "concept/subtrahend", "method/addition", "method/collecting-like-terms", "method/subtraction" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-17", "set": "17", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-subtraction", "practices": [ "concept/parenthesis", "concept/polynomial", "method/addition", "method/collecting-like-terms", "method/subtraction", "theorem/removing-parentheses-preceded-by-minus", "theorem/removing-parentheses-preceded-by-plus" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-18", "set": "18", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "practices": [ "concept/coefficient", "concept/exponent", "concept/product", "method/multiplication", "method/multiplying-a-monomial-by-a-monomial" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-19", "set": "19", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "practices": [ "concept/like-terms", "method/addition", "method/multiplying-a-compound-expression", "method/multiplying-a-monomial-by-a-monomial" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-20", "set": "20", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "practices": [ "concept/binomial", "concept/like-terms", "method/multiplying-two-binomials" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-21", "set": "21", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "practices": [ "concept/exponent", "concept/power", "method/raising-a-monomial-to-a-power" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-22", "set": "22", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "practices": [ "concept/numerical-value", "method/addition", "method/subtraction", "theorem/binomial-theorem" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-23", "set": "23", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-multiplication", "practices": [ "method/addition", "method/collecting-like-terms", "method/multiplying-a-compound-expression", "method/multiplying-a-monomial-by-a-monomial", "method/raising-a-monomial-to-a-power", "method/subtraction" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-24", "set": "24", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-division", "practices": [ "concept/coefficient", "concept/exponent", "method/dividing-a-monomial-by-a-monomial", "theorem/index-law-in-division", "theorem/law-of-signs-in-division" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-25", "set": "25", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-division", "practices": [ "concept/coefficient", "concept/monomial", "concept/polynomial", "method/dividing-a-polynomial-by-a-monomial" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-26", "set": "26", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-division", "practices": [ "concept/dividend", "concept/divisor", "concept/quotient", "concept/remainder", "method/dividing-a-polynomial-by-a-polynomial" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-27", "set": "27", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-division", "practices": [ "concept/radical-sign", "concept/root", "method/extracting-the-root-of-a-fraction", "method/extracting-the-root-of-a-monomial" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-28", "set": "28", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-division", "practices": [ "concept/complete-divisor", "concept/trial-divisor", "method/extracting-the-square-root", "theorem/square-of-a-sum" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-29", "set": "29", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-division", "practices": [ "concept/trial-divisor", "method/extracting-the-cube-root", "theorem/cube-of-a-sum" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-30", "set": "30", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-division", "practices": [ "concept/radical-sign", "concept/root", "method/extracting-the-cube-root", "method/extracting-the-square-root" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-31", "set": "31", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "practices": [ "concept/common-factor", "method/dividing-a-polynomial-by-a-monomial", "method/factoring", "method/factoring-by-taking-out-a-common-factor" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-32", "set": "32", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "practices": [ "method/factoring", "method/factoring-by-grouping" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-33", "set": "33", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "practices": [ "method/factoring", "theorem/difference-of-two-squares" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-34", "set": "34", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "practices": [ "method/factoring", "theorem/sum-of-two-cubes" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-35", "set": "35", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "practices": [ "method/factoring", "theorem/difference-of-two-cubes" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-36", "set": "36", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "practices": [ "concept/perfect-square", "method/factoring", "method/factoring-a-perfect-square-trinomial", "theorem/square-of-a-sum" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-37", "set": "37", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "practices": [ "method/factoring", "method/factoring-a-trinomial-of-the-form-x-2-ax-b" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-38", "set": "38", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-factoring", "practices": [ "method/dividing-a-polynomial-by-a-polynomial", "method/extracting-the-cube-root", "method/factoring", "method/factoring-a-perfect-square-trinomial", "method/factoring-a-trinomial-of-the-form-x-2-ax-b", "method/factoring-by-grouping", "theorem/difference-of-two-cubes", "theorem/difference-of-two-squares", "theorem/sum-of-two-cubes" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-39", "set": "39", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-greatest-common-factor", "practices": [ "concept/algebraic-expression", "concept/common-factor", "concept/factor", "concept/highest-common-factor", "concept/polynomial", "method/factoring", "method/finding-the-highest-common-factor", "theorem/difference-of-two-cubes", "theorem/difference-of-two-squares" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-40", "set": "40", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-least-common-multiple", "practices": [ "concept/common-multiple", "concept/factor", "concept/lowest-common-multiple", "method/factoring", "method/finding-the-lowest-common-multiple" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-41", "set": "41", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-least-common-multiple", "practices": [ "concept/equivalent-fractions", "concept/lowest-common-denominator", "concept/lowest-terms", "concept/mixed-number", "method/adding-fractions", "method/dividing-by-a-fraction", "method/multiplying-fractions", "method/reducing-a-fraction-to-lowest-terms", "method/reducing-fractions-to-lowest-common-denominator", "method/simplifying-a-complex-fraction" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-42", "set": "42", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "practices": [ "concept/algebraic-fraction", "concept/highest-common-factor", "concept/lowest-terms", "method/factoring", "method/reducing-a-fraction-to-lowest-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-43", "set": "43", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-reduction-of-fractions", "practices": [ "concept/equivalent-fractions", "concept/lowest-common-denominator", "concept/lowest-common-multiple", "concept/mixed-number", "method/reducing-a-fraction-to-an-integral-or-mixed-expression", "method/reducing-a-mixed-expression-to-a-fraction", "method/reducing-fractions-to-lowest-common-denominator" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-44", "set": "44", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "practices": [ "concept/algebraic-fraction", "concept/equivalent-fractions", "concept/lowest-common-denominator", "concept/lowest-terms", "method/adding-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-45", "set": "45", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "practices": [ "concept/algebraic-fraction", "concept/lowest-common-denominator", "method/adding-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-46", "set": "46", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "practices": [ "concept/algebraic-fraction", "method/multiplying-a-fraction-by-an-expression" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-47", "set": "47", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "practices": [ "concept/algebraic-fraction", "method/dividing-a-fraction-by-an-expression" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-48", "set": "48", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "practices": [ "concept/lowest-terms", "method/factoring", "method/multiplying-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-49", "set": "49", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "practices": [ "method/dividing-by-a-fraction", "method/factoring", "method/multiplying-fractions" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-50", "set": "50", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-operations-upon-fractions", "practices": [ "method/extracting-the-root-of-a-fraction", "method/factoring", "method/raising-a-fraction-to-a-power", "theorem/difference-of-two-cubes", "theorem/difference-of-two-squares", "theorem/sum-of-two-cubes" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-51", "set": "51", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-complex-fractions", "practices": [ "concept/algebraic-fraction", "concept/complex-fraction", "concept/lowest-common-multiple", "method/adding-fractions", "method/simplifying-a-complex-fraction" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-52", "set": "52", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-complex-fractions", "practices": [ "concept/complex-fraction", "concept/highest-common-factor", "concept/lowest-common-multiple", "concept/lowest-terms", "method/adding-fractions", "method/dividing-a-polynomial-by-a-polynomial", "method/dividing-by-a-fraction", "method/factoring", "method/multiplying-fractions", "method/simplifying-a-complex-fraction" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53", "set": "53", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-equations", "practices": [ "concept/equation", "concept/fractional-equation", "concept/unknown", "method/clearing-an-equation-of-fractions", "method/collecting-like-terms", "method/solving-an-equation", "method/stating-a-problem-as-an-equation", "method/transposing-the-terms" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-54", "set": "54", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-equations", "practices": [ "concept/equation", "concept/unknown", "method/solving-an-equation", "method/stating-a-problem-as-an-equation" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-55", "set": "55", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "practices": [ "concept/linear-equation", "concept/simultaneous-equations", "method/clearing-an-equation-of-fractions", "method/elimination", "method/stating-a-problem-as-an-equation" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-56", "set": "56", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "practices": [ "concept/fractional-equation", "concept/pure-quadratic-equation", "method/clearing-an-equation-of-fractions", "method/extracting-the-square-root" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-57", "set": "57", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "practices": [ "concept/affected-quadratic-equation", "concept/fractional-equation", "concept/quadratic-equation", "method/clearing-an-equation-of-fractions", "method/factoring", "method/stating-a-problem-as-an-equation" ] }, { "id": "boyden-first-book-in-algebra-1895/ex-58", "set": "58", "page": null, "chapter": "boyden-first-book-in-algebra-1895/ch-simultaneous-equations", "practices": [ "concept/fractional-equation", "concept/simultaneous-equations", "method/dividing-a-polynomial-by-a-polynomial", "method/extracting-the-square-root", "method/factoring", "method/finding-the-highest-common-factor" ] } ], "problems": [ { "id": "boyden-first-book-in-algebra-1895/ex-1/1", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 1", "problem_latex": "The greater of two numbers is twice the less, and the sum of\nthe numbers is 129. What are the numbers?", "markdown": "The greater of two numbers is twice the less, and the sum of the numbers is 129. What are the numbers?", "answer_latex": [ "43; 86." ], "answer_markdown": [ "43; 86." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 43, y: 86}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(a + x, 129))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/10", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 10", "problem_latex": "A house cost \\$2880 more than a lot of land, and five times\nthe cost of the lot equals the cost of the house. What was the\ncost of each?", "markdown": "A house cost $2880 more than a lot of land, and five times the cost of the lot equals the cost of the house. What was the cost of each?", "answer_latex": [ "Lot, \\$720; house, \\$3600." ], "answer_markdown": [ "Lot, $720; house, $3600." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{L: 720, H: 3600}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 2880), Eq(5*x, a))" ], "shape": [ "solve: (Eq(a, N + x), Eq(N*x, a))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/11", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 11", "problem_latex": "Mr. A. is 48 years older than his son, but he is only three\ntimes as old. How old is each?", "markdown": "Mr. A. is 48 years older than his son, but he is only three times as old. How old is each?", "answer_latex": [ "Mr. A, 72; son, 24." ], "answer_markdown": [ "Mr. A, 72; son, 24." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{A: 72, s: 24}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 3*a), Eq(x, a + 48))" ], "shape": [ "solve: (Eq(x, N*a), Eq(x, N + a))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/12", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 12", "problem_latex": "Two farms differ by 250 acres, and one is six times as large\nas the other. How many acres in each?", "markdown": "Two farms differ by 250 acres, and one is six times as large as the other. How many acres in each?", "answer_latex": [ "50 A.; 300 A." ], "answer_markdown": [ "50 A.; 300 A." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{s: 50, l: 300}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 6*x), Eq(a - x, 250))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a - x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/13", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 13", "problem_latex": "William paid eight times as much for a dictionary as for a\nrhetoric. If the difference in price was \\$6.30, how much did he\npay for each?", "markdown": "William paid eight times as much for a dictionary as for a rhetoric. If the difference in price was $6.30, how much did he pay for each?", "answer_latex": [ "Dict., \\$7.20; rhet, \\$.90." ], "answer_markdown": [ "Dict., $7.20; rhet, $.90." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{r: Rational(9, 10), d: Rational(36, 5)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 8*x), Eq(a - x, 63/10))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a - x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/14", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 14", "problem_latex": "The sum of two numbers is 4256, and one is 37 times as\ngreat as the other. What are the numbers?", "markdown": "The sum of two numbers is 4256, and one is 37 times as great as the other. What are the numbers?", "answer_latex": [ "112; 4144." ], "answer_markdown": [ "112; 4144." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 112, y: 4144}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 37*x), Eq(a + x, 4256))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/15", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 15", "problem_latex": "Aleck has 48 cents more than Arthur, and seven times\nArthur's money equals Aleck's. How much has each?", "markdown": "Aleck has 48 cents more than Arthur, and seven times Arthur’s money equals Aleck’s. How much has each?", "answer_latex": [ "Aleck, 56; Arthur, 8." ], "answer_markdown": [ "Aleck, 56; Arthur, 8." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 8, k: 56}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(7*x, a), Eq(a, x + 48))" ], "shape": [ "solve: (Eq(N*x, a), Eq(a, N + x))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/16", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 16", "problem_latex": "The sum of the ages of a mother and daughter is 32 years,\nand the age of the mother is seven times that of the daughter.\nWhat is the age of each?", "markdown": "The sum of the ages of a mother and daughter is 32 years, and the age of the mother is seven times that of the daughter. What is the age of each?", "answer_latex": [ "Mother, 28; daughter, 4." ], "answer_markdown": [ "Mother, 28; daughter, 4." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{m: 28, d: 4}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 7*a), Eq(a + x, 32))" ], "shape": [ "solve: (Eq(x, N*a), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/17", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 17", "problem_latex": "John's age is three times that of Mary, and he is 10 years\nolder. What is the age of each?", "markdown": "John’s age is three times that of Mary, and he is 10 years older. What is the age of each?", "answer_latex": [ "J, 15 yrs.; M, 5 yrs." ], "answer_markdown": [ "J, 15 yrs.; M, 5 yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{J: 15, M: 5}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 3*a), Eq(x, a + 10))" ], "shape": [ "solve: (Eq(x, N*a), Eq(x, N + a))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/2", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 2", "problem_latex": "A man bought a horse and carriage for \\$500, paying three\ntimes as much for the carriage as for the horse. How much did each\ncost?", "markdown": "A man bought a horse and carriage for $500, paying three times as much for the carriage as for the horse. How much did each cost?", "answer_latex": [ "Carriage, \\$375; horse, \\$125." ], "answer_markdown": [ "Carriage, $375; horse, $125." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{h: 125, c: 375}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 3*x), Eq(a + x, 500))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/3", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 3", "problem_latex": "Two brothers, counting their money, found that together they\nhad \\$186, and that John had five times as much as Charles. How\nmuch had each?", "markdown": "Two brothers, counting their money, found that together they had $186, and that John had five times as much as Charles. How much had each?", "answer_latex": [ "C, \\$31; J, \\$155." ], "answer_markdown": [ "C, $31; J, $155." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{C: 31, J: 155}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 5*x), Eq(a + x, 186))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/4", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 4", "problem_latex": "Divide the number 64 into two parts so that one part shall\nbe seven times the other.", "markdown": "Divide the number 64 into two parts so that one part shall be seven times the other.", "answer_latex": [ "8; 56." ], "answer_markdown": [ "8; 56." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 8, y: 56}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 7*x), Eq(a + x, 64))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/5", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 5", "problem_latex": "A man walked 24 miles in a day. If he walked twice as far\nin the forenoon as in the afternoon, how far did he walk in the\nafternoon?", "markdown": "A man walked 24 miles in a day. If he walked twice as far in the forenoon as in the afternoon, how far did he walk in the afternoon?", "answer_latex": [ "8 miles." ], "answer_markdown": [ "8 miles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 8}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*x, 24)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "24 ENTER 2 ENTER 1 + ÷" ], "constants": [ { "value": "2", "source": "the 2 in 'twice as far' (2x, the forenoon distance)" }, { "value": "1", "source": "the implicit coefficient of x in '+ x' (the afternoon distance is 1x), so 2x + x = 3x and x = 24 ÷ (2 + 1)" } ], "calculator_value": "+8E+0", "printed_value": "8", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/6", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 6", "problem_latex": "For 72 cents Martha bought some needles and thread, paying\neight times as much for the thread as for the needles. How much\ndid she pay for each?", "markdown": "For 72 cents Martha bought some needles and thread, paying eight times as much for the thread as for the needles. How much did she pay for each?", "answer_latex": [ "Needles, 8; thread, 64." ], "answer_markdown": [ "Needles, 8; thread, 64." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{n: 8, t: 64}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 8*x), Eq(a + x, 72))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/7", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 7", "problem_latex": "In a school there are 672 pupils. If there are twice as\nmany boys as girls, how many boys are there?", "markdown": "In a school there are 672 pupils. If there are twice as many boys as girls, how many boys are there?", "answer_latex": [ "224 girls; 448 boys." ], "answer_markdown": [ "224 girls; 448 boys." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{g: 224, b: 448}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(a + x, 672))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/8", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 8", "problem_latex": "Find two numbers such that their difference is 250 and one\nis eleven times the other.", "markdown": "Find two numbers such that their difference is 250 and one is eleven times the other.", "answer_latex": [ "25; 275." ], "answer_markdown": [ "25; 275." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 25, y: 275}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 11*x), Eq(a - x, 250))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a - x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/9", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem 9", "problem_latex": "James gathered 12 quarts of nuts more than Henry gathered.\nHow many did each gather if James gathered three times as many as\nHenry?", "markdown": "James gathered 12 quarts of nuts more than Henry gathered. How many did each gather if James gathered three times as many as Henry?", "answer_latex": [ "H, 6 qts.; J, 18 qts." ], "answer_markdown": [ "H, 6 qts.; J, 18 qts." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{h: 6, j: 18}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 3*x), Eq(a, x + 12))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a, N + x))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-1/none", "set": "boyden-first-book-in-algebra-1895/ex-1", "number": null, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 1, problem None", "problem_latex": "The sum of two numbers is 60, and\nthe\ngreater is four times the less. What are the numbers?", "markdown": "The sum of two numbers is 60, and the greater is four times the less. What are the numbers?", "answer_latex": [ "The numbers are 12 and 48.", "The numbers are 12 and 60." ], "answer_markdown": [ "The numbers are 12 and 48.", "The numbers are 12 and 60." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "12" }, { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 12, y: 60}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED", "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(5*x, 60)", "solve: (Eq(a, 5*x), Eq(a - x, 48))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a - x, N))", "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "60 ENTER 1 ENTER 4 + ÷" ], "constants": [ { "value": "1", "source": "the coefficient of x in the first term of Eq(x + 4*x, 60), i.e. the 'the less' x written with an implicit 1" }, { "value": "4", "source": "the 4 in 'the greater is four times the less' (the 4*x term)" } ], "calculator_value": "+12E+0", "printed_value": "12", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/1", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 1", "problem_latex": "Charles walked $x$ miles and rode 9 miles. How far did he\ngo?", "markdown": "Charles walked $x$ miles and rode 9 miles. How far did he go?", "answer_latex": [ "$x + 9$." ], "answer_markdown": [ "$x + 9$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x + 9" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/10", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 10", "problem_latex": "If $d$ is a whole number, what is the next larger number?", "markdown": "If $d$ is a whole number, what is the next larger number?", "answer_latex": [ "$d + 1$." ], "answer_markdown": [ "$d + 1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "d + 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/11", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 11", "problem_latex": "A boy bought a pound of butter for $y$ cents, a pound of\nmeat for $z$ cents, and a bunch of lettuce for $s$ cents. How much\ndid they all cost?", "markdown": "A boy bought a pound of butter for $y$ cents, a pound of meat for $z$ cents, and a bunch of lettuce for $s$ cents. How much did they all cost?", "answer_latex": [ "$y + z + s$ cts." ], "answer_markdown": [ "$y + z + s$ cts." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "y + z + s" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/12", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 12", "problem_latex": "What is the next whole number larger than $m$?", "markdown": "What is the next whole number larger than $m$?", "answer_latex": [ "$m + 1$." ], "answer_markdown": [ "$m + 1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "m + 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/13", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 13", "problem_latex": "What is the sum of $x$ taken $y$ times?", "markdown": "What is the sum of $x$ taken $y$ times?", "answer_latex": [ "$yx$." ], "answer_markdown": [ "$yx$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/14", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 14", "problem_latex": "A merchant sold $x$ barrels of flour one week, 40 the next\nweek, and $a$ barrels the following week. How many barrels did he\nsell?", "markdown": "A merchant sold $x$ barrels of flour one week, 40 the next week, and $a$ barrels the following week. How many barrels did he sell?", "answer_latex": [ "$x + 40 + a$." ], "answer_markdown": [ "$x + 40 + a$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x + 40 + a" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/15", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 15", "problem_latex": "Find two numbers whose sum is 74 and whose difference is 18.", "markdown": "Find two numbers whose sum is 74 and whose difference is 18.", "answer_latex": [ "$28$; $46$." ], "answer_markdown": [ "$28$; $46$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 46, y: 28}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(-a + x, 18), Eq(a + x, 74))" ], "shape": [ "solve: (Eq(-a + x, N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/2", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 2", "problem_latex": "A merchant bought $a$ barrels of sugar and $p$ barrels of\nmolasses. How many barrels in all did he buy?", "markdown": "A merchant bought $a$ barrels of sugar and $p$ barrels of molasses. How many barrels in all did he buy?", "answer_latex": [ "$a + p$." ], "answer_markdown": [ "$a + p$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "a + p" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/3", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 3", "problem_latex": "What is the sum of $b$ + $b$ + $b$ + etc. written eight\ntimes?", "markdown": "What is the sum of $b$ + $b$ + $b$ + etc. written eight times?", "answer_latex": [ "$8b$." ], "answer_markdown": [ "$8b$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "b + b + b + b + b + b + b + b", "answer_expr": "8*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 8*x" ], "shape": [ "identity: N*x" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/4", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 4", "problem_latex": "Express the sum of $x$ and $y$.", "markdown": "Express the sum of $x$ and $y$.", "answer_latex": [ "$x + y$." ], "answer_markdown": [ "$x + y$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x + y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/5", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 5", "problem_latex": "There are $c$ boys at play, and 5 others join them. How many\nboys are there in all?", "markdown": "There are $c$ boys at play, and 5 others join them. How many boys are there in all?", "answer_latex": [ "$c + 5$." ], "answer_markdown": [ "$c + 5$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "c + 5" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/6", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 6", "problem_latex": "What is the sum of $x$ + $x$ + $x$ + etc. written $d$ times?", "markdown": "What is the sum of $x$ + $x$ + $x$ + etc. written $d$ times?", "answer_latex": [ "$dx$." ], "answer_markdown": [ "$dx$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "d*x" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/7", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 7", "problem_latex": "A lady bought a silk dress for $m$ dollars, a muff for $l$\ndollars, a shawl for $v$ dollars, and a pair of gloves for $c$\ndollars. What was the entire cost?", "markdown": "A lady bought a silk dress for $m$ dollars, a muff for $l$ dollars, a shawl for $v$ dollars, and a pair of gloves for $c$ dollars. What was the entire cost?", "answer_latex": [ "$m + l + v + c$ dols." ], "answer_markdown": [ "$m + l + v + c$ dols." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "m + l + v + c" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/8", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 8", "problem_latex": "George is $x$ years old, Martin is $y$, and Morgan is $z$\nyears. What is the sum of their ages?", "markdown": "George is $x$ years old, Martin is $y$, and Morgan is $z$ years. What is the sum of their ages?", "answer_latex": [ "$x + y + z$ yrs." ], "answer_markdown": [ "$x + y + z$ yrs." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x + y + z" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-10/9", "set": "boyden-first-book-in-algebra-1895/ex-10", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 10, problem 9", "problem_latex": "What is the sum of $m$ taken $b$ times?", "markdown": "What is the sum of $m$ taken $b$ times?", "answer_latex": [ "$bm$." ], "answer_markdown": [ "$bm$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "b*m" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/1", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 1", "problem_latex": "Express the double of $x$.", "markdown": "Express the double of $x$.", "answer_latex": [ "$2x$." ], "answer_markdown": [ "$2x$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/10", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 10", "problem_latex": "Express the product of $a$ factors each equal to $d$.", "markdown": "Express the product of $a$ factors each equal to $d$.", "answer_latex": [ "$d^a$." ], "answer_markdown": [ "$d^a$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/11", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 11", "problem_latex": "Write the second power of $a$ added to three times the cube\nof $m$.", "markdown": "Write the second power of $a$ added to three times the cube of $m$.", "answer_latex": [ "$3m^3 + a^2$." ], "answer_markdown": [ "$3m^3 + a^2$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/12", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 12", "problem_latex": "Express $x$ to the power $2m$, plus $x$ to the power $m$.", "markdown": "Express $x$ to the power $2m$, plus $x$ to the power $m$.", "answer_latex": [ "$x^{2m} + x^m$." ], "answer_markdown": [ "$x^{2m} + x^m$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/13", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 13", "problem_latex": "What is the interest on $x$ dollars for $m$ years at 6 \\%?", "markdown": "What is the interest on $x$ dollars for $m$ years at 6 %?", "answer_latex": [ "$\\frac{6}{100}mx$ dols., or $6mx$ cts." ], "answer_markdown": [ "$\\frac{6}{100}mx$ dols., or $6mx$ cts." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(I, x*m*6/100)", "answer_expr": "6*m*x/100" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x, 3*a*b/50)" ], "shape": [ "solve: Eq(x, N*a*b)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/14a", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 14, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 14a", "problem_latex": "In a certain school there are $c$ girls, and three times as\nmany boys less 8. How many boys, and how many boys and girls\ntogether?", "markdown": "In a certain school there are $c$ girls, and three times as many boys less 8. How many boys, and how many boys and girls together?", "answer_latex": [ "$3c - 8$ boys; $4c - 8$ boys and girls." ], "answer_markdown": [ "$3c - 8$ boys; $4c - 8$ boys and girls." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(B, 3*c - 8)", "answer_expr": "3*c - 8" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x, 3*a - 8)" ], "shape": [ "solve: Eq(x, N*a + N)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/14b", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 14, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 14b", "problem_latex": "In a certain school there are $c$ girls, and three times as\nmany boys less 8. How many boys, and how many boys and girls\ntogether?", "markdown": "In a certain school there are $c$ girls, and three times as many boys less 8. How many boys, and how many boys and girls together?", "answer_latex": [ "$3c - 8$ boys; $4c - 8$ boys and girls." ], "answer_markdown": [ "$3c - 8$ boys; $4c - 8$ boys and girls." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(T, c + (3*c - 8))", "answer_expr": "4*c - 8" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x, 4*a - 8)" ], "shape": [ "solve: Eq(x, N*a + N)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/15", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 15", "problem_latex": "If $x$ men can do a piece of work in 9 days, how many days\nwould it take 1 man to perform the same work?", "markdown": "If $x$ men can do a piece of work in 9 days, how many days would it take 1 man to perform the same work?", "answer_latex": [ "$9x$ days." ], "answer_markdown": [ "$9x$ days." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x*9, d)", "answer_expr": "9*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(9*a, x)" ], "shape": [ "solve: Eq(N*a, x)" ], "same_problem_in": [], "needs": [ "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/16", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 16", "problem_latex": "How many thirds are there in $x$?", "markdown": "How many thirds are there in $x$?", "answer_latex": [ "$3x$ thirds." ], "answer_markdown": [ "$3x$ thirds." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(N/3, x)", "answer_expr": "3*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x/3, a)" ], "shape": [ "solve: Eq(N*x, a)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/17", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 17", "problem_latex": "How many fifths are there in $b$?", "markdown": "How many fifths are there in $b$?", "answer_latex": [ "$5b$ fifths." ], "answer_markdown": [ "$5b$ fifths." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(N/5, b)", "answer_expr": "5*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x/5, a)" ], "shape": [ "solve: Eq(N*x, a)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/18", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 18", "problem_latex": "A man bought a horse for $x$ dollars, paid 2 dollars a week\nfor his keeping, and received 4 dollars a week for his work. At\nthe expiration of $a$ weeks he sold him for $m$ dollars. How much\ndid he gain?", "markdown": "A man bought a horse for $x$ dollars, paid 2 dollars a week for his keeping, and received 4 dollars a week for his work. At the expiration of $a$ weeks he sold him for $m$ dollars. How much did he gain?", "answer_latex": [ "$m - x + 2a$ dols." ], "answer_markdown": [ "$m - x + 2a$ dols." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(G, m - (x + 2*a) + 4*a)", "answer_expr": "m - x + 2*a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x, 2*a + b - c)" ], "shape": [ "solve: Eq(x, N*a + b - c)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/19", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 19", "problem_latex": "James has $a$ walnuts, John twice as many less 8, and Joseph\nthree times as many as James and John less 7. How many have all\ntogether?", "markdown": "James has $a$ walnuts, John twice as many less 8, and Joseph three times as many as James and John less 7. How many have all together?", "answer_latex": [ "$12a - 39$." ], "answer_markdown": [ "$12a - 39$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(T, a + (2*a - 8) + (3*(a + (2*a - 8)) - 7))", "answer_expr": "12*a - 39" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x, 12*a - 39)" ], "shape": [ "solve: Eq(x, N*a + N)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/2", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 2", "problem_latex": "Express the product of $x, y$, and $z$.", "markdown": "Express the product of $x, y$, and $z$.", "answer_latex": [ "$xyz$." ], "answer_markdown": [ "$xyz$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/3", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 3", "problem_latex": "How many cents in $x$ dollars?", "markdown": "How many cents in $x$ dollars?", "answer_latex": [ "$100x$ cts." ], "answer_markdown": [ "$100x$ cts." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/4", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 4", "problem_latex": "Write $a$ times $b$ times $c$.", "markdown": "Write $a$ times $b$ times $c$.", "answer_latex": [ "$abc$." ], "answer_markdown": [ "$abc$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/5", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 5", "problem_latex": "What will $a$ quarts of cherries cost at $d$ cents a quart?", "markdown": "What will $a$ quarts of cherries cost at $d$ cents a quart?", "answer_latex": [ "$ad$ cts." ], "answer_markdown": [ "$ad$ cts." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/6", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 6", "problem_latex": "If a stage coach, goes $b$ miles an hour, how far will it go\nin $m$ hours?", "markdown": "If a stage coach, goes $b$ miles an hour, how far will it go in $m$ hours?", "answer_latex": [ "$mb$ miles." ], "answer_markdown": [ "$mb$ miles." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/7", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 7", "problem_latex": "In a cornfield there are $x$ rows, and $a$ hills in a row.\nHow many hills in the field?", "markdown": "In a cornfield there are $x$ rows, and $a$ hills in a row. How many hills in the field?", "answer_latex": [ "$ax$ hills." ], "answer_markdown": [ "$ax$ hills." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/8", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 8", "problem_latex": "Write the cube of $x$.", "markdown": "Write the cube of $x$.", "answer_latex": [ "$x^3$." ], "answer_markdown": [ "$x^3$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:verbal-to-symbol" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-12/9", "set": "boyden-first-book-in-algebra-1895/ex-12", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 12, problem 9", "problem_latex": "Express in a different way $a \\times a \\times a \\times a\n\\times a \\times a \\times a \\times a \\times a$.", "markdown": "Express in a different way $a \\times a \\times a \\times a \\times a \\times a \\times a \\times a \\times a$.", "answer_latex": [ "$a^9$." ], "answer_markdown": [ "$a^9$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "a*a*a*a*a*a*a*a*a", "answer_expr": "a**9" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: x**9" ], "shape": [ "identity: x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/1", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 1", "problem_latex": "Express five times $a$ divided by three times $c$.", "markdown": "Express five times $a$ divided by three times $c$.", "answer_latex": [ "$\\frac{5a}{3c}$." ], "answer_markdown": [ "$\\frac{5a}{3c}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "5*a/(3*c)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/10", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 10", "problem_latex": "A boy who earns $b$ dollars a day spends $x$ dollars a week.\nHow much has he at the end of 3 weeks?", "markdown": "A boy who earns $b$ dollars a day spends $x$ dollars a week. How much has he at the end of 3 weeks?", "answer_latex": [ "$18b - 3x$ dols." ], "answer_markdown": [ "$18b - 3x$ dols." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "18*b - 3*x" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/11a", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 11, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 11a", "problem_latex": "A can perform a piece of work in $x$ days, B in $y$ days,\nand C in $z$ days. Express the part of the work that each can do\nin one day. Express what part they can all do in one day.", "markdown": "A can perform a piece of work in $x$ days, B in $y$ days, and C in $z$ days. Express the part of the work that each can do in one day. Express what part they can all do in one day.", "answer_latex": [ "$\\displaystyle \\frac{1}{x}$" ], "answer_markdown": [ "$\\displaystyle \\frac{1}{x}$" ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "1/x" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/11b", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 11, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 11b", "problem_latex": "A can perform a piece of work in $x$ days, B in $y$ days,\nand C in $z$ days. Express the part of the work that each can do\nin one day. Express what part they can all do in one day.", "markdown": "A can perform a piece of work in $x$ days, B in $y$ days, and C in $z$ days. Express the part of the work that each can do in one day. Express what part they can all do in one day.", "answer_latex": [ "$\\displaystyle \n\\frac{1}{y}$" ], "answer_markdown": [ "$\\displaystyle \\frac{1}{y}$" ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "1/y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/11c", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 11, "part": "c", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 11c", "problem_latex": "A can perform a piece of work in $x$ days, B in $y$ days,\nand C in $z$ days. Express the part of the work that each can do\nin one day. Express what part they can all do in one day.", "markdown": "A can perform a piece of work in $x$ days, B in $y$ days, and C in $z$ days. Express the part of the work that each can do in one day. Express what part they can all do in one day.", "answer_latex": [ "$\\displaystyle \\frac{1}{z}$" ], "answer_markdown": [ "$\\displaystyle \\frac{1}{z}$" ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "1/z" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/11d", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 11, "part": "d", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 11d", "problem_latex": "A can perform a piece of work in $x$ days, B in $y$ days,\nand C in $z$ days. Express the part of the work that each can do\nin one day. Express what part they can all do in one day.", "markdown": "A can perform a piece of work in $x$ days, B in $y$ days, and C in $z$ days. Express the part of the work that each can do in one day. Express what part they can all do in one day.", "answer_latex": [ "$\\displaystyle \n\\frac{1}{x} + \\frac{1}{y} + \\frac{1}{z}$" ], "answer_markdown": [ "$\\displaystyle \\frac{1}{x} + \\frac{1}{y} + \\frac{1}{z}$" ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "1/x + 1/y + 1/z" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/12", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 12", "problem_latex": "How many square feet in a garden $a$ feet on each side?", "markdown": "How many square feet in a garden $a$ feet on each side?", "answer_latex": [ "$a^2$ sq. ft." ], "answer_markdown": [ "$a^2$ sq. ft." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "a**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/13", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 13", "problem_latex": "A money drawer contains $a$ dollars, $b$ dimes, and $c$\nquarters. Express the whole amount in cents.", "markdown": "A money drawer contains $a$ dollars, $b$ dimes, and $c$ quarters. Express the whole amount in cents.", "answer_latex": [ "$100a + 10b + 25c$ cts." ], "answer_markdown": [ "$100a + 10b + 25c$ cts." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "100*a + 10*b + 25*c" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/14", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 14", "problem_latex": "$x$ is how many times $y$?", "markdown": "$x$ is how many times $y$?", "answer_latex": [ "$\\displaystyle \\frac{x}{y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x}{y}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x/y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/15", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 15", "problem_latex": "If $m$ apples are worth $n$ chestnuts, how many chestnuts is\none apple worth?", "markdown": "If $m$ apples are worth $n$ chestnuts, how many chestnuts is one apple worth?", "answer_latex": [ "$\\displaystyle \\frac{n}{m}$ chestnuts." ], "answer_markdown": [ "$\\displaystyle \\frac{n}{m}$ chestnuts." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "n/m" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/16", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 16", "problem_latex": "Divide 30 apples between two boys so that the younger may\nhave two-thirds as many as the elder.", "markdown": "Divide 30 apples between two boys so that the younger may have two-thirds as many as the elder.", "answer_latex": [ "12; 18 apples." ], "answer_markdown": [ "12; 18 apples." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{y: 12, x: 18}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 2*E/3), Eq(x + E, 30))", "solve: (Eq(x, 2*a/3), Eq(a + x, 30))" ], "shape": [ "solve: (Eq(x, E*N), Eq(x + E, N))", "solve: (Eq(x, N*a), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/2", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 2", "problem_latex": "How many dollars in $y$ cents?", "markdown": "How many dollars in $y$ cents?", "answer_latex": [ "$\\frac{y}{100}$ dols." ], "answer_markdown": [ "$\\frac{y}{100}$ dols." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "y/100" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/3", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 3", "problem_latex": "How many books at $a$ dimes each can be bought for $x$\ndimes?", "markdown": "How many books at $a$ dimes each can be bought for $x$ dimes?", "answer_latex": [ "$\\frac{x}{a}$ books." ], "answer_markdown": [ "$\\frac{x}{a}$ books." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x/a" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/4", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 4", "problem_latex": "How many days will a man be required to work for $m$ dollars\nif he receive $y$ dollars a day?", "markdown": "How many days will a man be required to work for $m$ dollars if he receive $y$ dollars a day?", "answer_latex": [ "$\\frac{m}{y}$ days." ], "answer_markdown": [ "$\\frac{m}{y}$ days." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "m/y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/5", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 5", "problem_latex": "$x$ dollars were given for $b$ barrels of flour. What was\nthe cost per barrel?", "markdown": "$x$ dollars were given for $b$ barrels of flour. What was the cost per barrel?", "answer_latex": [ "$\\frac{x}{b}$ dols." ], "answer_markdown": [ "$\\frac{x}{b}$ dols." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x/b" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/6", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 6", "problem_latex": "Express $a$ plus $b$, divided by $c$.", "markdown": "Express $a$ plus $b$, divided by $c$.", "answer_latex": [ "$\\frac{a + b}{c}$." ], "answer_markdown": [ "$\\frac{a + b}{c}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "(a + b)/c" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/7", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 7", "problem_latex": "Express $a$, plus $b$ divided by $c$.", "markdown": "Express $a$, plus $b$ divided by $c$.", "answer_latex": [ "$a + \\frac{b}{c}$." ], "answer_markdown": [ "$a + \\frac{b}{c}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "a + b/c" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/8", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 8", "problem_latex": "A man had $a$ sons and half as many daughters. How many\nchildren had he?", "markdown": "A man had $a$ sons and half as many daughters. How many children had he?", "answer_latex": [ "$a + \\frac{a}{2}$, or $\\frac{3}{2}a$." ], "answer_markdown": [ "$a + \\frac{a}{2}$, or $\\frac{3}{2}a$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "a + a/2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-13/9", "set": "boyden-first-book-in-algebra-1895/ex-13", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 13, problem 9", "problem_latex": "If the number of minutes in an hour be represented by $x$,\nwhat will express the number of seconds in 5 hours?", "markdown": "If the number of minutes in an hour be represented by $x$, what will express the number of seconds in 5 hours?", "answer_latex": [ "$300x$." ], "answer_markdown": [ "$300x$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "300*x" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/1", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 1", "problem_latex": "Write a polynomial of five terms. Of what degree is it?", "markdown": "Write a polynomial of five terms. Of what degree is it?", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:construct" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/10", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 10", "problem_latex": "$2a + 3b + c$.", "markdown": "$2a + 3b + c$.", "answer_latex": [ "11." ], "answer_markdown": [ "11." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 11.0, printed 11 (half-unit 0.5; correctly rounded at the printed digits: 11.0)", "problem_expr": "2*a + 3*b + c", "answer_expr": "11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 2*a + 3*b + c at a=1, b=2, c=3" ], "shape": [ "evaluate: N*a + N*b + c" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#11,5E-1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "2 ENTER 1 ×", "3 ENTER 2 × +", "3 +" ], "constants": [ { "value": "2", "source": "the 2 in '2a' in the expression 2a + 3b + c" }, { "value": "1", "source": "given value a = 1" }, { "value": "3", "source": "the 3 in '3b' in the expression 2a + 3b + c" }, { "value": "2", "source": "given value b = 2" }, { "value": "3", "source": "given value c = 3" } ], "calculator_value": "+11E+0", "printed_value": "11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/11", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 11", "problem_latex": "$5b + 3a - 2c + 6x$.", "markdown": "$5b + 3a - 2c + 6x$.", "answer_latex": [ "7." ], "answer_markdown": [ "7." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 7.0, printed 7 (half-unit 0.5; correctly rounded at the printed digits: 7.0)", "problem_expr": "5*b + 3*a - 2*c + 6*x", "answer_expr": "7" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 3*a + 5*b - 2*c + 6*d at a=1, b=2, c=3, x=0" ], "shape": [ "evaluate: N*a + N*b + N*c + N*d" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#7,5E-1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "2 ENTER 5 ×", "1 ENTER 3 ×", "+", "3 ENTER 2 ×", "−", "0 ENTER 6 ×", "+" ], "constants": [ { "value": "5", "source": "the 5 in '5b' in the expression 5b + 3a − 2c + 6x" }, { "value": "2", "source": "b = 2 in the given values; also the 2 in '−2c'" }, { "value": "1", "source": "a = 1 in the given values" }, { "value": "3", "source": "the 3 in '3a'; also c = 3 in the given values" }, { "value": "6", "source": "the 6 in '6x'" }, { "value": "0", "source": "x = 0 in the given values (the printed problem reads 'x = O', taken as zero)" } ], "calculator_value": "+7000000000000000000000000000000000E-33", "printed_value": "7", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/12", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 12", "problem_latex": "$6bc - 3ax + 2xb - 5ac + 2cx$.", "markdown": "$6bc - 3ax + 2xb - 5ac + 2cx$.", "answer_latex": [ "21." ], "answer_markdown": [ "21." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 21.0, printed 21 (half-unit 0.5; correctly rounded at the printed digits: 21.0)", "problem_expr": "6*b*c - 3*a*x + 2*x*b - 5*a*c + 2*c*x", "answer_expr": "21" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: -5*a*c - 3*a*d + 6*b*c + 2*b*d + 2*c*d at a=1, b=2, c=3, x=0" ], "shape": [ "evaluate: N*a*c + N*a*d + N*b*c + N*b*d + N*c*d" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#21,5E-1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "6 ENTER 2 × 3 ×", "3 ENTER 1 × 0 × −", "2 ENTER 0 × 2 × +", "5 ENTER 1 × 3 × −", "2 ENTER 3 × 0 × +" ], "constants": [ { "value": "1", "source": "given value a = 1 (the 1 in 'a = 1')" }, { "value": "0", "source": "given value x = 0 (printed as 'x = O'; read as zero per the GIVEN VALUES)" } ], "calculator_value": "+2100000000000000000000000000000000E-32", "printed_value": "21", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/13", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 13", "problem_latex": "$3bcd + 5cxa - 7xab + abc$.", "markdown": "$3bcd + 5cxa - 7xab + abc$.", "answer_latex": [ "78." ], "answer_markdown": [ "78." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 78.0, printed 78 (half-unit 0.5; correctly rounded at the printed digits: 78.0)", "problem_expr": "3*b*c*d + 5*c*x*a - 7*x*a*b + a*b*c", "answer_expr": "78" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: a*b*c - 7*a*b*e + 5*a*c*e + 3*b*c*d at a=1, b=2, c=3, d=4, x=0" ], "shape": [ "evaluate: N*a*b*e + N*a*c*e + N*b*c*d + a*b*c" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#78,5E-1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "3 ENTER 2 × 3 × 4 ×", "5 ENTER 3 × 0 × 1 × +", "7 ENTER 0 × 1 × 2 × −", "1 ENTER 2 × 3 × +" ], "constants": [ { "value": "0", "source": "x = 0 in the given values; the printed problem shows 'x = O', which is read as zero because the printed answer 78 reproduces only with x = 0" } ], "calculator_value": "+7800000000000000000000000000000000E-32", "printed_value": "78", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/14", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 14", "problem_latex": "$2c^2 + 3b^3 + 4a^4$.", "markdown": "$2c^2 + 3b^3 + 4a^4$.", "answer_latex": [ "46." ], "answer_markdown": [ "46." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 46.0, printed 46 (half-unit 0.5; correctly rounded at the printed digits: 46.0)", "problem_expr": "2*c**2 + 3*b**3 + 4*a**4", "answer_expr": "46" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 4*a**4 + 3*b**3 + 2*c**2 at a=1, b=2, c=3" ], "shape": [ "evaluate: N*a**N + N*b**N + N*c**N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#46,5E-1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "2 ENTER 3 GOLD x² ×", "2 ENTER 3 yˣ 3 × +", "1 ENTER 4 yˣ 4 × +" ], "constants": [ { "value": "2", "source": "the 2 in '2c^2' and the 2 in the value b = 2" }, { "value": "3", "source": "the 3 in '2c^2', the 3 in '3b^3', and the value c = 3" }, { "value": "4", "source": "the 4 in '4a^4'" }, { "value": "1", "source": "the value a = 1" } ], "calculator_value": "+46E+0", "printed_value": "46", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/15", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 15", "problem_latex": "$\\frac{1}{2}a^3c - b^3 - c^3 - \\frac{3}{4}abc^3$.", "markdown": "$\\frac{1}{2}a^3c - b^3 - c^3 - \\frac{3}{4}abc^3$.", "answer_latex": [ "$-74$." ], "answer_markdown": [ "$-74$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed -74.0, printed -74 (half-unit 0.5; correctly rounded at the printed digits: -74.0)", "problem_expr": "Rational(1, 2)*a**3*c - b**3 - c**3 - Rational(3, 4)*a*b*c**3", "answer_expr": "-74" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: a**3*c/2 - 3*a*b*c**3/4 - b**3 - c**3 at a=1, b=2, c=3" ], "shape": [ "evaluate: N*a*b*c**N + N*a**N*c - b**N - c**N" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": "X#-74,5E-1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "1 ENTER 2 ÷ 1 ENTER 3 yˣ × 3 ×", "2 ENTER 3 yˣ −", "3 ENTER 3 yˣ −", "3 ENTER 4 ÷ 1 × 2 × 3 ENTER 3 yˣ × −" ], "constants": [ { "value": "1", "source": "a = 1 in the givens, and the 1 of the 1/2 in the expression" }, { "value": "2", "source": "the 2 of the denominator in 1/2, and b = 2 in the givens" }, { "value": "3", "source": "c = 3 in the givens, the exponent 3 in a^3, b^3, c^3, and the numerator of 3/4" }, { "value": "4", "source": "the denominator of 3/4 in the expression" } ], "calculator_value": "-7400E-2", "printed_value": "-74", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/16", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 16", "problem_latex": "$2a - b - \\frac{2ab}{a + b}$.", "markdown": "$2a - b - \\frac{2ab}{a + b}$.", "answer_latex": [ "$-1\\frac{1}{3}$." ], "answer_markdown": [ "$-1\\frac{1}{3}$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed -1.33333333333, printed -4/3 (half-unit 1.0e-40; correctly rounded at the printed digits: -1.33333333333)", "problem_expr": "2*a - b - 2*a*b/(a + b)", "answer_expr": "-Rational(4, 3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: -2*a*b/(a + b) + 2*a - b at a=1, b=2" ], "shape": [ "evaluate: N*a*b/(a + b) + N*a - b" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": "X#-1\\frac{1}{3},5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/17", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 17", "problem_latex": "$2bc - \\frac{3}{4}c^3 + 3ab - 2a - x + \\frac{4}{15}bx$.", "markdown": "$2bc - \\frac{3}{4}c^3 + 3ab - 2a - x + \\frac{4}{15}bx$.", "answer_latex": [ "$-4\\frac{1}{4}$." ], "answer_markdown": [ "$-4\\frac{1}{4}$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed -4.25, printed -17/4 (half-unit 1.0e-40; correctly rounded at the printed digits: -4.25)", "problem_expr": "2*b*c - Rational(3, 4)*c**3 + 3*a*b - 2*a - x + Rational(4, 15)*b*x", "answer_expr": "-Rational(17, 4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 3*a*b - 2*a + 2*b*c + 4*b*d/15 - 3*c**3/4 - d at a=1, b=2, c=3, x=0" ], "shape": [ "evaluate: N*a*b + N*a + N*b*c + N*b*d + N*c**N - d" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": "X#-4\\frac{1}{4},5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/18", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 18", "problem_latex": "$\\frac{a^2bx + ab^2c + abc^2 + xac^2}{abc}$.", "markdown": "$\\frac{a^2bx + ab^2c + abc^2 + xac^2}{abc}$.", "answer_latex": [ "5." ], "answer_markdown": [ "5." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 5.0, printed 5 (half-unit 0.5; correctly rounded at the printed digits: 5.0)", "problem_expr": "(a**2*b*x + a*b**2*c + a*b*c**2 + x*a*c**2)/(a*b*c)", "answer_expr": "5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: (a**2*b*d + a*b**2*c + a*b*c**2 + a*c**2*d)/(a*b*c) at a=1, b=2, c=3, x=0" ], "shape": [ "evaluate: (a*b*c**N + a*b**N*c + a*c**N*d + a**N*b*d)/(a*b*c)" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": "X#5,5E-1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "1 GOLD x² 2 × 0 ×", "1 ENTER 2 GOLD x² × 3 × +", "1 ENTER 2 × 3 GOLD x² × +", "0 ENTER 1 × 3 GOLD x² × +", "1 ENTER 2 × 3 × ÷" ], "constants": [ { "value": "1", "source": "a = 1 in 'When a = 1'" }, { "value": "2", "source": "b = 2 in 'b = 2'; also the exponent 2 in a² and b²" }, { "value": "3", "source": "c = 3 in 'c = 3'; also the exponent 2 in c²" }, { "value": "0", "source": "x = 0, from the given values (printed as 'x = O' in the problem text, read as zero)" } ], "calculator_value": "+500000000000000000000000000000000E-32", "printed_value": "5", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/19", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 19", "problem_latex": "Henry bought some apples at 3 cents apiece, and twice as\nmany pears at 4 cents apiece, paying for the whole 66 cents. How\nmany of each did he buy?", "markdown": "Henry bought some apples at 3 cents apiece, and twice as many pears at 4 cents apiece, paying for the whole 66 cents. How many of each did he buy?", "answer_latex": [ "6 apples; 12 pears." ], "answer_markdown": [ "6 apples; 12 pears." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 6, p: 12}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, 2*a), Eq(3*a + 4*b, 66))" ], "shape": [ "solve: (Eq(b, N*a), Eq(N*a + N*b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/2", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 2", "problem_latex": "Write a binomial of the fourth degree.", "markdown": "Write a binomial of the fourth degree.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:construct" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/20", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 20", "problem_latex": "Sarah's father told her that the difference between\ntwo-thirds and five-sixths of his age was 6 years. How old was he?", "markdown": "Sarah’s father told her that the difference between two-thirds and five-sixths of his age was 6 years. How old was he?", "answer_latex": [ "36 years." ], "answer_markdown": [ "36 years." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{A: 36}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x/6, 6)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "5 ENTER 6 ÷", "2 ENTER 3 ÷ −", "6 x↔y ÷" ], "constants": [ { "value": "5", "source": "the 5 in Rational(5, 6) in the SymPy expression, five-sixths of his age" }, { "value": "6", "source": "the 6 in Rational(5, 6) in the SymPy expression, the denominator of five-sixths" }, { "value": "2", "source": "the 2 in Rational(2, 3) in the SymPy expression, two-thirds of his age" }, { "value": "3", "source": "the 3 in Rational(2, 3) in the SymPy expression, the denominator of two-thirds" }, { "value": "6", "source": "the 6 in Eq(..., 6) in the SymPy expression, the difference is 6 years" } ], "calculator_value": "+3600000000000000000000000000000001E-32", "printed_value": "36", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/3", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 3", "problem_latex": "Write a polynomial with the terms of different degrees.", "markdown": "Write a polynomial with the terms of different degrees.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:construct" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/4", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 4", "problem_latex": "Write a homogeneous trinomial of the third degree.", "markdown": "Write a homogeneous trinomial of the third degree.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:construct" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/5", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 5", "problem_latex": "Write two similar monomials of the fifth degree which shall\ndiffer as much as possible.", "markdown": "Write two similar monomials of the fifth degree which shall differ as much as possible.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:construct" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/6", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 6", "problem_latex": "Write a homogeneous trinomial with one of its terms of the\nsecond degree.", "markdown": "Write a homogeneous trinomial with one of its terms of the second degree.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:construct" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/7", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 7", "problem_latex": "Arrange according to the descending powers of $a$:\n$-80a^3b^3 + 60a^4b^2 + 108ab^5 + 48a^5b + 3a^6 - 27b^6 -\n90a^2b^4$.\n\nWhat name? What degree?", "markdown": "Arrange according to the descending powers of $a$: $-80a^3b^3 + 60a^4b^2 + 108ab^5 + 48a^5b + 3a^6 - 27b^6 - 90a^2b^4$. What name? What degree?", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:arrange.polynomial" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/8", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 8", "problem_latex": "Write a polynomial of the fifth degree containing six terms.", "markdown": "Write a polynomial of the fifth degree containing six terms.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:construct" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-14/9", "set": "boyden-first-book-in-algebra-1895/ex-14", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 14, problem 9", "problem_latex": "Arrange according to the ascending powers of $x$:\n\n\\[ 15x^2y^3 + 7x^5 - 3xy^5 - 60x^4y + y^7 + 21x^3y^2 \\]\n\nWhat name? What degree? What is the degree of\neach term?", "markdown": "Arrange according to the ascending powers of $x$: 15x^2y^3 + 7x^5 - 3xy^5 - 60x^4y + y^7 + 21x^3y^2 What name? What degree? What is the degree of each term?", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:arrange.polynomial" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/1", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 1", "problem_latex": "$3x$, $5x$, $x$, $4x$, $11x$.", "markdown": "$3x$, $5x$, $x$, $4x$, $11x$.", "answer_latex": [ "$24x$." ], "answer_markdown": [ "$24x$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "3*x + 5*x + x + 4*x + 11*x", "answer_expr": "24*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 24*x" ], "shape": [ "identity: N*x" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-46/17", "wentworth-first-steps-in-algebra-1894/ex-15/2" ], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/10", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 10", "problem_latex": "$x^5 + 5a^4b - 7ab - 2x^5 + 10ab + 3a^4b$.", "markdown": "$x^5 + 5a^4b - 7ab - 2x^5 + 10ab + 3a^4b$.", "answer_latex": [ "$8a^4b + 3ab - x^5$." ], "answer_markdown": [ "$8a^4b + 3ab - x^5$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x**5 + 5*a**4*b - 7*a*b - 2*x**5 + 10*a*b + 3*a**4*b", "answer_expr": "8*a**4*b + 3*a*b - x**5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 8*a**4*b + 3*a*b - x**5" ], "shape": [ "identity: N*a*b + N*a**N*b - x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/11", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 11", "problem_latex": "$\\frac{1}{3}a - \\frac{1}{2}a + \\frac{2}{3}a + a$.", "markdown": "$\\frac{1}{3}a - \\frac{1}{2}a + \\frac{2}{3}a + a$.", "answer_latex": [ "$\\frac{3}{2}a$." ], "answer_markdown": [ "$\\frac{3}{2}a$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "Rational(1,3)*a - Rational(1,2)*a + Rational(2,3)*a + a", "answer_expr": "Rational(3,2)*a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*x/2" ], "shape": [ "identity: N*x" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/12", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 12", "problem_latex": "$\\frac{2}{3}b - \\frac{3}{4}b - 2b - \\frac{1}{3}b +\n\\frac{5}{6}b + b$.", "markdown": "$\\frac{2}{3}b - \\frac{3}{4}b - 2b - \\frac{1}{3}b + \\frac{5}{6}b + b$.", "answer_latex": [ "$-\\frac{7}{12}b$." ], "answer_markdown": [ "$-\\frac{7}{12}b$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "Rational(2,3)*b - Rational(3,4)*b - 2*b - Rational(1,3)*b + Rational(5,6)*b + b", "answer_expr": "-Rational(7,12)*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -7*x/12" ], "shape": [ "identity: N*x" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/13", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 13", "problem_latex": "A lady bought a ribbon for $m$ cents, some tape for $d$\ncents, and some thread for $c$ cents. She paid $x$ cents on the\nbill. How much remains due?", "markdown": "A lady bought a ribbon for $m$ cents, some tape for $d$ cents, and some thread for $c$ cents. She paid $x$ cents on the bill. How much remains due?", "answer_latex": [ "$m + d + c - x$ cts." ], "answer_markdown": [ "$m + d + c - x$ cts." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "m + d + c - x" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/14", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 14", "problem_latex": "A man travels $a$ miles north, then $x$ miles south, then 5\nmiles further south, and then $y$ miles north. How far is he from\nhis starting point?", "markdown": "A man travels $a$ miles north, then $x$ miles south, then 5 miles further south, and then $y$ miles north. How far is he from his starting point?", "answer_latex": [ "$a - x - 5 + y$ miles." ], "answer_markdown": [ "$a - x - 5 + y$ miles." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "a - x - 5 + y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/15", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 15", "problem_latex": "$a + 2b + 3c$, $5a + 3b + c$, $c - a - b$.", "markdown": "$a + 2b + 3c$, $5a + 3b + c$, $c - a - b$.", "answer_latex": [ "$5a + 4b + 5c$." ], "answer_markdown": [ "$5a + 4b + 5c$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "a + 2*b + 3*c + 5*a + 3*b + c + c - a - b", "answer_expr": "5*a + 4*b + 5*c" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*a + 5*b + 5*x" ], "shape": [ "identity: N*a + N*b + N*x" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/16", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 16", "problem_latex": "$x + y - z$, $x - y - z$, $y - x + z$.", "markdown": "$x + y - z$, $x - y - z$, $y - x + z$.", "answer_latex": [ "$x + y - z$." ], "answer_markdown": [ "$x + y - z$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x + y - z + x - y - z + y - x + z", "answer_expr": "x + y - z" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a - b + x" ], "shape": [ "identity: a - b + x" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-16/18" ], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/17", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 17", "problem_latex": "$x + 2y - 3z + a$, $2x - 3y + z - 4a$, $2a - 3x + y - z$.", "markdown": "$x + 2y - 3z + a$, $2x - 3y + z - 4a$, $2a - 3x + y - z$.", "answer_latex": [ "$-3z - a$." ], "answer_markdown": [ "$-3z - a$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x + 2*y - 3*z + a + 2*x - 3*y + z - 4*a + 2*a - 3*x + y - z", "answer_expr": "-3*z - a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a - 3*b" ], "shape": [ "identity: N*b - a" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/18", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 18", "problem_latex": "$x^3 + 3x^2 - x + 5$, $4x^2 - 5x^3 + 3 - 4x$, $3x + 6x^3 -\n3x^2 + 9$.", "markdown": "$x^3 + 3x^2 - x + 5$, $4x^2 - 5x^3 + 3 - 4x$, $3x + 6x^3 - 3x^2 + 9$.", "answer_latex": [ "$2x^3 + 4x^2 - 2x + 17$." ], "answer_markdown": [ "$2x^3 + 4x^2 - 2x + 17$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x**3 + 3*x**2 - x + 5 + 4*x**2 - 5*x**3 + 3 - 4*x + 3*x + 6*x**3 - 3*x**2 + 9", "answer_expr": "2*x**3 + 4*x**2 - 2*x + 17" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*x**3 + 4*x**2 - 2*x + 17" ], "shape": [ "identity: N*x + 2*N*x**N + N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/19", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 19", "problem_latex": "$ca - bc + c^3$, $ab + b^3 - ca$, $a^3 - ab + bc$.", "markdown": "$ca - bc + c^3$, $ab + b^3 - ca$, $a^3 - ab + bc$.", "answer_latex": [ "$a^3 + b^3 + c^3$." ], "answer_markdown": [ "$a^3 + b^3 + c^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "c*a - b*c + c**3 + a*b + b**3 - c*a + a**3 - a*b + b*c", "answer_expr": "a**3 + b**3 + c**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**3 + b**3 + x**3" ], "shape": [ "identity: a**N + b**N + x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/2", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 2", "problem_latex": "$5ab$, $6ab$, $ab$, $13ab$.", "markdown": "$5ab$, $6ab$, $ab$, $13ab$.", "answer_latex": [ "$25ab$." ], "answer_markdown": [ "$25ab$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "5*a*b + 6*a*b + a*b + 13*a*b", "answer_expr": "25*a*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 25*a*x" ], "shape": [ "identity: N*a*x" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/20", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 20", "problem_latex": "$3a^m - a^{m-1} - 1$, $3a^{m-1} + 1 - 2a^m$, $a^{m-1} + 1$.", "markdown": "$3a^m - a^{m-1} - 1$, $3a^{m-1} + 1 - 2a^m$, $a^{m-1} + 1$.", "answer_latex": [ "$2a^m + 1$." ], "answer_markdown": [ "$2a^m + 1$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "12.338170024189132968", "9.5036275181418497264" ], "problem_expr": "3*a**m - a**(m-1) - 1 + 3*a**(m-1) + 1 - 2*a**m + a**(m-1) + 1", "answer_expr": "2*a**m + 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: x**a + 3*x**(a - 1) + 1" ], "shape": [ "identity: N*x**(a - 1) + x**a + 1" ], "same_problem_in": [], "needs": [ "cas.simplify", "other:symbolic exponents" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/21", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 21", "problem_latex": "$5a^5 - 16a^4b - 11a^2b^2c + 13ab$, $-2a^5 + 4a^4b +\n12a^2b^2c - 10ab$, $6a^5 - a^4b - 6a^2b^2c + 10ab$, $-10a^5 +\n8a^4b + a^2b^2c - 6ab$, $a^5 + 5a^4b + 6a^2b^2c - 7ab$.", "markdown": "$5a^5 - 16a^4b - 11a^2b^2c + 13ab$, $-2a^5 + 4a^4b + 12a^2b^2c - 10ab$, $6a^5 - a^4b - 6a^2b^2c + 10ab$, $-10a^5 + 8a^4b + a^2b^2c - 6ab$, $a^5 + 5a^4b + 6a^2b^2c - 7ab$.", "answer_latex": [ "$2a^2b^2c$." ], "answer_markdown": [ "$2a^2b^2c$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "5*a**5 - 16*a**4*b - 11*a**2*b**2*c + 13*a*b - 2*a**5 + 4*a**4*b + 12*a**2*b**2*c - 10*a*b + 6*a**5 - a**4*b - 6*a**2*b**2*c + 10*a*b - 10*a**5 + 8*a**4*b + a**2*b**2*c - 6*a*b + a**5 + 5*a**4*b + 6*a**2*b**2*c - 7*a*b", "answer_expr": "2*a**2*b**2*c" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a**2*b*x**2" ], "shape": [ "identity: N*a**N*b*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/22", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 22", "problem_latex": "$15x^3 + 35x^2 + 3x +7$, $7x^3 + 15x - 11x^2 + 9$, $9x - 10\n+ x^3 - 4x^2$.", "markdown": "$15x^3 + 35x^2 + 3x +7$, $7x^3 + 15x - 11x^2 + 9$, $9x - 10 + x^3 - 4x^2$.", "answer_latex": [ "$23x^3 - 20x^2 + 27x + 6$." ], "answer_markdown": [ "$23x^3 - 20x^2 + 27x + 6$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "21.472", "15.072" ], "problem_expr": "15*x**3 + 35*x**2 + 3*x + 7 + 7*x**3 + 15*x - 11*x**2 + 9 + 9*x - 10 + x**3 - 4*x**2", "answer_expr": "23*x**3 - 20*x**2 + 27*x + 6" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: 23*x**3 + 20*x**2 + 27*x + 6" ], "shape": [ "identity: N*x + 2*N*x**N + N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/23", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 23", "problem_latex": "$9x^5y - 6x^4y^2 + x^3y^3 - 25xy^5$, $-22x^3y^3 - 3xy^5 -\n9x^5y - 3x^4y^2$, $5x^3y^3 + x^5y + 21x^4y^2 + 20xy^5$.", "markdown": "$9x^5y - 6x^4y^2 + x^3y^3 - 25xy^5$, $-22x^3y^3 - 3xy^5 - 9x^5y - 3x^4y^2$, $5x^3y^3 + x^5y + 21x^4y^2 + 20xy^5$.", "answer_latex": [ "$x^5y + 12x^4y^2 - 16x^3y^3 - 8xy^5$." ], "answer_markdown": [ "$x^5y + 12x^4y^2 - 16x^3y^3 - 8xy^5$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "9*x**5*y - 6*x**4*y**2 + x**3*y**3 - 25*x*y**5 - 22*x**3*y**3 - 3*x*y**5 - 9*x**5*y - 3*x**4*y**2 + 5*x**3*y**3 + x**5*y + 21*x**4*y**2 + 20*x*y**5", "answer_expr": "x**5*y + 12*x**4*y**2 - 16*x**3*y**3 - 8*x*y**5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -8*a**5*x - 16*a**3*x**3 + 12*a**2*x**4 + a*x**5" ], "shape": [ "identity: N*a**N*x + 2*N*a**N*x**N + a*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/24", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 24", "problem_latex": "$x - y - z - a - b$, $x + y + z + a + b$, $x + y + z + a -\nb$, $x + y - z - a - b$, $x + y + z - a - b$.", "markdown": "$x - y - z - a - b$, $x + y + z + a + b$, $x + y + z + a - b$, $x + y - z - a - b$, $x + y + z - a - b$.", "answer_latex": [ "$5x + 3y + z - a - 3b$." ], "answer_markdown": [ "$5x + 3y + z - a - 3b$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x - y - z - a - b + x + y + z + a + b + x + y + z + a - b + x + y - z - a - b + x + y + z - a - b", "answer_expr": "5*x + 3*y + z - a - 3*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a - 3*b + 3*c + d + 5*x" ], "shape": [ "identity: N*b + N*c + N*x - a + d" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/25", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 25", "problem_latex": "$a^2c + b^2c + c^3 - abc - bc^2 - ac^2$, $a^2b + b^3 - bc^2\n- ab^2 - b^2c - abc$, $a^3 + ab^2 + ac^2 - a^2b - abc - a^2c$.", "markdown": "$a^2c + b^2c + c^3 - abc - bc^2 - ac^2$, $a^2b + b^3 - bc^2 - ab^2 - b^2c - abc$, $a^3 + ab^2 + ac^2 - a^2b - abc - a^2c$.", "answer_latex": [ "$a^3 + b^3 + c^3 - 3abc$." ], "answer_markdown": [ "$a^3 + b^3 + c^3 - 3abc$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "6.0732390188070922042", "10.489369159458584056" ], "problem_expr": "a**2*c + b**2*c + c**3 - a*b*c - b*c**2 - a*c**2 + a**2*b + b**3 - b*c**2 - a*b**2 - b**2*c - a*b*c + a**3 + a*b**2 + a*c**2 - a**2*b - a*b*c - a**2*c", "answer_expr": "a**3 + b**3 + c**3 - 3*a*b*c" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: a**3 - 2*a*b**2 - 3*a*b*x + b**3 + x**3" ], "shape": [ "identity: N*a*b*x + N*a*b**N + a**N + b**N + x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/26", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 26", "problem_latex": "A regiment is drawn up in $m$ ranks of $b$ men each, and\nthere are $c$ men over. How many men in the regiment?", "markdown": "A regiment is drawn up in $m$ ranks of $b$ men each, and there are $c$ men over. How many men in the regiment?", "answer_latex": [ "$mb + c$ men." ], "answer_markdown": [ "$mb + c$ men." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "m*b + c" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/27", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 27", "problem_latex": "A man had $x$ cows and $z$ horses. After exchanging 10 cows\nwith another man for 19 horses, what will represent the number\nthat he has of each?", "markdown": "A man had $x$ cows and $z$ horses. After exchanging 10 cows with another man for 19 horses, what will represent the number that he has of each?", "answer_latex": [ "$x - 10$ cows; $z + 19$ horses." ], "answer_markdown": [ "$x - 10$ cows; $z + 19$ horses." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x - 10; z + 19" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/28", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 28", "problem_latex": "In a class of 52 pupils there are 8 more boys than girls.\nHow many are there of each?", "markdown": "In a class of 52 pupils there are 8 more boys than girls. How many are there of each?", "answer_latex": [ "22 girls; 30 boys." ], "answer_markdown": [ "22 girls; 30 boys." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{g: 22, b: 30}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 8), Eq(a + x, 52))" ], "shape": [ "solve: (Eq(a, N + x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/3", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 3", "problem_latex": "$-3ax^3$, $-5ax^3$, $-9ax^3$, $-ax^3$.", "markdown": "$-3ax^3$, $-5ax^3$, $-9ax^3$, $-ax^3$.", "answer_latex": [ "$-18ax^3$." ], "answer_markdown": [ "$-18ax^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "-3*a*x**3 - 5*a*x**3 - 9*a*x**3 - a*x**3", "answer_expr": "-18*a*x**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -18*a**3*x" ], "shape": [ "identity: N*a**N*x" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/4", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 4", "problem_latex": "$-x$, $-5x$, $-11x$, $-25x$.", "markdown": "$-x$, $-5x$, $-11x$, $-25x$.", "answer_latex": [ "$-42x$." ], "answer_markdown": [ "$-42x$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "-x - 5*x - 11*x - 25*x", "answer_expr": "-42*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -42*x" ], "shape": [ "identity: N*x" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/5", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 5", "problem_latex": "$-2a^2$, $5a^2$, $3a^2$, $-7a^2$, $11a^2$.", "markdown": "$-2a^2$, $5a^2$, $3a^2$, $-7a^2$, $11a^2$.", "answer_latex": [ "$10a^2$." ], "answer_markdown": [ "$10a^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "-2*a**2 + 5*a**2 + 3*a**2 - 7*a**2 + 11*a**2", "answer_expr": "10*a**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 10*x**2" ], "shape": [ "identity: N*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/6", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 6", "problem_latex": "$2abc^2$, $-5abc^2$, $abc^2$, $-8abc^2$.", "markdown": "$2abc^2$, $-5abc^2$, $abc^2$, $-8abc^2$.", "answer_latex": [ "$-10abc^2$." ], "answer_markdown": [ "$-10abc^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "2*a*b*c**2 - 5*a*b*c**2 + a*b*c**2 - 8*a*b*c**2", "answer_expr": "-10*a*b*c**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -10*a*b**2*x" ], "shape": [ "identity: N*a*b**N*x" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/7", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 7", "problem_latex": "$5x^2$, $3ab$, $-2ab$, $-4a^2$, $5ab$, $-2a^2$.", "markdown": "$5x^2$, $3ab$, $-2ab$, $-4a^2$, $5ab$, $-2a^2$.", "answer_latex": [ "$6ab-x^2$." ], "answer_markdown": [ "$6ab-x^2$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "4.9145618683081665903", "56.110693351176778501" ], "problem_expr": "5*x**2 + 3*a*b - 2*a*b - 4*a**2 + 5*a*b - 2*a**2", "answer_expr": "6*a*b - x**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: -6*a**2 + 6*a*b + 5*x**2" ], "shape": [ "identity: N*a*b + N*a**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/8", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 8", "problem_latex": "$5ax$, $-3bc$, $-2ax$, $7ax$, $bc$, $-2bc$.", "markdown": "$5ax$, $-3bc$, $-2ax$, $7ax$, $bc$, $-2bc$.", "answer_latex": [ "$10ax - 4bc$." ], "answer_markdown": [ "$10ax - 4bc$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "5*a*x - 3*b*c - 2*a*x + 7*a*x + b*c - 2*b*c", "answer_expr": "10*a*x - 4*b*c" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -4*a*b + 10*c*x" ], "shape": [ "identity: N*a*b + N*c*x" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-15/9", "set": "boyden-first-book-in-algebra-1895/ex-15", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 15, problem 9", "problem_latex": "$4a^2 - 5a^2 - 8a^2 - 7a^2$.", "markdown": "$4a^2 - 5a^2 - 8a^2 - 7a^2$.", "answer_latex": [ "$-16a^2$." ], "answer_markdown": [ "$-16a^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "4*a**2 - 5*a**2 - 8*a**2 - 7*a**2", "answer_expr": "-16*a**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -16*x**2" ], "shape": [ "identity: N*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/1", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 1", "problem_latex": "From $5a^{3}$ take $3a^{3}$.", "markdown": "From $5a^{3}$ take $3a^{3}$.", "answer_latex": [ "$2a^3$." ], "answer_markdown": [ "$2a^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "5*a**3 - 3*a**3", "answer_expr": "2*a**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*x**3" ], "shape": [ "identity: N*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/10", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 10", "problem_latex": "From $9x - 4y + 3z$ take $5x - 3y + z$.", "markdown": "From $9x - 4y + 3z$ take $5x - 3y + z$.", "answer_latex": [ "$4x - y + 2z$." ], "answer_markdown": [ "$4x - y + 2z$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(9*x - 4*y + 3*z) - (5*x - 3*y + z)", "answer_expr": "4*x - y + 2*z" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a + 2*b + 4*x" ], "shape": [ "identity: N*b + N*x - a" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/11", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 11", "problem_latex": "Subtract $3x^{4} - x^{2} + 7x - 14$ from $11x^{4} - 2x^{3} -\n8x$.", "markdown": "Subtract $3x^{4} - x^{2} + 7x - 14$ from $11x^{4} - 2x^{3} - 8x$.", "answer_latex": [ "$8x^4 - 2x^3 + 4x^2 - 15x + 14$." ], "answer_markdown": [ "$8x^4 - 2x^3 + 4x^2 - 15x + 14$." ], "checks": [ { "task": "identity", "verdict": "FLAG-INTERPRETED", "judge_why": "interpreted, and no truncation given to check", "problem_expr": "11*x**4 - 2*x**3 - 8*x - (3*x**4 - x**2 + 7*x - 14)", "answer_expr": "8*x**4 - 2*x**3 + 4*x**2 - 15*x + 14" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "identity: 8*x**4 - 2*x**3 + x**2 - 15*x + 14" ], "shape": [ "identity: N*x + 2*N*x**N + N + x**N" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/12", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 12", "problem_latex": "From $10a^{2}b^{2} + 15ab^{2} + 8a^{2}b$ take $-10a^{2}b^{2}\n+ 15ab^{2} - 8a^{2}b$.", "markdown": "From $10a^{2}b^{2} + 15ab^{2} + 8a^{2}b$ take $-10a^{2}b^{2} + 15ab^{2} - 8a^{2}b$.", "answer_latex": [ "$20a^2b^2 + 16a^2b$." ], "answer_markdown": [ "$20a^2b^2 + 16a^2b$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(10*a**2*b**2 + 15*a*b**2 + 8*a**2*b) - (-10*a**2*b**2 + 15*a*b**2 - 8*a**2*b)", "answer_expr": "20*a**2*b**2 + 16*a**2*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 20*a**2*x**2 + 16*a*x**2" ], "shape": [ "identity: N*a*x**N + N*a**N*x**N" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/13", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 13", "problem_latex": "Subtract $1- x + x^{2} - 3x^{3}$ from $x^{3} - 1 + x^{2} -\nx$.", "markdown": "Subtract $1- x + x^{2} - 3x^{3}$ from $x^{3} - 1 + x^{2} - x$.", "answer_latex": [ "$4x^3 - 2$." ], "answer_markdown": [ "$4x^3 - 2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**3 - 1 + x**2 - x) - (1 - x + x**2 - 3*x**3)", "answer_expr": "4*x**3 - 2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*x**3 - 2" ], "shape": [ "identity: N*x**N + N" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/14", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 14", "problem_latex": "From $x^{m} - 2x^{2m} + x^{3m}$ take $2x^{3m} - x^{2m} -\nx^{m}$.", "markdown": "From $x^{m} - 2x^{2m} + x^{3m}$ take $2x^{3m} - x^{2m} - x^{m}$.", "answer_latex": [ "$2x^m - x^{2m} - x^{3m}$" ], "answer_markdown": [ "$2x^m - x^{2m} - x^{3m}$" ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**m - 2*x**(2*m) + x**(3*m)) - (2*x**(3*m) - x**(2*m) - x**m)", "answer_expr": "2*x**m - x**(2*m) - x**(3*m)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -x**(3*a) - x**(2*a) + 2*x**a" ], "shape": [ "identity: N*x**a - 2*x**(N*a)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/15", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 15", "problem_latex": "Subtract $a^{2n} + a^{n}x^{n} + x^{2n}$ from $3a^{2n} -\n17a^{n}x^{n} - 8x^{2n}$.", "markdown": "Subtract $a^{2n} + a^{n}x^{n} + x^{2n}$ from $3a^{2n} - 17a^{n}x^{n} - 8x^{2n}$.", "answer_latex": [ "$2a^{2n} - 18a^nx^n - 9x^{2n}$." ], "answer_markdown": [ "$2a^{2n} - 18a^nx^n - 9x^{2n}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3*a**(2*n) - 17*a**n*x**n - 8*x**(2*n)) - (a**(2*n) + a**n*x**n + x**(2*n))", "answer_expr": "2*a**(2*n) - 18*a**n*x**n - 9*x**(2*n)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -9*b**(2*a) - 18*b**a*x**a + 2*x**(2*a)" ], "shape": [ "identity: N*b**a*x**a + N*b**(N*a) + N*x**(N*a)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/16", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 16", "problem_latex": "From $\\frac{2}{3}a^{2} - \\frac{5}{2}a - 1$ take\n$-\\frac{2}{3}a^{2} + a -\\frac{1}{2}$.", "markdown": "From $\\frac{2}{3}a^{2} - \\frac{5}{2}a - 1$ take $-\\frac{2}{3}a^{2} + a -\\frac{1}{2}$.", "answer_latex": [ "$\\frac{4}{3}a^2 - \\frac{7}{2}a - \\frac{1}{2}$." ], "answer_markdown": [ "$\\frac{4}{3}a^2 - \\frac{7}{2}a - \\frac{1}{2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(2,3)*a**2 - Rational(5,2)*a - 1) - (-Rational(2,3)*a**2 + a - Rational(1,2))", "answer_expr": "Rational(4,3)*a**2 - Rational(7,2)*a - Rational(1,2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*x**2/3 - 7*x/2 - 1/2" ], "shape": [ "identity: N*x + N*x**N + N" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/17", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 17", "problem_latex": "From $x^{5} + 3xy^{4}$ take $x^{5} + 2x^{4}y + 3x^{3}y^{2} -\n2xy^{4} + y^{5}$.", "markdown": "From $x^{5} + 3xy^{4}$ take $x^{5} + 2x^{4}y + 3x^{3}y^{2} - 2xy^{4} + y^{5}$.", "answer_latex": [ "$-2x^4y - 3x^3y^2 + 5xy^4 - y^5$." ], "answer_markdown": [ "$-2x^4y - 3x^3y^2 + 5xy^4 - y^5$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**5 + 3*x*y**4) - (x**5 + 2*x**4*y + 3*x**3*y**2 - 2*x*y**4 + y**5)", "answer_expr": "-2*x**4*y - 3*x**3*y**2 + 5*x*y**4 - y**5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**5 + 5*a**4*x - 3*a**2*x**3 - 2*a*x**4" ], "shape": [ "identity: N*a*x**N + N*a**N*x + N*a**N*x**N - a**N" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/18", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 18", "problem_latex": "From $x$ take $y - a$.", "markdown": "From $x$ take $y - a$.", "answer_latex": [ "$x - y + a$." ], "answer_markdown": [ "$x - y + a$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x - (y - a)", "answer_expr": "x - y + a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a - b + x" ], "shape": [ "identity: a - b + x" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-15/16" ], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/19", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 19", "problem_latex": "From $6a^3 + 4a + 7$ take the sum of $2a^3 + 4a^2 + 9$ and\n$4a^3 - a^2 + 4a - 2$.", "markdown": "From $6a^3 + 4a + 7$ take the sum of $2a^3 + 4a^2 + 9$ and $4a^3 - a^2 + 4a - 2$.", "answer_latex": [ "$-3a^2$." ], "answer_markdown": [ "$-3a^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(6*a**3 + 4*a + 7) - ((2*a**3 + 4*a**2 + 9) + (4*a**3 - a**2 + 4*a - 2))", "answer_expr": "-3*a**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -3*x**2" ], "shape": [ "identity: N*x**N" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/2", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 2", "problem_latex": "From $7a^{2}b$ take $-5a^{2}b$.", "markdown": "From $7a^{2}b$ take $-5a^{2}b$.", "answer_latex": [ "$12a^2b$." ], "answer_markdown": [ "$12a^2b$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "7*a**2*b - (-5*a**2*b)", "answer_expr": "12*a**2*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 12*a*x**2" ], "shape": [ "identity: N*a*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/20", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 20", "problem_latex": "Subtract $3x - 7x^3 + 5x^2$ from the sum of $2 + 8x^2 - x^3$\nand $2x^3 - 3x^2 + x - 2$.", "markdown": "Subtract $3x - 7x^3 + 5x^2$ from the sum of $2 + 8x^2 - x^3$ and $2x^3 - 3x^2 + x - 2$.", "answer_latex": [ "$8x^3 - 2x$." ], "answer_markdown": [ "$8x^3 - 2x$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((2 + 8*x**2 - x**3) + (2*x**3 - 3*x**2 + x - 2)) - (3*x - 7*x**3 + 5*x**2)", "answer_expr": "8*x**3 - 2*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 8*x**3 - 2*x" ], "shape": [ "identity: N*x + N*x**N" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/21", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 21", "problem_latex": "What must be subtracted from $15y^3 + z^3 + 4yz^2 - 5z^2x -\n2xy^2$ to leave a remainder of $6x^3 - 12y^3 + 4z^3 - 2xy^2 +\n6z^2x$?", "markdown": "What must be subtracted from $15y^3 + z^3 + 4yz^2 - 5z^2x - 2xy^2$ to leave a remainder of $6x^3 - 12y^3 + 4z^3 - 2xy^2 + 6z^2x$?", "answer_latex": [ "$27y^3 - 3z^3 - 6x^3 + 4yz^2 - 11z^2x$." ], "answer_markdown": [ "$27y^3 - 3z^3 - 6x^3 + 4yz^2 - 11z^2x$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(15*y**3 + z**3 + 4*y*z**2 - 5*z**2*x - 2*x*y**2 - s, 6*x**3 - 12*y**3 + 4*z**3 - 2*x*y**2 + 6*z**2*x)", "answer_expr": "27*y**3 - 3*z**3 - 6*x**3 + 4*y*z**2 - 11*z**2*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(-2*a*b**2 - 5*a*c**2 + 15*b**3 + 4*b*c**2 + c**3 - x, 6*a**3 - 2*a*b**2 + 6*a*c**2 - 12*b**3 + 4*c**3)" ], "shape": [ "solve: Eq(N*a*b**N + N*a*c**N + N*b*c**N + N*b**N + c**N - x, N*a*b**N + N*a*c**N + N*a**N + N*b**N + N*c**N)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/22", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 22", "problem_latex": "How much must be added to $x^3 - 4x^2 + 16x$ to produce $x^3\n+ 64$?", "markdown": "How much must be added to $x^3 - 4x^2 + 16x$ to produce $x^3 + 64$?", "answer_latex": [ "$4x^2 - 16x + 64$." ], "answer_markdown": [ "$4x^2 - 16x + 64$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x**3 - 4*x**2 + 16*x + s, x**3 + 64)", "answer_expr": "4*x**2 - 16*x + 64" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a**3 - 4*a**2 + 16*a + x, a**3 + 64)" ], "shape": [ "solve: Eq(N*a + N*a**N + a**N + x, N + a**N)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/23", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 23", "problem_latex": "To what must $4a^2 - 6b^2 + 8bc - 6ab$ be added to produce\nzero?", "markdown": "To what must $4a^2 - 6b^2 + 8bc - 6ab$ be added to produce zero?", "answer_latex": [ "$-4a^2 + 6b^2 - 8bc + 6ab$." ], "answer_markdown": [ "$-4a^2 + 6b^2 - 8bc + 6ab$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(4*a**2 - 6*b**2 + 8*b*c - 6*a*b + s, 0)", "answer_expr": "-4*a**2 + 6*b**2 - 8*b*c + 6*a*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(4*a**2 - 6*a*b - 6*b**2 + 8*b*c + x, 0)" ], "shape": [ "solve: Eq(N*a*b + N*a**N + N*b*c + N*b**N + x, 0)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/24", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 24", "problem_latex": "From what must $2x^4 - 3x^2 + 2x - 5$ be subtracted to\nproduce unity?", "markdown": "From what must $2x^4 - 3x^2 + 2x - 5$ be subtracted to produce unity?", "answer_latex": [ "$2x^4 - 3x^2 + 2x - 4$." ], "answer_markdown": [ "$2x^4 - 3x^2 + 2x - 4$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(t - (2*x**4 - 3*x**2 + 2*x - 5), 1)", "answer_expr": "2*x**4 - 3*x**2 + 2*x - 4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(-2*a**4 + 3*a**2 - 2*a + x + 5, 1)" ], "shape": [ "solve: Eq(N*a + 2*N*a**N + N + x, 1)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/25", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 25", "problem_latex": "What must be subtracted from the sum of $3a^3 + 7a + 1$ and\n$2a^2 - 5a - 3$ to leave a remainder of $2a^2 - 2a^3 - 4$?", "markdown": "What must be subtracted from the sum of $3a^3 + 7a + 1$ and $2a^2 - 5a - 3$ to leave a remainder of $2a^2 - 2a^3 - 4$?", "answer_latex": [ "$5a^3 + 2a + 2$." ], "answer_markdown": [ "$5a^3 + 2a + 2$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq((3*a**3 + 7*a + 1) + (2*a**2 - 5*a - 3) - s, 2*a**2 - 2*a**3 - 4)", "answer_expr": "5*a**3 + 2*a + 2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*a**3 + 2*a**2 + 2*a - x - 2, -2*a**3 + 2*a**2 - 4)" ], "shape": [ "solve: Eq(N*a + 2*N*a**N + N - x, 2*N*a**N + N)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/26", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 26", "problem_latex": "From the difference between $10a^{2}b + 8ab^{2} - 8a^{2}b^{2} - b^{3}$\nand $5a^{2}b - 6ab^{3} - 7a^{2}b^{2}$ take the sum of $10a^{2}b^{2} + 15ab^{2} +\n8a^{2}b$ and $8a^{2}b - 5ab^{2} + a^{2}b^{2}$.", "markdown": "From the difference between $10a^{2}b + 8ab^{2} - 8a^{2}b^{2} - b^{3}$ and $5a^{2}b - 6ab^{3} - 7a^{2}b^{2}$ take the sum of $10a^{2}b^{2} + 15ab^{2} + 8a^{2}b$ and $8a^{2}b - 5ab^{2} + a^{2}b^{2}$.", "answer_latex": [ "$-11a^2b + 4ab^2 - 12a^2b^2 - b^3$." ], "answer_markdown": [ "$-11a^2b + 4ab^2 - 12a^2b^2 - b^3$." ], "checks": [ { "task": "identity", "verdict": "FLAG-EXTRACTION", "judge_why": "interpreted, and no truncation given to check", "problem_expr": "(10*a**2*b + 8*a*b**2 - 8*a**2*b**2 - b**3) - (5*a**2*b - 6*a*b**3 - 7*a**2*b**2) - ((10*a**2*b**2 + 15*a*b**2 + 8*a**2*b) + (8*a**2*b - 5*a*b**2 + a**2*b**2))", "answer_expr": "-11*a**2*b + 4*a*b**2 - 12*a**2*b**2 - b**3" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "identity: 6*a**3*x - a**3 - 12*a**2*x**2 - 2*a**2*x - 11*a*x**2" ], "shape": [ "identity: N*a*x**N + 2*N*a**N*x + N*a**N*x**N - a**N" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/27", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 27", "problem_latex": "What must be added to $a$ to make $b$?", "markdown": "What must be added to $a$ to make $b$?", "answer_latex": [ "$b - a$." ], "answer_markdown": [ "$b - a$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(a + s, b)", "answer_expr": "b - a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a + x, b)" ], "shape": [ "solve: Eq(a + x, b)" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/28", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 28", "problem_latex": "By how much does $3x - 2$ exceed $2x + 1$?", "markdown": "By how much does $3x - 2$ exceed $2x + 1$?", "answer_latex": [ "$x - 3$." ], "answer_markdown": [ "$x - 3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3*x - 2) - (2*x + 1)", "answer_expr": "x - 3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: x - 3" ], "shape": [ "identity: N + x" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/29", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 29", "problem_latex": "In $y$ years a man will be 40 years old. What is his present\nage?", "markdown": "In $y$ years a man will be 40 years old. What is his present age?", "answer_latex": [ "$40 - y$ yrs." ], "answer_markdown": [ "$40 - y$ yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(p + y, 40)", "answer_expr": "40 - y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a + x, 40)" ], "shape": [ "solve: Eq(a + x, N)" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-7/1" ], "needs": [ "cas.expand", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/3", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 3", "problem_latex": "Subtract $7xy^{3}$ from $-2xy^{3}$.", "markdown": "Subtract $7xy^{3}$ from $-2xy^{3}$.", "answer_latex": [ "$-9xy^3$." ], "answer_markdown": [ "$-9xy^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "-2*x*y**3 - 7*x*y**3", "answer_expr": "-9*x*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -9*a**3*x" ], "shape": [ "identity: N*a**N*x" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/30", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 30", "problem_latex": "How many hours will it take to go 23 miles at $a$ miles an\nhour?", "markdown": "How many hours will it take to go 23 miles at $a$ miles an hour?", "answer_latex": [ "$\\frac{23}{a}$ hrs." ], "answer_markdown": [ "$\\frac{23}{a}$ hrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(h*a, 23)", "answer_expr": "23/a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a*x, 23)" ], "shape": [ "solve: Eq(a*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/4", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 4", "problem_latex": "From $-3x^{m}y$ take $-7x^{m}y$.", "markdown": "From $-3x^{m}y$ take $-7x^{m}y$.", "answer_latex": [ "$4x^my$." ], "answer_markdown": [ "$4x^my$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "-3*x**m*y - (-7*x**m*y)", "answer_expr": "4*x**m*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*b*x**a" ], "shape": [ "identity: N*b*x**a" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/5", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 5", "problem_latex": "Subtract $3ax$ from $8x^{2}$.", "markdown": "Subtract $3ax$ from $8x^{2}$.", "answer_latex": [ "$8x^2 - 3ax$." ], "answer_markdown": [ "$8x^2 - 3ax$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(8*x**2) - (3*a*x)", "answer_expr": "8*x**2 - 3*a*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -3*a*x + 8*x**2" ], "shape": [ "identity: N*a*x + N*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/6", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 6", "problem_latex": "From $5xy$ take $-7by$.", "markdown": "From $5xy$ take $-7by$.", "answer_latex": [ "$5xy + 7by$." ], "answer_markdown": [ "$5xy + 7by$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "5*x*y - (-7*b*y)", "answer_expr": "5*x*y + 7*b*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 7*a*b + 5*b*x" ], "shape": [ "identity: N*a*b + N*b*x" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/7", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 7", "problem_latex": "What is the difference between $4a^{m}$ and $2a^{m}$?", "markdown": "What is the difference between $4a^{m}$ and $2a^{m}$?", "answer_latex": [ "$2a^m$." ], "answer_markdown": [ "$2a^m$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "4*a**m - 2*a**m", "answer_expr": "2*a**m" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*x**a" ], "shape": [ "identity: N*x**a" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/8", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 8", "problem_latex": "From the difference between $5a^{2}x$ and $-3a^{2}x$ take\nthe sum of $2a^{2}x$ and $-3a^{2}x$.", "markdown": "From the difference between $5a^{2}x$ and $-3a^{2}x$ take the sum of $2a^{2}x$ and $-3a^{2}x$.", "answer_latex": [ "$9 ax$." ], "answer_markdown": [ "$9 ax$." ], "checks": [ { "task": "identity", "verdict": "FLAG-INTERPRETED", "judge_why": "interpreted, and no truncation given to check", "problem_expr": "(5*a**2*x - (-3*a**2*x)) - (2*a**2*x + (-3*a**2*x))", "answer_expr": "9*a*x" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "identity: 9*a*x**2" ], "shape": [ "identity: N*a*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-16/9", "set": "boyden-first-book-in-algebra-1895/ex-16", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 16, problem 9", "problem_latex": "From $2a + b + 7c$ take $5a + 2b - 7c$.", "markdown": "From $2a + b + 7c$ take $5a + 2b - 7c$.", "answer_latex": [ "$-3a - b + 14c$." ], "answer_markdown": [ "$-3a - b + 14c$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*a + b + 7*c) - (5*a + 2*b - 7*c)", "answer_expr": "-3*a - b + 14*c" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a + 14*b - 3*x" ], "shape": [ "identity: N*b + N*x - a" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/1", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 1", "problem_latex": "$x + (a + b) + y + (c - d) + (x - y)$.", "markdown": "$x + (a + b) + y + (c - d) + (x - y)$.", "answer_latex": [ "$2x + a + b + c - d$." ], "answer_markdown": [ "$2x + a + b + c - d$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x + (a + b) + y + (c - d) + (x - y)", "answer_expr": "2*x + a + b + c - d" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a + b + c - d + 2*e" ], "shape": [ "identity: N*e + a + b + c - d" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/10", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 10", "problem_latex": "$2 a^2 + 3a^3x-ab^2 + by^2$.", "markdown": "$2 a^2 + 3a^3x-ab^2 + by^2$.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "2*a**2 + 3*a**3*x - a*b**2 + b*y**2", "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:regroup-terms" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/11", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 11", "problem_latex": "$10 m^3 +31m^2-20m-21$.", "markdown": "$10 m^3 +31m^2-20m-21$.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "10*m**3 + 31*m**2 - 20*m - 21", "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:regroup-terms" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/12", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 12", "problem_latex": "$ax^4 - x^3 + 2x - 2ax^2$.", "markdown": "$ax^4 - x^3 + 2x - 2ax^2$.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "a*x**4 - x**3 + 2*x - 2*a*x**2", "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:regroup-terms" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/13", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 13", "problem_latex": "$a^4 + a^3x + a^2x^2 - ax^3- 4x^4$.", "markdown": "$a^4 + a^3x + a^2x^2 - ax^3- 4x^4$.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "a**4 + a**3*x + a**2*x**2 - a*x**3 - 4*x**4", "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:regroup-terms" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/14", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 14", "problem_latex": "$a^4 + a^3-6a^2+a + 3$.", "markdown": "$a^4 + a^3-6a^2+a + 3$.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "a**4 + a**3 - 6*a**2 + a + 3", "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:regroup-terms" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/15", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 15", "problem_latex": "$6a^3 - 17 a^2x + 14 ax^2 - 3x^3$.", "markdown": "$6a^3 - 17 a^2x + 14 ax^2 - 3x^3$.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "6*a**3 - 17*a**2*x + 14*a*x**2 - 3*x**3", "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:regroup-terms" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/16", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 16", "problem_latex": "$ax^3 + 2ax^2 + ax + 2a$.", "markdown": "$ax^3 + 2ax^2 + ax + 2a$.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "a*x**3 + 2*a*x**2 + a*x + 2*a", "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:regroup-terms" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/17", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 17", "problem_latex": "A man pumps $x$ gallons of water into a tank each day, and\ndraws off $y$ gallons each day. How much water will remain in the\ntank at the end of five days?", "markdown": "A man pumps $x$ gallons of water into a tank each day, and draws off $y$ gallons each day. How much water will remain in the tank at the end of five days?", "answer_latex": [ "$5(x - y)$." ], "answer_markdown": [ "$5(x - y)$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "5*(x - y)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/18", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 18", "problem_latex": "Two men are 150 miles apart, and approach each other, one at\nthe rate of $x$ miles an hour, the other at the rate of $y$ miles\nan hour. How far apart will they be at the end of seven hours?", "markdown": "Two men are 150 miles apart, and approach each other, one at the rate of $x$ miles an hour, the other at the rate of $y$ miles an hour. How far apart will they be at the end of seven hours?", "answer_latex": [ "$150 - 7(x + y)$." ], "answer_markdown": [ "$150 - 7(x + y)$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "150 - 7*(x + y)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/19", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 19", "problem_latex": "Eight years ago A was $x$ years old. How old is he now?", "markdown": "Eight years ago A was $x$ years old. How old is he now?", "answer_latex": [ "$x + 8$ yrs." ], "answer_markdown": [ "$x + 8$ yrs." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x + 8" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/2", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 2", "problem_latex": "$a + (b - c) - b + (a + c) + (c - a)$.", "markdown": "$a + (b - c) - b + (a + c) + (c - a)$.", "answer_latex": [ "$a + c$." ], "answer_markdown": [ "$a + c$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "a + (b - c) - b + (a + c) + (c - a)", "answer_expr": "a + c" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a + b" ], "shape": [ "identity: a + b" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/20", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 20", "problem_latex": "A had $x$ dollars, but after giving \\$35 to B he has\none-third as much as B. How much has B?", "markdown": "A had $x$ dollars, but after giving $35 to B he has one-third as much as B. How much has B?", "answer_latex": [ "$3(x - 35)$ dols." ], "answer_markdown": [ "$3(x - 35)$ dols." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "3*(x - 35)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/3", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 3", "problem_latex": "$a^{2}b - (a^{3} + b^{3}) - a^{3} - (ab^{2} - a^{2}b)\n-(b^{3} - a^{3})$.", "markdown": "$a^{2}b - (a^{3} + b^{3}) - a^{3} - (ab^{2} - a^{2}b) -(b^{3} - a^{3})$.", "answer_latex": [ "$2a^2b-a^3-2b^3-ab^2$." ], "answer_markdown": [ "$2a^2b-a^3-2b^3-ab^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2*b - (a**3 + b**3) - a**3 - (a*b**2 - a**2*b) - (b**3 - a**3)", "answer_expr": "2*a**2*b - a**3 - 2*b**3 - a*b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**3 + 2*a**2*b - a*b**2 - 2*b**3" ], "shape": [ "identity: N*a**N*b + N*b**N - a*b**N - a**N" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/4", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 4", "problem_latex": "$xy - (x^{2} + y^{2}) - y^{2} - (x^{2} - 2xy) - (y^{2} -\nx^{2})$.", "markdown": "$xy - (x^{2} + y^{2}) - y^{2} - (x^{2} - 2xy) - (y^{2} - x^{2})$.", "answer_latex": [ "$3xy - x^2 - 3y^2$." ], "answer_markdown": [ "$3xy - x^2 - 3y^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x*y - (x**2 + y**2) - y**2 - (x**2 - 2*x*y) - (y**2 - x**2)", "answer_expr": "3*x*y - x**2 - 3*y**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**2 + 3*a*b - 3*b**2" ], "shape": [ "identity: N*a*b + N*b**N - a**N" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/5", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 5", "problem_latex": "$(a + b - c) - (a - b + c) + (b - a - c) - (c - a - b)$.", "markdown": "$(a + b - c) - (a - b + c) + (b - a - c) - (c - a - b)$.", "answer_latex": [ "$4b - 4c$." ], "answer_markdown": [ "$4b - 4c$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a + b - c) - (a - b + c) + (b - a - c) - (c - a - b)", "answer_expr": "4*b - 4*c" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*a - 4*b" ], "shape": [ "identity: N*a + N*b" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-2/9" ], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/6", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 6", "problem_latex": "$(x - y + z) + (x + y + z) - (y + x + z) - (z + x + y)$.", "markdown": "$(x - y + z) + (x + y + z) - (y + x + z) - (z + x + y)$.", "answer_latex": [ "$-2y$." ], "answer_markdown": [ "$-2y$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - y + z) + (x + y + z) - (y + x + z) - (z + x + y)", "answer_expr": "-2*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -2*a" ], "shape": [ "identity: N*a" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/7", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 7", "problem_latex": "$a - (3b - 2c + a) - (2b - a - c) - (6 - c + a)$.", "markdown": "$a - (3b - 2c + a) - (2b - a - c) - (6 - c + a)$.", "answer_latex": [ "$-6b + 4c$." ], "answer_markdown": [ "$-6b + 4c$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-9.0062582345191040843", "-3.99538866930171278" ], "problem_expr": "a - (3*b - 2*c + a) - (2*b - a - c) - (6 - c + a)", "answer_expr": "-6*b + 4*c" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: -5*a + 4*b - 6" ], "shape": [ "identity: N*a + N*b + N" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/8", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 8", "problem_latex": "$\\frac{1}{2}a - \\frac{1}{2}c - (\\frac{2}{3}b - \\frac{1}{2}c)\n- (a + \\frac{1}{4}c - \\frac{1}{3}b) - (\\frac{2}{3}b - \\frac{1}{4}c\n- \\frac{1}{2}a)$.", "markdown": "$\\frac{1}{2}a - \\frac{1}{2}c - (\\frac{2}{3}b - \\frac{1}{2}c) - (a + \\frac{1}{4}c - \\frac{1}{3}b) - (\\frac{2}{3}b - \\frac{1}{4}c - \\frac{1}{2}a)$.", "answer_latex": [ "$-b$." ], "answer_markdown": [ "$-b$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "Rational(1,2)*a - Rational(1,2)*c - (Rational(2,3)*b - Rational(1,2)*c) - (a + Rational(1,4)*c - Rational(1,3)*b) - (Rational(2,3)*b - Rational(1,4)*c - Rational(1,2)*a)", "answer_expr": "-b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a" ], "shape": [ "identity: -a" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-17/9", "set": "boyden-first-book-in-algebra-1895/ex-17", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 17, problem 9", "problem_latex": "$x - y + 2c - d$.", "markdown": "$x - y + 2c - d$.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "x - y + 2*c - d", "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:regroup-terms" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/1", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 1", "problem_latex": "$5x$ and $7c$.", "markdown": "$5x$ and $7c$.", "answer_latex": [ "$35 cx$." ], "answer_markdown": [ "$35 cx$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "5*x*7*c", "answer_expr": "35*c*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 35*a*b" ], "shape": [ "identity: N*a*b" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/10", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 10", "problem_latex": "$-\\frac{2}{3} a^{2}b^{2}$, $\\frac{1}{4} c^{2}$,\n$-\\frac{6}{5}ac$, and $-\\frac{3}{4} b^{3}c$.", "markdown": "$-\\frac{2}{3} a^{2}b^{2}$, $\\frac{1}{4} c^{2}$, $-\\frac{6}{5}ac$, and $-\\frac{3}{4} b^{3}c$.", "answer_latex": [ "$-\\frac{3}{20}a^3b^5c^4$." ], "answer_markdown": [ "$-\\frac{3}{20}a^3b^5c^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-Rational(2, 3)*a**2*b**2)*(Rational(1, 4)*c**2)*(-Rational(6, 5)*a*c)*(-Rational(3, 4)*b**3*c)", "answer_expr": "-Rational(3, 20)*a**3*b**5*c**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -3*a**3*b**5*c**4/20" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/11", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 11", "problem_latex": "In how many days will $a$ boys eat 100 apples if each boy\neats $b$ apples a day?", "markdown": "In how many days will $a$ boys eat 100 apples if each boy eats $b$ apples a day?", "answer_latex": [ "$\\frac{100}{ab}$." ], "answer_markdown": [ "$\\frac{100}{ab}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "100/(a*b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a*b*x, 100)" ], "shape": [ "solve: Eq(a*b*x, N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/12", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 12", "problem_latex": "How many units in $x$ hundreds?", "markdown": "How many units in $x$ hundreds?", "answer_latex": [ "$100x$." ], "answer_markdown": [ "$100x$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "100*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x, 100*a)" ], "shape": [ "solve: Eq(x, N*a)" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/13", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 13", "problem_latex": "If there are $a$ hundreds, $b$ tens, and $c$ units in a\nnumber, what will represent the whole number of units?", "markdown": "If there are $a$ hundreds, $b$ tens, and $c$ units in a number, what will represent the whole number of units?", "answer_latex": [ "$100a + 10b + c$." ], "answer_markdown": [ "$100a + 10b + c$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "100*a + 10*b + c" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x, 100*a + 10*b + c)" ], "shape": [ "solve: Eq(x, N*a + N*b + c)" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/14", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 14", "problem_latex": "If the difference between two numbers is 7, and one of the\nnumbers is $x$, what is the other number?", "markdown": "If the difference between two numbers is 7, and one of the numbers is $x$, what is the other number?", "answer_latex": [ "$x + 7$ or $x - 7$." ], "answer_markdown": [ "$x + 7$ or $x - 7$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "[x + 7, x - 7]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(Abs(a - x), 7)" ], "shape": [ "solve: Eq(Abs(a - x), N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/2", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 2", "problem_latex": "$51cy$ and $-xa$.", "markdown": "$51cy$ and $-xa$.", "answer_latex": [ "$-51 acxy$." ], "answer_markdown": [ "$-51 acxy$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "51*c*y*(-x*a)", "answer_expr": "-51*a*c*x*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -51*a*b*c*d" ], "shape": [ "identity: N*a*b*c*d" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/3", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 3", "problem_latex": "$3x^{3}y$ and $7axy^{2}$.", "markdown": "$3x^{3}y$ and $7axy^{2}$.", "answer_latex": [ "$21ax^4y^3$." ], "answer_markdown": [ "$21ax^4y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3*x**3*y)*(7*a*x*y**2)", "answer_expr": "21*a*x**4*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 21*a*b**4*c**3" ], "shape": [ "identity: N*a*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/4", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 4", "problem_latex": "$5a^{2}bc$ and $2ab^{2}c^{3}$.", "markdown": "$5a^{2}bc$ and $2ab^{2}c^{3}$.", "answer_latex": [ "$10a^3b^3c^4$." ], "answer_markdown": [ "$10a^3b^3c^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(5*a**2*b*c)*(2*a*b**2*c**3)", "answer_expr": "10*a**3*b**3*c**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 10*a**3*b**3*c**4" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/5", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 5", "problem_latex": "$-3x^{2}y$, $-2ax$, and $3cy^{2}$.", "markdown": "$-3x^{2}y$, $-2ax$, and $3cy^{2}$.", "answer_latex": [ "$18acx^3y^3$." ], "answer_markdown": [ "$18acx^3y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-3*x**2*y)*(-2*a*x)*(3*c*y**2)", "answer_expr": "18*a*c*x**3*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 18*a*b*c**3*d**3" ], "shape": [ "identity: N*a*b*c**N*d**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/6", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 6", "problem_latex": "$5a^{2}$, $-3bc^{3}$, and $-2abc$.", "markdown": "$5a^{2}$, $-3bc^{3}$, and $-2abc$.", "answer_latex": [ "$30a^3b^2c^4$." ], "answer_markdown": [ "$30a^3b^2c^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(5*a**2)*(-3*b*c**3)*(-2*a*b*c)", "answer_expr": "30*a**3*b**2*c**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 30*a**3*b**2*c**4" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/7", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 7", "problem_latex": "$15x^{2}y^{2}$, $-\\frac{2}{3} xz$, and $\\frac{1}{10}\nyz^{2}$.", "markdown": "$15x^{2}y^{2}$, $-\\frac{2}{3} xz$, and $\\frac{1}{10} yz^{2}$.", "answer_latex": [ "$-x^3y^3z^3$." ], "answer_markdown": [ "$-x^3y^3z^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(15*x**2*y**2)*(-Rational(2, 3)*x*z)*(Rational(1, 10)*y*z**2)", "answer_expr": "-x**3*y**3*z**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**3*b**3*c**3" ], "shape": [ "identity: -a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/8", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 8", "problem_latex": "$20a^{3}b^{2}$, $\\frac{2}{5} ab^{2}$, and $-\\frac{1}{8}\nbc^{2}$.", "markdown": "$20a^{3}b^{2}$, $\\frac{2}{5} ab^{2}$, and $-\\frac{1}{8} bc^{2}$.", "answer_latex": [ "$-a^4b^5c^2$." ], "answer_markdown": [ "$-a^4b^5c^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(20*a**3*b**2)*(Rational(2, 5)*a*b**2)*(-Rational(1, 8)*b*c**2)", "answer_expr": "-a**4*b**5*c**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**4*b**5*c**2" ], "shape": [ "identity: -a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-18/9", "set": "boyden-first-book-in-algebra-1895/ex-18", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 18, problem 9", "problem_latex": "$\\frac{1}{2} xy$, $-\\frac{2}{3} cx^{2}$, $-\\frac{2}{5}\na^{2}y$, and $-\\frac{5}{3} x^{2}y^{2}$.", "markdown": "$\\frac{1}{2} xy$, $-\\frac{2}{3} cx^{2}$, $-\\frac{2}{5} a^{2}y$, and $-\\frac{5}{3} x^{2}y^{2}$.", "answer_latex": [ "$-\\frac{2}{9}a^2cx^6y^4$." ], "answer_markdown": [ "$-\\frac{2}{9}a^2cx^6y^4$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-10.509033388361779045", "-22.677387838043838993" ], "problem_expr": "(Rational(1, 2)*x*y)*(-Rational(2, 3)*c*x**2)*(-Rational(2, 5)*a**2*y)*(-Rational(5, 3)*x**2*y**2)", "answer_expr": "-Rational(2, 9)*a**2*c*x**6*y**4" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: -2*a**2*b*c**5*d**4/9" ], "shape": [ "identity: N*a**N*b*c**N*d**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/1", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 1", "problem_latex": "$ x^2 + xy + y^2 \\mbox{by} x^2y^2 $.", "markdown": "$ x^2 + xy + y^2 \\mbox{by} x^2y^2 $.", "answer_latex": [ "$x^4y^2 + x^3y^3 + x^2y^4$." ], "answer_markdown": [ "$x^4y^2 + x^3y^3 + x^2y^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2 + x*y + y**2)*(x**2*y**2)", "answer_expr": "x**4*y**2 + x**3*y**3 + x**2*y**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**2*x**2*(a**2 + a*x + x**2)" ], "shape": [ "identity: a**N*x**N*(a*x + a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/10", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 10", "problem_latex": "$x^4 - x^3 + x^2 - x + 1$ by $2 + 3x + 2x^2 + x^3$.", "markdown": "$x^4 - x^3 + x^2 - x + 1$ by $2 + 3x + 2x^2 + x^3$.", "answer_latex": [ "$x^7 + x^6 + 2x^5 + x^2 + x + 2$." ], "answer_markdown": [ "$x^7 + x^6 + 2x^5 + x^2 + x + 2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**4 - x**3 + x**2 - x + 1)*(2 + 3*x + 2*x**2 + x**3)", "answer_expr": "x**7 + x**6 + 2*x**5 + x**2 + x + 2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**3 + 2*x**2 + 3*x + 2)*(x**4 - x**3 + x**2 - x + 1)" ], "shape": [ "identity: (-x + x**N + 1)*(N*x + N*x**N + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/11", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 11", "problem_latex": "$a^5 - a^4b + a^3b^2 - a^2b^3 + ab^4 - b^5$ by $a + b$.", "markdown": "$a^5 - a^4b + a^3b^2 - a^2b^3 + ab^4 - b^5$ by $a + b$.", "answer_latex": [ "$a^6 + b^6$." ], "answer_markdown": [ "$a^6 + b^6$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-91.792412721006624671", "105.16443769928800826" ], "problem_expr": "(a**5 - a**4*b + a**3*b**2 - a**2*b**3 + a*b**4 - b**5)*(a + b)", "answer_expr": "a**6 + b**6" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (a + x)*(-a**5 + a**4*x - a**3*x**2 + a**2*x**3 - a*x**4 + x**5)" ], "shape": [ "identity: (a + x)*(-a*x**N + a**N*x - a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/12", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 12", "problem_latex": "$x^2 - xy + y^2 - yz + z^2 - xz$ by $x + y + z$.", "markdown": "$x^2 - xy + y^2 - yz + z^2 - xz$ by $x + y + z$.", "answer_latex": [ "$x^3 - 3xyz + y^3 + z^3$." ], "answer_markdown": [ "$x^3 - 3xyz + y^3 + z^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2 - x*y + y**2 - y*z + z**2 - x*z)*(x + y + z)", "answer_expr": "x**3 - 3*x*y*z + y**3 + z**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a + b + x)*(a**2 - a*b - a*x + b**2 - b*x + x**2)" ], "shape": [ "identity: (a + b + x)*(-a*b - a*x + a**N - b*x + b**N + x**N)" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-25/8" ], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/13", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 13", "problem_latex": "$x^6 + x^5y + x^4y^2 + x^3y^3 + x^2y^4 + xy^5 + y^6$ by $x -\ny$.", "markdown": "$x^6 + x^5y + x^4y^2 + x^3y^3 + x^2y^4 + xy^5 + y^6$ by $x - y$.", "answer_latex": [ "$x^7 - y^7$." ], "answer_markdown": [ "$x^7 - y^7$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**6 + x**5*y + x**4*y**2 + x**3*y**3 + x**2*y**4 + x*y**5 + y**6)*(x - y)", "answer_expr": "x**7 - y**7" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a + x)*(a**6 + a**5*x + a**4*x**2 + a**3*x**3 + a**2*x**4 + a*x**5 + x**6)" ], "shape": [ "identity: (-a + x)*(a*x**N + a**N*x + 3*a**N*x**N + a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/14", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 14", "problem_latex": "$x^4 - 4a^2x^2 + 4a^4$ by $x^4 + 4a^2x^2 + 4a^4$.", "markdown": "$x^4 - 4a^2x^2 + 4a^4$ by $x^4 + 4a^2x^2 + 4a^4$.", "answer_latex": [ "$x^8 - 8x^4a^4 + 16a^8$." ], "answer_markdown": [ "$x^8 - 8x^4a^4 + 16a^8$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**4 - 4*a**2*x**2 + 4*a**4)*(x**4 + 4*a**2*x**2 + 4*a**4)", "answer_expr": "x**8 - 8*x**4*a**4 + 16*a**8" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (4*a**4 - 4*a**2*x**2 + x**4)*(4*a**4 + 4*a**2*x**2 + x**4)" ], "shape": [ "identity: (N*a**N*x**N + N*a**N + x**N)**2" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/15", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 15", "problem_latex": "$a^3 - 3a^2y^2 + y^3$ by $a^3 + 3a^2y^2 +y^3$.", "markdown": "$a^3 - 3a^2y^2 + y^3$ by $a^3 + 3a^2y^2 +y^3$.", "answer_latex": [ "$a^6 + 2a^3y^3 - 9a^4y^4 + y^6$." ], "answer_markdown": [ "$a^6 + 2a^3y^3 - 9a^4y^4 + y^6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**3 - 3*a**2*y**2 + y**3)*(a**3 + 3*a**2*y**2 + y**3)", "answer_expr": "a**6 + 2*a**3*y**3 - 9*a**4*y**4 + y**6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3 - 3*a**2*x**2 + x**3)*(a**3 + 3*a**2*x**2 + x**3)" ], "shape": [ "identity: (N*a**N*x**N + a**N + x**N)**2" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/16", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 16", "problem_latex": "$x^4 + 10x + 12 + 9x^2 + 3x^3$ by $-2x + x^2 - 1$.", "markdown": "$x^4 + 10x + 12 + 9x^2 + 3x^3$ by $-2x + x^2 - 1$.", "answer_latex": [ "$x^6 + x^5 + 2x^4 - 11x^3 - 17x^2 - 34x - 12$." ], "answer_markdown": [ "$x^6 + x^5 + 2x^4 - 11x^3 - 17x^2 - 34x - 12$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**4 + 3*x**3 + 9*x**2 + 10*x + 12)*(x**2 - 2*x - 1)", "answer_expr": "x**6 + x**5 + 2*x**4 - 11*x**3 - 17*x**2 - 34*x - 12" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**2 - 2*x - 1)*(x**4 + 3*x**3 + 9*x**2 + 10*x + 12)" ], "shape": [ "identity: (N*x + x**N - 1)*(N*x + 2*N*x**N + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/17", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 17", "problem_latex": "$3x^2 - 2 + x^3 - 3x + 6x^4$ by $-2 + x^2 - 3x$.", "markdown": "$3x^2 - 2 + x^3 - 3x + 6x^4$ by $-2 + x^2 - 3x$.", "answer_latex": [ "$6x^6 - 17x^5 - 12x^4 - 14x^3 + x^2 + 12x + 4$." ], "answer_markdown": [ "$6x^6 - 17x^5 - 12x^4 - 14x^3 + x^2 + 12x + 4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(6*x**4 + x**3 + 3*x**2 - 3*x - 2)*(x**2 - 3*x - 2)", "answer_expr": "6*x**6 - 17*x**5 - 12*x**4 - 14*x**3 + x**2 + 12*x + 4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**2 - 3*x - 2)*(6*x**4 + x**3 + 3*x**2 - 3*x - 2)" ], "shape": [ "identity: (N*x + N + x**N)*(N*x + 2*N*x**N + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/18a", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 18, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 18a", "problem_latex": "If $x$ represent the number of miles a man can row in an\nhour in still water, how far can the man row in 5 hours down a\nstream which flows $y$ miles an hour? How far up the same stream\nin 4 hours?", "markdown": "If $x$ represent the number of miles a man can row in an hour in still water, how far can the man row in 5 hours down a stream which flows $y$ miles an hour? How far up the same stream in 4 hours?", "answer_latex": [ "$5(x + y)$" ], "answer_markdown": [ "$5(x + y)$" ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "5*(x + y)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/18b", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 18, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 18b", "problem_latex": "If $x$ represent the number of miles a man can row in an\nhour in still water, how far can the man row in 5 hours down a\nstream which flows $y$ miles an hour? How far up the same stream\nin 4 hours?", "markdown": "If $x$ represent the number of miles a man can row in an hour in still water, how far can the man row in 5 hours down a stream which flows $y$ miles an hour? How far up the same stream in 4 hours?", "answer_latex": [ "$4(x - y)$" ], "answer_markdown": [ "$4(x - y)$" ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "4*(x - y)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/19", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 19", "problem_latex": "A can reap a field in 7 hours, and B can reap the same field\nin 5 hours. How much of the field can they do in one hour, working\ntogether?", "markdown": "A can reap a field in 7 hours, and B can reap the same field in 5 hours. How much of the field can they do in one hour, working together?", "answer_latex": [ "$\\frac{12}{35}$ of the field." ], "answer_markdown": [ "$\\frac{12}{35}$ of the field." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 0.342857142857, printed 12/35 (half-unit 1.0e-40; correctly rounded at the printed digits: 0.342857142857)", "problem_expr": "Rational(1, 7) + Rational(1, 5)", "answer_expr": null } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 12/35" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": "X#\\frac{12}{35},5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/2", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 2", "problem_latex": "$ a^2 - ab + b^2 \\mbox{by} a^2b $.", "markdown": "$ a^2 - ab + b^2 \\mbox{by} a^2b $.", "answer_latex": [ "$a^4b - a^3b^2 +a^2b^3$." ], "answer_markdown": [ "$a^4b - a^3b^2 +a^2b^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**2 - a*b + b**2)*(a**2*b)", "answer_expr": "a**4*b - a**3*b**2 + a**2*b**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a*x**2*(a**2 - a*x + x**2)" ], "shape": [ "identity: a*x**N*(-a*x + a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/20", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 20", "problem_latex": "A tank can be filled by two pipes in $a$ hours and $b$ hours\nrespectively. What part of the tank will be filled by both pipes\nrunning together for one hour?", "markdown": "A tank can be filled by two pipes in $a$ hours and $b$ hours respectively. What part of the tank will be filled by both pipes running together for one hour?", "answer_latex": [ "$\\frac{1}{a} + \\frac{1}{b}$." ], "answer_markdown": [ "$\\frac{1}{a} + \\frac{1}{b}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "1/a + 1/b" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/3", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 3", "problem_latex": "$ a^3 - 3a^2b + b^3 \\mbox{by} -2ab $.", "markdown": "$ a^3 - 3a^2b + b^3 \\mbox{by} -2ab $.", "answer_latex": [ "$-2a^4b + 6a^3b^2 - 2ab^4$." ], "answer_markdown": [ "$-2a^4b + 6a^3b^2 - 2ab^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**3 - 3*a**2*b + b**3)*(-2*a*b)", "answer_expr": "-2*a**4*b + 6*a**3*b**2 - 2*a*b**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -2*a*x*(a**3 - 3*a*x**2 + x**3)" ], "shape": [ "identity: N*a*x*(N*a*x**N + a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/4", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 4", "problem_latex": "$ 8x^3 + 36x^2y + 27y^3 by 3xy^2 $.", "markdown": "$ 8x^3 + 36x^2y + 27y^3 by 3xy^2 $.", "answer_latex": [ "$24x^4y^2 + 108x^3y^3 + 81xy^5$." ], "answer_markdown": [ "$24x^4y^2 + 108x^3y^3 + 81xy^5$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(8*x**3 + 36*x**2*y + 27*y**3)*(3*x*y**2)", "answer_expr": "24*x**4*y**2 + 108*x**3*y**3 + 81*x*y**5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*a**2*x*(27*a**3 + 36*a*x**2 + 8*x**3)" ], "shape": [ "identity: N*a**N*x*(N*a*x**N + N*a**N + N*x**N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/5", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 5", "problem_latex": "$ \\frac{5}{6}a^4 - \\frac{1}{5}a^3b - \\frac{1}{3}a^2b^2\n\\mbox{by} \\frac{6}{5}ab^2 $.", "markdown": "$ \\frac{5}{6}a^4 - \\frac{1}{5}a^3b - \\frac{1}{3}a^2b^2 \\mbox{by} \\frac{6}{5}ab^2 $.", "answer_latex": [ "$a^5b^2 - \\frac{6}{25}a^4b^3 - \\frac{2}{5}a^3b^4$." ], "answer_markdown": [ "$a^5b^2 - \\frac{6}{25}a^4b^3 - \\frac{2}{5}a^3b^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(5, 6)*a**4 - Rational(1, 5)*a**3*b - Rational(1, 3)*a**2*b**2)*(Rational(6, 5)*a*b**2)", "answer_expr": "a**5*b**2 - Rational(6, 25)*a**4*b**3 - Rational(2, 5)*a**3*b**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 6*a**2*x*(-a**2*x**2/3 - a*x**3/5 + 5*x**4/6)/5" ], "shape": [ "identity: N*a**N*x*(N*a*x**N + N*a**N*x**N + N*x**N)" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/6", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 6", "problem_latex": "$ x^2 - xy + y^2 \\mbox{by} x + y $.", "markdown": "$ x^2 - xy + y^2 \\mbox{by} x + y $.", "answer_latex": [ "$x^3 + y^3$." ], "answer_markdown": [ "$x^3 + y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2 - x*y + y**2)*(x + y)", "answer_expr": "x**3 + y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a + x)*(a**2 - a*x + x**2)" ], "shape": [ "identity: (a + x)*(-a*x + a**N + x**N)" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-22/20" ], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/7", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 7", "problem_latex": "$x^4 - 3x^3 + 2x^2 - x + 1$ by $x-1$.", "markdown": "$x^4 - 3x^3 + 2x^2 - x + 1$ by $x-1$.", "answer_latex": [ "$x^5 - 4x^4 + 5x^3 - 3x^2 + 2x - 1$." ], "answer_markdown": [ "$x^5 - 4x^4 + 5x^3 - 3x^2 + 2x - 1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**4 - 3*x**3 + 2*x**2 - x + 1)*(x - 1)", "answer_expr": "x**5 - 4*x**4 + 5*x**3 - 3*x**2 + 2*x - 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 1)*(x**4 - 3*x**3 + 2*x**2 - x + 1)" ], "shape": [ "identity: (x - 1)*(2*N*x**N - x + x**N + 1)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/8", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 8", "problem_latex": "$x^3 - 2x^2 + x$ by $x^2 + 3x + 1$.", "markdown": "$x^3 - 2x^2 + x$ by $x^2 + 3x + 1$.", "answer_latex": [ "$x^5 + x^4 - 4x^3 + x^2 + x$." ], "answer_markdown": [ "$x^5 + x^4 - 4x^3 + x^2 + x$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**3 - 2*x**2 + x)*(x**2 + 3*x + 1)", "answer_expr": "x**5 + x**4 - 4*x**3 + x**2 + x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**2 + 3*x + 1)*(x**3 - 2*x**2 + x)" ], "shape": [ "identity: (N*x + x**N + 1)*(N*x**N + x + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-19/9", "set": "boyden-first-book-in-algebra-1895/ex-19", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 19, problem 9", "problem_latex": "$xy + mn - xm - yn$ by $xy - mn + xm - yn$.", "markdown": "$xy + mn - xm - yn$ by $xy - mn + xm - yn$.", "answer_latex": [ "$x^2y^2 - 2xy^2n + y^2n^2 - m^2n^2 + 2xm^2n - x^2m^2$." ], "answer_markdown": [ "$x^2y^2 - 2xy^2n + y^2n^2 - m^2n^2 + 2xm^2n - x^2m^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x*y + m*n - x*m - y*n)*(x*y - m*n + x*m - y*n)", "answer_expr": "x**2*y**2 - 2*x*y**2*n + y**2*n**2 - m**2*n**2 + 2*x*m**2*n - x**2*m**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a*b + a*x - b*c + c*x)*(a*b - a*x - b*c + c*x)" ], "shape": [ "identity: (-a*b + a*x - b*c + c*x)*(a*b - a*x - b*c + c*x)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/1", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 1", "problem_latex": "A man bought a hat, a pair of boots, and a necktie\nfor \\$7.50; the hat cost four times as much as the necktie,\nand the boots cost five times as much as the necktie. What\nwas the cost of each?", "markdown": "A man bought a hat, a pair of boots, and a necktie for $7.50; the hat cost four times as much as the necktie, and the boots cost five times as much as the necktie. What was the cost of each?", "answer_latex": [ "Necktie, \\$.75; hat, \\$3; boots, \\$3.75." ], "answer_markdown": [ "Necktie, $.75; hat, $3; boots, $3.75." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{n: 0.75, h: 3, b: 3.75}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 5*c), Eq(b, 4*c), Eq(a + b + c, 15/2))" ], "shape": [ "solve: (Eq(a, N*c), Eq(b, N*c), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/10", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 10", "problem_latex": "There are 120 pigeons in three flocks. In the second\nthere are three times as many as in the first, and in the\nthird as many as in the first and second combined. How\nmany pigeons in each flock?", "markdown": "There are 120 pigeons in three flocks. In the second there are three times as many as in the first, and in the third as many as in the first and second combined. How many pigeons in each flock?", "answer_latex": [ "15; 45; 60 pigeons." ], "answer_markdown": [ "15; 45; 60 pigeons." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{f1: 15, f2: 45, f3: 60}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, 3*a), Eq(c, a + b), Eq(a + b + c, 120))" ], "shape": [ "solve: (Eq(b, N*a), Eq(c, a + b), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/11", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 11", "problem_latex": "Divide 209 into three parts so that the first part\nshall be five times the second, and the second three times\nthe third.", "markdown": "Divide 209 into three parts so that the first part shall be five times the second, and the second three times the third.", "answer_latex": [ "165; 33; 11." ], "answer_markdown": [ "165; 33; 11." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{f: 165, s: 33, t: 11}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 5*b), Eq(b, 3*c), Eq(a + b + c, 209))" ], "shape": [ "solve: (Eq(a, N*b), Eq(b, N*c), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/12", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 12", "problem_latex": "Three men, A, B, and C, earned \\$110; A earned\nfour times as much as B, and C as much as both A and B.\nHow much did each earn?", "markdown": "Three men, A, B, and C, earned $110; A earned four times as much as B, and C as much as both A and B. How much did each earn?", "answer_latex": [ "A, \\$44; B, \\$11; C, \\$55." ], "answer_markdown": [ "A, $44; B, $11; C, $55." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{A: 44, B: 11, C: 55}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 4*b), Eq(c, a + b), Eq(a + b + c, 110))" ], "shape": [ "solve: (Eq(a, N*b), Eq(c, a + b), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/13", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 13", "problem_latex": "A farmer bought a horse, a cow, and a calf for \\$72; the cow\ncost twice as much as the calf, and the horse three times as much\nas the cow. What was the cost of each?", "markdown": "A farmer bought a horse, a cow, and a calf for $72; the cow cost twice as much as the calf, and the horse three times as much as the cow. What was the cost of each?", "answer_latex": [ "Calf, \\$8; cow, \\$16; horse, \\$48." ], "answer_markdown": [ "Calf, $8; cow, $16; horse, $48." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{k: 8, c: 16, h: 48}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*c), Eq(b, 3*a), Eq(a + b + c, 72))" ], "shape": [ "solve: (Eq(a, N*c), Eq(b, N*a), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/14", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 14", "problem_latex": "A cistern, containing 1200 gallons of water, is emptied by\ntwo pipes in two hours. One pipe discharges three times as many\ngallons per hour as the other. How many gallons does each pipe\ndischarge in an hour?", "markdown": "A cistern, containing 1200 gallons of water, is emptied by two pipes in two hours. One pipe discharges three times as many gallons per hour as the other. How many gallons does each pipe discharge in an hour?", "answer_latex": [ "150; 450 gal." ], "answer_markdown": [ "150; 450 gal." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{s: 150, f: 450}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 3*b), Eq(2*a + 2*b, 1200))" ], "shape": [ "solve: (Eq(a, N*b), Eq(N*a + N*b, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/15", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 15", "problem_latex": "A butcher bought a cow and a lamb, paying six times as much\nfor the cow as for the lamb, and the difference of the prices was\n\\$25. How much did he pay for each?", "markdown": "A butcher bought a cow and a lamb, paying six times as much for the cow as for the lamb, and the difference of the prices was $25. How much did he pay for each?", "answer_latex": [ "Cow, \\$30; lamb, \\$5." ], "answer_markdown": [ "Cow, $30; lamb, $5." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{c: 30, l: 5}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 6*b), Eq(a - b, 25))" ], "shape": [ "solve: (Eq(a, N*b), Eq(a - b, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/16", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 16", "problem_latex": "A grocer sold one pound of tea and two pounds of coffee for\n\\$1.50, and the price of the tea per pound was three times that of\nthe coffee. What was the price of each?", "markdown": "A grocer sold one pound of tea and two pounds of coffee for $1.50, and the price of the tea per pound was three times that of the coffee. What was the price of each?", "answer_latex": [ "Tea, 90; coffee, 30." ], "answer_markdown": [ "Tea, 90; coffee, 30." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{t: 90, c: 30}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, 3*a), Eq(2*a + b, 150))" ], "shape": [ "solve: (Eq(b, N*a), Eq(N*a + b, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/17", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 17", "problem_latex": "By will Mrs. Cabot was to receive five times as much as her\nson Henry. If Henry received \\$20,000 less than his mother, how\nmuch did each receive?", "markdown": "By will Mrs. Cabot was to receive five times as much as her son Henry. If Henry received $20,000 less than his mother, how much did each receive?", "answer_latex": [ "Mrs. C, \\$25,000; Henry, \\$5000." ], "answer_markdown": [ "Mrs. C, $25,000; Henry, $5000." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{m: 25000, h: 5000}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b - 20000), Eq(b, 5*a))" ], "shape": [ "solve: (Eq(a, N + b), Eq(b, N*a))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/2", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 2", "problem_latex": "A man traveled 90 miles in three days. If he traveled\ntwice as far the first day as he did the third, and\nthree times as far the second day as the third, how far\ndid he go each day?", "markdown": "A man traveled 90 miles in three days. If he traveled twice as far the first day as he did the third, and three times as far the second day as the third, how far did he go each day?", "answer_latex": [ "30; 45; 15 miles." ], "answer_markdown": [ "30; 45; 15 miles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{d1: 30, d2: 45, d3: 15}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*c), Eq(b, 3*c), Eq(a + b + c, 90))" ], "shape": [ "solve: (Eq(a, N*c), Eq(b, N*c), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/3", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 3", "problem_latex": "James had 30 marbles. He gave a certain number\nto his sister, twice as many to his brother, and had three\ntimes as many left as he gave his sister. How many did\neach then have?", "markdown": "James had 30 marbles. He gave a certain number to his sister, twice as many to his brother, and had three times as many left as he gave his sister. How many did each then have?", "answer_latex": [ "James, 15; sister, 5; brother, 10." ], "answer_markdown": [ "James, 15; sister, 5; brother, 10." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{j: 15, s: 5, b: 10}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*c), Eq(b, 3*c), Eq(a + b + c, 30))" ], "shape": [ "solve: (Eq(a, N*c), Eq(b, N*c), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/4", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 4", "problem_latex": "A farmer bought a horse, cow, and pig for \\$90. If\nhe paid three times as much for the cow as for the pig, and\nfive times as much for the horse as for the pig, what was\nthe price of each?", "markdown": "A farmer bought a horse, cow, and pig for $90. If he paid three times as much for the cow as for the pig, and five times as much for the horse as for the pig, what was the price of each?", "answer_latex": [ "Pig, \\$10; cow, \\$30; horse, \\$50." ], "answer_markdown": [ "Pig, $10; cow, $30; horse, $50." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{p: 10, c: 30, h: 50}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 3*c), Eq(b, 5*c), Eq(a + b + c, 90))" ], "shape": [ "solve: (Eq(a, N*c), Eq(b, N*c), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/5", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 5", "problem_latex": "A had seven times as many apples, and B three times\nas many as C had. If they all together had 55 apples, how\nmany had each?", "markdown": "A had seven times as many apples, and B three times as many as C had. If they all together had 55 apples, how many had each?", "answer_latex": [ "A, 35; B, 15; C, 5." ], "answer_markdown": [ "A, 35; B, 15; C, 5." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 35, b: 15, c: 5}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 7*c), Eq(b, 3*c), Eq(a + b + c, 55))" ], "shape": [ "solve: (Eq(a, N*c), Eq(b, N*c), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/6", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 6", "problem_latex": "The difference between two numbers is 36, and one\nis four times the other. What are the numbers?", "markdown": "The difference between two numbers is 36, and one is four times the other. What are the numbers?", "answer_latex": [ "12; 48." ], "answer_markdown": [ "12; 48." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{s: 12, L: 48}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 4*b), Eq(a - b, 36))" ], "shape": [ "solve: (Eq(a, N*b), Eq(a - b, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/7", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 7", "problem_latex": "In a company of 48 people there is one man to each\nfive women. How many are there of each?", "markdown": "In a company of 48 people there is one man to each five women. How many are there of each?", "answer_latex": [ "8 men; 40 women." ], "answer_markdown": [ "8 men; 40 women." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{m: 8, w: 40}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, 5*a), Eq(a + b, 48))" ], "shape": [ "solve: (Eq(b, N*a), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/8", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 8", "problem_latex": "A man left \\$1400 to be distributed among three\nsons in such a way that James was to receive double\nwhat John received, and John double what Henry received.\nHow much did each receive?", "markdown": "A man left $1400 to be distributed among three sons in such a way that James was to receive double what John received, and John double what Henry received. How much did each receive?", "answer_latex": [ "Henry, \\$200; John, \\$400; James, \\$800." ], "answer_markdown": [ "Henry, $200; John, $400; James, $800." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{h: 200, j: 400, a: 800}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*c), Eq(c, 2*b), Eq(a + b + c, 1400))" ], "shape": [ "solve: (Eq(a, N*c), Eq(c, N*b), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-2/9", "set": "boyden-first-book-in-algebra-1895/ex-2", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 2, problem 9", "problem_latex": "A field containing 45,000 feet was divided into three\nlots so that the second lot was three times the first, and\nthe third twice the second. How large was each lot?", "markdown": "A field containing 45,000 feet was divided into three lots so that the second lot was three times the first, and the third twice the second. How large was each lot?", "answer_latex": [ "4500 ft.; 13,500 ft.; 27,000 ft." ], "answer_markdown": [ "4500 ft.; 13,500 ft.; 27,000 ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 4500, y: 13500, z: 27000}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, 3*a), Eq(c, 2*b), Eq(a + b + c, 45000))" ], "shape": [ "solve: (Eq(b, N*a), Eq(c, N*b), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/1", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 1", "problem_latex": "$(x + 2)(x + 7)$.", "markdown": "$(x + 2)(x + 7)$.", "answer_latex": [ "$x^2 + 9x + 14$." ], "answer_markdown": [ "$x^2 + 9x + 14$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x + 2)*(x + 7)", "answer_expr": "x**2 + 9*x + 14" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x + 2)*(x + 7)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/10", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 10", "problem_latex": "$(x - 13)(x - 1)$.", "markdown": "$(x - 13)(x - 1)$.", "answer_latex": [ "$x^2 - 14x + 13$." ], "answer_markdown": [ "$x^2 - 14x + 13$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - 13)*(x - 1)", "answer_expr": "x**2 - 14*x + 13" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 13)*(x - 1)" ], "shape": [ "identity: (N + x)*(x - 1)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/11", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 11", "problem_latex": "$(y + 7)(y - 9)$.", "markdown": "$(y + 7)(y - 9)$.", "answer_latex": [ "$y^2 - 2y - 63$." ], "answer_markdown": [ "$y^2 - 2y - 63$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(y + 7)*(y - 9)", "answer_expr": "y**2 - 2*y - 63" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 9)*(x + 7)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/12", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 12", "problem_latex": "$(x + 3)(x + 17)$.", "markdown": "$(x + 3)(x + 17)$.", "answer_latex": [ "$x^2 + 20x + 51$." ], "answer_markdown": [ "$x^2 + 20x + 51$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x + 3)*(x + 17)", "answer_expr": "x**2 + 20*x + 51" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x + 3)*(x + 17)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/13", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 13", "problem_latex": "$(y+2)(y-15)$.", "markdown": "$(y+2)(y-15)$.", "answer_latex": [ "$y^2 - 13y - 30$." ], "answer_markdown": [ "$y^2 - 13y - 30$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(y + 2)*(y - 15)", "answer_expr": "y**2 - 13*y - 30" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 15)*(x + 2)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/14", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 14", "problem_latex": "$(y+2)(y+16)$.", "markdown": "$(y+2)(y+16)$.", "answer_latex": [ "$y^2 + 18y + 32$." ], "answer_markdown": [ "$y^2 + 18y + 32$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(y + 2)*(y + 16)", "answer_expr": "y**2 + 18*y + 32" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x + 2)*(x + 16)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/15", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 15", "problem_latex": "$(a^2 + 7)(a^2 - 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\\frac{1}{2})(x - \\frac{1}{4})$.", "markdown": "$(x - \\frac{1}{2})(x - \\frac{1}{4})$.", "answer_latex": [ "$x^2 - \\frac{3}{4}x + \\frac{1}{8}$." ], "answer_markdown": [ "$x^2 - \\frac{3}{4}x + \\frac{1}{8}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - Rational(1, 2))*(x - Rational(1, 4))", "answer_expr": "x**2 - Rational(3, 4)*x + Rational(1, 8)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 1/2)*(x - 1/4)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/2", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 2", "problem_latex": "$(x + 1)(x + 6)$.", "markdown": "$(x + 1)(x + 6)$.", "answer_latex": [ "$x^2 + 7x + 6$." ], "answer_markdown": [ "$x^2 + 7x + 6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x + 1)*(x + 6)", "answer_expr": "x**2 + 7*x + 6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x + 1)*(x + 6)" ], "shape": [ "identity: (N + x)*(x + 1)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/20", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 20", "problem_latex": "$(y + \\frac{1}{3})(y + \\frac{1}{6})$.", "markdown": "$(y + \\frac{1}{3})(y + \\frac{1}{6})$.", "answer_latex": [ "$y^2 + \\frac{1}{2}y + \\frac{1}{18}$." ], "answer_markdown": [ "$y^2 + \\frac{1}{2}y + \\frac{1}{18}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(y + Rational(1, 3))*(y + Rational(1, 6))", "answer_expr": "y**2 + Rational(1, 2)*y + Rational(1, 18)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x + 1/6)*(x + 1/3)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/21", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 21", "problem_latex": "$(m + \\frac{2}{3})(m - \\frac{1}{3})$.", "markdown": "$(m + \\frac{2}{3})(m - \\frac{1}{3})$.", "answer_latex": [ "$m^2 + \\frac{1}{3}m - \\frac{2}{9}$." ], "answer_markdown": [ "$m^2 + \\frac{1}{3}m - \\frac{2}{9}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(m + Rational(2, 3))*(m - Rational(1, 3))", "answer_expr": "m**2 + Rational(1, 3)*m - Rational(2, 9)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 1/3)*(x + 2/3)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/22", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 22", "problem_latex": "$(a - \\frac{2}{5})(a + \\frac{3}{5})$.", "markdown": "$(a - \\frac{2}{5})(a + \\frac{3}{5})$.", "answer_latex": [ "$a^2 + \\frac{1}{5}a - \\frac{6}{25}$." ], "answer_markdown": [ "$a^2 + \\frac{1}{5}a - \\frac{6}{25}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a - Rational(2, 5))*(a + Rational(3, 5))", "answer_expr": "a**2 + Rational(1, 5)*a - Rational(6, 25)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 2/5)*(x + 3/5)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/23", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 23", "problem_latex": "$(x - \\frac{2}{3})(x - \\frac{1}{2})$.", "markdown": "$(x - \\frac{2}{3})(x - \\frac{1}{2})$.", "answer_latex": [ "$x^2 - \\frac{7}{6}x + \\frac{1}{3}$." ], "answer_markdown": [ "$x^2 - \\frac{7}{6}x + \\frac{1}{3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - Rational(2, 3))*(x - Rational(1, 2))", "answer_expr": "x**2 - Rational(7, 6)*x + Rational(1, 3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 2/3)*(x - 1/2)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/24", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 24", "problem_latex": "$(y + \\frac{3}{4})(y + \\frac{1}{5})$.", "markdown": "$(y + \\frac{3}{4})(y + \\frac{1}{5})$.", "answer_latex": [ "$y^2 + \\frac{19}{20}y + \\frac{3}{20}$." ], "answer_markdown": [ "$y^2 + \\frac{19}{20}y + \\frac{3}{20}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(y + Rational(3, 4))*(y + Rational(1, 5))", "answer_expr": "y**2 + Rational(19, 20)*y + Rational(3, 20)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x + 1/5)*(x + 3/4)" ], "shape": [ "identity: (N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-20/25", "set": "boyden-first-book-in-algebra-1895/ex-20", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 20, problem 25", "problem_latex": "$(3-x)(7-x)$.", "markdown": "$(3-x)(7-x)$.", "answer_latex": [ "$21 - 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"PASS" ] }, "form": [ "identity: a**2*b**6*c**4/4" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/12", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 12", "problem_latex": "$(-\\frac{1}{3}ab^3c)^2$.", "markdown": "$(-\\frac{1}{3}ab^3c)^2$.", "answer_latex": [ "$\\frac{1}{9} a^2b^6c^2$." ], "answer_markdown": [ "$\\frac{1}{9} a^2b^6c^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-Rational(1, 3)*a*b**3*c)**2", "answer_expr": "Rational(1, 9)*a**2*b**6*c**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**2*b**6*c**2/9" ], "shape": [ "identity: N*a**N*b**N*c**N" ], 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"$(-x^8yz^3m^2n)^5$.", "answer_latex": [ "$-x^{40}y^5z^{15}m^{10}n^5$." ], "answer_markdown": [ "$-x^{40}y^5z^{15}m^{10}n^5$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-x**8*y*z**3*m**2*n)**5", "answer_expr": "-x**40*y**5*z**15*m**10*n**5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**10*b**5*c**40*d**5*e**15" ], "shape": [ "identity: -a**N*b**N*c**N*d**N*e**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/17", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 17", "problem_latex": "$(-\\frac{2}{3}a^2bc^4)^2$.", "markdown": "$(-\\frac{2}{3}a^2bc^4)^2$.", "answer_latex": [ "$\\frac{4}{9} a^4b^2c^8$." ], "answer_markdown": [ "$\\frac{4}{9} a^4b^2c^8$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-Rational(2, 3)*a**2*b*c**4)**2", "answer_expr": "Rational(4, 9)*a**4*b**2*c**8" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*a**4*b**2*c**8/9" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/18", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 18", "problem_latex": "$(\\frac{5}{6}mn^2x^3)^2$.", "markdown": "$(\\frac{5}{6}mn^2x^3)^2$.", "answer_latex": [ "$\\frac{25}{36} m^2n^4x^6$." ], "answer_markdown": [ "$\\frac{25}{36} m^2n^4x^6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(5, 6)*m*n**2*x**3)**2", "answer_expr": "Rational(25, 36)*m**2*n**4*x**6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 25*a**2*b**4*c**6/36" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/19", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 19", "problem_latex": "In how many days can one man do as much as $b$ men in 8\ndays?", "markdown": "In how many days can one man do as much as $b$ men in 8 days?", "answer_latex": [ "$8 b$ days." ], "answer_markdown": [ "$8 b$ days." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(d, 8*b)", "answer_expr": "{d: 8*b}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x, 8*a)" ], "shape": [ "solve: Eq(x, N*a)" ], "same_problem_in": [], "needs": [ "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/2", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 2", "problem_latex": "$(xy^2)^3$.", "markdown": "$(xy^2)^3$.", "answer_latex": [ "$x^3y^6$." ], "answer_markdown": [ "$x^3y^6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x*y**2)**3", "answer_expr": "x**3*y**6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**3*b**6" ], "shape": [ "identity: a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/20a", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 20, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 20a", "problem_latex": "How many mills in $a$ cents? How many dollars?", "markdown": "How many mills in $a$ cents? How many dollars?", "answer_latex": [ "$10 a$ mills; $\\frac{a}{100}$ dols." ], "answer_markdown": [ "$10 a$ mills; $\\frac{a}{100}$ dols." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "symbolic printed value '10 a' equals 10*a", "problem_expr": "10*a", "answer_expr": "10*a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 10*a" ], "shape": [ "evaluate: N*a" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#10 a,5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/20b", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 20, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 20b", "problem_latex": "How many mills in $a$ cents? How many dollars?", "markdown": "How many mills in $a$ cents? How many dollars?", "answer_latex": [ "$10 a$ mills; $\\frac{a}{100}$ dols." ], "answer_markdown": [ "$10 a$ mills; $\\frac{a}{100}$ dols." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "symbolic printed value '\\\\frac{a}{100}' equals a/100", "problem_expr": "a/100", "answer_expr": "a/100" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: a/100" ], "shape": [ "evaluate: N*a" ], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": "X#\\frac{a}{100},5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/3", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 3", "problem_latex": "$(-a^4b)^2$.", "markdown": "$(-a^4b)^2$.", "answer_latex": [ "$a^8b^2$." ], "answer_markdown": [ "$a^8b^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-a**4*b)**2", "answer_expr": "a**8*b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**8*b**2" ], "shape": [ "identity: a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/4", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 4", "problem_latex": "$(-x^3y^2)^3$.", "markdown": "$(-x^3y^2)^3$.", "answer_latex": [ "$-x^9y^6$." ], "answer_markdown": [ "$-x^9y^6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-x**3*y**2)**3", "answer_expr": "-x**9*y**6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**9*b**6" ], "shape": [ "identity: -a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/5", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 5", "problem_latex": "$(3a^2y)^3$.", "markdown": "$(3a^2y)^3$.", "answer_latex": [ "$27 a^6y^3$." ], "answer_markdown": [ "$27 a^6y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3*a**2*y)**3", "answer_expr": "27*a**6*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 27*a**6*b**3" ], "shape": [ "identity: N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/6", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 6", "problem_latex": "$(-7ab^2c^3)^2$.", "markdown": "$(-7ab^2c^3)^2$.", "answer_latex": [ "$49 a^2b^4c^6$." ], "answer_markdown": [ "$49 a^2b^4c^6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-7*a*b**2*c**3)**2", "answer_expr": "49*a**2*b**4*c**6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 49*a**2*b**4*c**6" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/7", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 7", "problem_latex": "$(xyz^2)^5$.", "markdown": "$(xyz^2)^5$.", "answer_latex": [ "$x^5y^5z^{10}$." ], "answer_markdown": [ "$x^5y^5z^{10}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x*y*z**2)**5", "answer_expr": "x**5*y**5*z**10" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**5*b**5*c**10" ], "shape": [ "identity: a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/8", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 8", "problem_latex": "$(-m^2nd)^4$.", "markdown": "$(-m^2nd)^4$.", "answer_latex": [ "$m^8n^4d^4$." ], "answer_markdown": [ "$m^8n^4d^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-m**2*n*d)**4", "answer_expr": "m**8*n**4*d**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**4*b**8*c**4" ], "shape": [ "identity: a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-21/9", "set": "boyden-first-book-in-algebra-1895/ex-21", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 21, problem 9", "problem_latex": "$(-5x^3y^4z)^3$.", "markdown": "$(-5x^3y^4z)^3$.", "answer_latex": [ "$-125 x^9y^{12}z^3$." ], "answer_markdown": [ "$-125 x^9y^{12}z^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-5*x**3*y**4*z)**3", "answer_expr": "-125*x**9*y**12*z**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -125*a**9*b**12*c**3" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/1", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 1", "problem_latex": "$(z+x)^3$.", "markdown": "$(z+x)^3$.", "answer_latex": [ "$z^3 + 3z^2x + 3zx^2 + x^3$." ], "answer_markdown": [ "$z^3 + 3z^2x + 3zx^2 + x^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(z+x)**3", "answer_expr": "z**3 + 3*z**2*x + 3*z*x**2 + x**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a + b)**3" ], "shape": [ "identity: (a + b)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/10", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 10", "problem_latex": "$(y^2+z^4)^3$.", "markdown": "$(y^2+z^4)^3$.", "answer_latex": [ "$y^6 + 3y^4z^4 + 3y^2z^8 + z^{12}$." ], "answer_markdown": [ "$y^6 + 3y^4z^4 + 3y^2z^8 + z^{12}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(y**2+z**4)**3", "answer_expr": "y**6 + 3*y**4*z**4 + 3*y**2*z**8 + z**12" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 + b**4)**3" ], "shape": [ "identity: (a**N + b**N)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/11", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 11", "problem_latex": "$(x^2y+z)^2$.", "markdown": "$(x^2y+z)^2$.", "answer_latex": [ "$x^4y^2 + 2x^2yz + z^2$." ], "answer_markdown": [ "$x^4y^2 + 2x^2yz + z^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2*y+z)**2", "answer_expr": "x**4*y**2 + 2*x**2*y*z + z**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2*b + c)**2" ], "shape": [ "identity: (a**N*b + c)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/12", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 12", "problem_latex": "$(a^2b-c)^4$.", "markdown": "$(a^2b-c)^4$.", "answer_latex": [ "$a^8b^4 - 4a^6b^3c + 6a^4b^2c^2-4a^2bc^3 + c^4$." ], "answer_markdown": [ "$a^8b^4 - 4a^6b^3c + 6a^4b^2c^2-4a^2bc^3 + c^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**2*b-c)**4", "answer_expr": "a**8*b**4 - 4*a**6*b**3*c + 6*a**4*b**2*c**2 - 4*a**2*b*c**3 + c**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2*b - c)**4" ], "shape": [ "identity: (a**N*b - c)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/13", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 13", "problem_latex": "$(a^2-b^3c)^3$.", "markdown": "$(a^2-b^3c)^3$.", "answer_latex": [ "$a^6 - 3a^4b^3c + 3a^2b^6c^2-b^9c^3$." ], "answer_markdown": [ "$a^6 - 3a^4b^3c + 3a^2b^6c^2-b^9c^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**2-b**3*c)**3", "answer_expr": "a**6 - 3*a**4*b**3*c + 3*a**2*b**6*c**2 - b**9*c**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - b**3*c)**3" ], "shape": [ "identity: (a**N - b**N*c)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/14", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 14", "problem_latex": "$(x^2y-mn^3)^2$.", "markdown": "$(x^2y-mn^3)^2$.", "answer_latex": [ "$x^4y^2 - 2x^2ymn^3 + m^2n^6$." ], "answer_markdown": [ "$x^4y^2 - 2x^2ymn^3 + m^2n^6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2*y-m*n**3)**2", "answer_expr": "x**4*y**2 - 2*x**2*y*m*n**3 + m**2*n**6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a*b**3 + c**2*d)**2" ], "shape": [ "identity: (-a*b**N + c**N*d)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/15", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 15", "problem_latex": "$(x+1)^3$.", "markdown": "$(x+1)^3$.", "answer_latex": [ "$x^3 + 3x^2 + 3x + 1$." ], "answer_markdown": [ "$x^3 + 3x^2 + 3x + 1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x+1)**3", "answer_expr": "x**3 + 3*x**2 + 3*x + 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a + 1)**3" ], "shape": [ "identity: (a + 1)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/16", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 16", "problem_latex": "$(m-1)^2$.", "markdown": "$(m-1)^2$.", "answer_latex": [ "$m^2 - 2m + 1$." ], "answer_markdown": [ "$m^2 - 2m + 1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(m-1)**2", "answer_expr": "m**2 - 2*m + 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a - 1)**2" ], "shape": [ "identity: (a - 1)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/17", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 17", "problem_latex": "$(b^2-1)^4$.", "markdown": "$(b^2-1)^4$.", "answer_latex": [ "$b^8 - 4b^6 + 6b^4 - 4b^2 + 1$." ], "answer_markdown": [ "$b^8 - 4b^6 + 6b^4 - 4b^2 + 1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(b**2-1)**4", "answer_expr": "b**8 - 4*b**6 + 6*b**4 - 4*b**2 + 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - 1)**4" ], "shape": [ "identity: (a**N - 1)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/18", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 18", "problem_latex": "$(y^3+1)^3$.", "markdown": "$(y^3+1)^3$.", "answer_latex": [ "$y^9 + 3y^6 + 3y^3 + 1$." ], "answer_markdown": [ "$y^9 + 3y^6 + 3y^3 + 1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(y**3+1)**3", "answer_expr": "y**9 + 3*y**6 + 3*y**3 + 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3 + 1)**3" ], "shape": [ "identity: (a**N + 1)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/19", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 19", "problem_latex": "$(ab-2)^2$.", "markdown": "$(ab-2)^2$.", "answer_latex": [ "$a^2b^2 - 4ab + 4$." ], "answer_markdown": [ "$a^2b^2 - 4ab + 4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a*b-2)**2", "answer_expr": "a**2*b**2 - 4*a*b + 4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a*b - 2)**2" ], "shape": [ "identity: (N + a*b)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/2", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 2", "problem_latex": "$(a+y)^4$.", "markdown": "$(a+y)^4$.", "answer_latex": [ "$a^4 + 4a^3y + 6a^2y^2 + 4ay^3 + y^4$." ], "answer_markdown": [ "$a^4 + 4a^3y + 6a^2y^2 + 4ay^3 + y^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a+y)**4", "answer_expr": "a**4 + 4*a**3*y + 6*a**2*y**2 + 4*a*y**3 + y**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a + b)**4" ], "shape": [ "identity: (a + b)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/20", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 20", "problem_latex": "$(x^2y-3)^2$.", "markdown": "$(x^2y-3)^2$.", "answer_latex": [ "$x^4y^2 - 6x^2y + 9$." ], "answer_markdown": [ "$x^4y^2 - 6x^2y + 9$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2*y-3)**2", "answer_expr": "x**4*y**2 - 6*x**2*y + 9" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2*b - 3)**2" ], "shape": [ "identity: (N + a**N*b)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/21", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 21", "problem_latex": "$(1-x)^4$.", "markdown": "$(1-x)^4$.", "answer_latex": [ "$1 - 4x + 6x^2 - 4x^3 + x^4$." ], "answer_markdown": [ "$1 - 4x + 6x^2 - 4x^3 + x^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1-x)**4", "answer_expr": "1 - 4*x + 6*x**2 - 4*x**3 + x**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a + 1)**4" ], "shape": [ "identity: (-a + 1)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/22", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 22", "problem_latex": "$(1-y^2)^3$.", "markdown": "$(1-y^2)^3$.", "answer_latex": [ "$1 - 3y^2 + 3y^4 - y^6$." ], "answer_markdown": [ "$1 - 3y^2 + 3y^4 - y^6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1-y**2)**3", "answer_expr": "1 - 3*y**2 + 3*y**4 - y**6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a**2 + 1)**3" ], "shape": [ "identity: (-a**N + 1)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/23", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 23", "problem_latex": "$(2x+3y^2)^2$.", "markdown": "$(2x+3y^2)^2$.", "answer_latex": [ "$4x^2 + 12xy^2 + 9y^4$." ], "answer_markdown": [ "$4x^2 + 12xy^2 + 9y^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*x+3*y**2)**2", "answer_expr": "4*x**2 + 12*x*y**2 + 9*y**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a + 3*b**2)**2" ], "shape": [ "identity: (N*a + N*b**N)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/24", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 24", "problem_latex": "$(3ab-x^2y)^3$.", "markdown": "$(3ab-x^2y)^3$.", "answer_latex": [ "$27a^3b^3 - 27a^2b^2x^2y + 9abx^4y^2 - x^6y^3$." ], "answer_markdown": [ "$27a^3b^3 - 27a^2b^2x^2y + 9abx^4y^2 - x^6y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3*a*b-x**2*y)**3", "answer_expr": "27*a**3*b**3 - 27*a**2*b**2*x**2*y + 9*a*b*x**4*y**2 - x**6*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (3*a*b - c**2*d)**3" ], "shape": [ "identity: (N*a*b - c**N*d)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/25", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 25", "problem_latex": "$(4mn^3-3a^2b)^4$.", "markdown": "$(4mn^3-3a^2b)^4$.", "answer_latex": [ "$256m^4n^{12} - 768m^3n^9a^2b + 864m^2n^6a^4b^2\n - 432mn^3a^6b^3 + 81a^8b^4$." ], "answer_markdown": [ "$256m^4n^{12} - 768m^3n^9a^2b + 864m^2n^6a^4b^2 - 432mn^3a^6b^3 + 81a^8b^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*m*n**3-3*a**2*b)**4", "answer_expr": "256*m**4*n**12 - 768*m**3*n**9*a**2*b + 864*m**2*n**6*a**4*b**2 - 432*m*n**3*a**6*b**3 + 81*a**8*b**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-3*a**2*b + 4*c*d**3)**4" ], "shape": [ "identity: (N*a**N*b + N*c*d**N)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/26", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 26", "problem_latex": "$(\\frac{1}{2}x-y)^2$.", "markdown": "$(\\frac{1}{2}x-y)^2$.", "answer_latex": [ "$\\frac{1}{4}x^2 - xy + y^2$." ], "answer_markdown": [ "$\\frac{1}{4}x^2 - xy + y^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1/2*x-y)**2", "answer_expr": "Rational(1,4)*x**2 - x*y + y**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/2 - b)**2" ], "shape": [ "identity: (N*a - b)**N" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/27", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 27", "problem_latex": "$(1-\\frac{1}{3}x^2)^3$.", "markdown": "$(1-\\frac{1}{3}x^2)^3$.", "answer_latex": [ "$1 - x^2 + \\frac{1}{3}x^4 - \\frac{1}{27}x^6$." ], "answer_markdown": [ "$1 - x^2 + \\frac{1}{3}x^4 - \\frac{1}{27}x^6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1-Rational(1,3)*x**2)**3", "answer_expr": "1 - x**2 + Rational(1,3)*x**4 - Rational(1,27)*x**6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a**2/3 + 1)**3" ], "shape": [ "identity: (N*a**N + 1)**N" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/28", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 28", "problem_latex": "$(x^2-3)^4$.", "markdown": "$(x^2-3)^4$.", "answer_latex": [ "$x^8 - 12x^6 + 54x^4 - 108x^2 + 81$." ], "answer_markdown": [ "$x^8 - 12x^6 + 54x^4 - 108x^2 + 81$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2-3)**4", "answer_expr": "x**8 - 12*x**6 + 54*x**4 - 108*x**2 + 81" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - 3)**4" ], "shape": [ "identity: (N + a**N)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/29", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 29", "problem_latex": "John has $4a$ horses, James has $a$ times as many as John,\nand Charles has $d$ less than five times as many as James. How\nmany has Charles?", "markdown": "John has $4a$ horses, James has $a$ times as many as John, and Charles has $d$ less than five times as many as James. How many has Charles?", "answer_latex": [ "$20a^2 - d$ horses." ], "answer_markdown": [ "$20a^2 - d$ horses." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(C, 5*(a*(4*a)) - d)", "answer_expr": "{C: 20*a**2 - d}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(x, 5*b - d), Eq(a, 4*c), Eq(b, a*c))", "solve: Eq(x, 20*a**2 - b)" ], "shape": [ "solve: (Eq(x, N*b - d), Eq(a, N*c), Eq(b, a*c))", "solve: Eq(x, N*a**N - b)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/3", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 3", "problem_latex": "$(x-a)^4$.", "markdown": "$(x-a)^4$.", "answer_latex": [ "$x^4 - 4x^3a + 6x^2a^2 - 4xa^3 + a^4$." ], "answer_markdown": [ "$x^4 - 4x^3a + 6x^2a^2 - 4xa^3 + a^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x-a)**4", "answer_expr": "x**4 - 4*x**3*a + 6*x**2*a**2 - 4*x*a**3 + a**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a + b)**4" ], "shape": [ "identity: (-a + b)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/30", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 30", "problem_latex": "A man bought $a$ pounds of meat at $a$ cents a pound, and\nhanded the butcher an $x$-dollar bill. How many cents in change\nshould he receive?", "markdown": "A man bought $a$ pounds of meat at $a$ cents a pound, and handed the butcher an $x$-dollar bill. How many cents in change should he receive?", "answer_latex": [ "$100x - a^2$ cts." ], "answer_markdown": [ "$100x - a^2$ cts." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{M: a**2, B: 100*x, C: 100*x - a**2}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a, 100*d), Eq(x, a - b), Eq(b, c**2))" ], "shape": [ "solve: (Eq(a, N*d), Eq(x, a - b), Eq(b, c**N))" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.eqn", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/31", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 31, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 31", "problem_latex": "A grocer, having 25 bags of meal worth $a$ cents a bag, sold\n$x$ bags. What is the value of the meal left?", "markdown": "A grocer, having 25 bags of meal worth $a$ cents a bag, sold $x$ bags. What is the value of the meal left?", "answer_latex": [ "$a(25 - x)$ cts." ], "answer_markdown": [ "$a(25 - x)$ cts." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{V: a*(25 - x)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a, -c + 25), Eq(x, a*b))", "solve: Eq(x, a*(-b + 25))" ], "shape": [ "solve: (Eq(a, N - c), Eq(x, a*b))", "solve: Eq(x, a*(N - b))" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/32", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 32, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 32", "problem_latex": "If $a = 5$, $x\n= 4$, $y = 3$, find the numerical value of\n\\[\n\\frac{7a}{11x-3y} + \\frac{11x}{8x-7y} - \\frac{10y}{7a-5x}.\n\\]", "markdown": "If $a = 5$, $x = 4$, $y = 3$, find the numerical value of 7a11x-3y + 11x8x-7y - 10y7a-5x.", "answer_latex": [ "$3$." ], "answer_markdown": [ "$3$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 3.0, printed 3 (half-unit 0.5; correctly rounded at the printed digits: 3.0)", "problem_expr": "7*a/(11*x-3*y) + 11*x/(8*x-7*y) - 10*y/(7*a-5*x)", "answer_expr": "3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 7*a/(11*b - 3*c) + 11*b/(8*b - 7*c) - 10*c/(7*a - 5*b) at a=5, x=4, y=3" ], "shape": [ "evaluate: N*a/(N*b + N*c) + N*b/(N*b + N*c) + N*c/(N*a + N*b)" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": "X#3,5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/33", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 33, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 33", "problem_latex": "Find the value of\n\\[\na^2b - c^2d - (ab+cd)(ac-bd) - bc(a^2c-bd^2)\n\\]\nwhen $a = 2$, $b = 3$, $c = 4$, and $d = 0$.", "markdown": "Find the value of a^2b - c^2d - (ab+cd)(ac-bd) - bc(a^2c-bd^2) when $a = 2$, $b = 3$, $c = 4$, and $d = 0$.", "answer_latex": [ "$-228$." ], "answer_markdown": [ "$-228$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed -228.0, printed -228 (half-unit 0.5; correctly rounded at the printed digits: -228.0)", "problem_expr": "a**2*b - c**2*d - (a*b+c*d)*(a*c-b*d) - b*c*(a**2*c-b*d**2)", "answer_expr": "-228" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: a**2*b - b*c*(a**2*c - b*d**2) - c**2*d - (a*b + c*d)*(a*c - b*d) at a=2, b=3, c=4, d=0" ], "shape": [ "evaluate: a**N*b - b*c*(a**N*c - b*d**N) - c**N*d - (a*b + c*d)*(a*c - b*d)" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#-228,5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/4", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 4", "problem_latex": "$(a-m)^3$.", "markdown": "$(a-m)^3$.", "answer_latex": [ "$a^3 - 3a^2m + 3am^2 - m^3$." ], "answer_markdown": [ "$a^3 - 3a^2m + 3am^2 - m^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a-m)**3", "answer_expr": "a**3 - 3*a**2*m + 3*a*m**2 - m**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a - b)**3" ], "shape": [ "identity: (a - b)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/5", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 5", "problem_latex": "$(m+a)^2$.", "markdown": "$(m+a)^2$.", "answer_latex": [ "$m^2 + 2am + a^2$." ], "answer_markdown": [ "$m^2 + 2am + a^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(m+a)**2", "answer_expr": "m**2 + 2*a*m + a**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a + b)**2" ], "shape": [ "identity: (a + b)**N" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-26/1" ], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/6", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 6", "problem_latex": "$(x-y)^2$.", "markdown": "$(x-y)^2$.", "answer_latex": [ "$x^2 - 2xy + y^2$." ], "answer_markdown": [ "$x^2 - 2xy + y^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x-y)**2", "answer_expr": "x**2 - 2*x*y + y**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a - b)**2" ], "shape": [ "identity: (a - b)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/7", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 7", "problem_latex": "$(x^2+y^2)^3$.", "markdown": "$(x^2+y^2)^3$.", "answer_latex": [ "$x^6 + 3x^4y^2 + 3x^2y^4 + y^6$." ], "answer_markdown": [ "$x^6 + 3x^4y^2 + 3x^2y^4 + y^6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2+y**2)**3", "answer_expr": "x**6 + 3*x**4*y**2 + 3*x**2*y**4 + y**6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 + b**2)**3" ], "shape": [ "identity: (a**N + b**N)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/8", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 8", "problem_latex": "$(m^3-y^2)^2$.", "markdown": "$(m^3-y^2)^2$.", "answer_latex": [ "$m^6 - 2m^3y^2 + y^4$." ], "answer_markdown": [ "$m^6 - 2m^3y^2 + y^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(m**3-y**2)**2", "answer_expr": "m**6 - 2*m**3*y**2 + y**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3 - b**2)**2" ], "shape": [ "identity: (a**N - b**N)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-22/9", "set": "boyden-first-book-in-algebra-1895/ex-22", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 22, problem 9", "problem_latex": "$(c^2-d^2)^4$.", "markdown": "$(c^2-d^2)^4$.", "answer_latex": [ "$c^8 - 4c^6d^2 + 6c^4d^4 - 4c^2d^6 + d^8$." ], "answer_markdown": [ "$c^8 - 4c^6d^2 + 6c^4d^4 - 4c^2d^6 + d^8$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(c**2-d**2)**4", "answer_expr": "c**8 - 4*c**6*d**2 + 6*c**4*d**4 - 4*c**2*d**6 + d**8" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - b**2)**4" ], "shape": [ "identity: (a**N - b**N)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/1", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 1", "problem_latex": "Take the sum of $x^3 + 3x - 2$, $2x^3 + x^2 - x + 5$, and\n$4x^3 + 2x^2 - 7x + 4$ from the sum of $2x^3 + 9x$ and $5x^3 +\n3x^2$.", "markdown": "Take the sum of $x^3 + 3x - 2$, $2x^3 + x^2 - x + 5$, and $4x^3 + 2x^2 - 7x + 4$ from the sum of $2x^3 + 9x$ and $5x^3 + 3x^2$.", "answer_latex": [ "$14x - 7$." ], "answer_markdown": [ "$14x - 7$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*x**3 + 9*x) + (5*x**3 + 3*x**2) - ((x**3 + 3*x - 2) + (2*x**3 + x**2 - x + 5) + (4*x**3 + 2*x**2 - 7*x + 4))", "answer_expr": "14*x - 7" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 14*x - 7" ], "shape": [ "identity: N*x + N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/10", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 10", "problem_latex": "Simplify $(x-2)(x+7) + (x-8)(x-5)$.", "markdown": "Simplify $(x-2)(x+7) + (x-8)(x-5)$.", "answer_latex": [ "$2x^2 - 8x + 26$." ], "answer_markdown": [ "$2x^2 - 8x + 26$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - 2)*(x + 7) + (x - 8)*(x - 5)", "answer_expr": "2*x**2 - 8*x + 26" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 8)*(x - 5) + (x - 2)*(x + 7)" ], "shape": [ "identity: 2*(N + x)**2" ], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/11", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 11", "problem_latex": "Expand $(2a^2b-3xy)^3$.", "markdown": "Expand $(2a^2b-3xy)^3$.", "answer_latex": [ "$8a^6 b^3 - 36a^4 b^2 xy + 54a^2 bx^2 y^2 - 27x^3 y^3$." ], "answer_markdown": [ "$8a^6 b^3 - 36a^4 b^2 xy + 54a^2 bx^2 y^2 - 27x^3 y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*a**2*b - 3*x*y)**3", "answer_expr": "8*a**6*b**3 - 36*a**4*b**2*x*y + 54*a**2*b*x**2*y**2 - 27*x**3*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a*x**2 - 3*b*c)**3" ], "shape": [ "identity: (N*a*x**N + N*b*c)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/12", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 12", "problem_latex": "What must be subtracted from $x^3-3x^2+2y-5$ to produce\nunity?", "markdown": "What must be subtracted from $x^3-3x^2+2y-5$ to produce unity?", "answer_latex": [ "$x^3 - 3x^2 + 2y - 6$." ], "answer_markdown": [ "$x^3 - 3x^2 + 2y - 6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x**3 - 3*x**2 + 2*y - 5 - 1", "answer_expr": "x**3 - 3*x**2 + 2*y - 6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a + x**3 - 3*x**2 - 6" ], "shape": [ "identity: N*a + N*x**N + N + x**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/13", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 13", "problem_latex": "Multiply $x^3+ 3x^2y+3xy^2 + y^3$ by $3xy^2 -\n y^3-3x^2y+x^3$.", "markdown": "Multiply $x^3+ 3x^2y+3xy^2 + y^3$ by $3xy^2 - y^3-3x^2y+x^3$.", "answer_latex": [ "$x^6 - 3x^4 y^2 + 3x^2 y^4 - y^6$." ], "answer_markdown": [ "$x^6 - 3x^4 y^2 + 3x^2 y^4 - y^6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**3 + 3*x**2*y + 3*x*y**2 + y**3)*(3*x*y**2 - y**3 - 3*x**2*y + x**3)", "answer_expr": "x**6 - 3*x**4*y**2 + 3*x**2*y**4 - y**6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a**3 + 3*a**2*x - 3*a*x**2 + x**3)*(a**3 + 3*a**2*x + 3*a*x**2 + x**3)" ], "shape": [ "identity: (N*a*x**N + N*a**N*x - a**N + x**N)*(N*a*x**N + N*a**N*x + a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/14", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 14", "problem_latex": "Expand $(x+1)(x-1)(x^2+1)$.", "markdown": "Expand $(x+1)(x-1)(x^2+1)$.", "answer_latex": [ "$x^4 - 1$." ], "answer_markdown": [ "$x^4 - 1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x + 1)*(x - 1)*(x**2 + 1)", "answer_expr": "x**4 - 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 1)*(x + 1)*(x**2 + 1)" ], "shape": [ "identity: (x - 1)*(x + 1)*(x**N + 1)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/15", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 15", "problem_latex": "Add $4xy^3-4y^4$, $4x^3y-12x^2y^2+12xy^3-4y^4$,\n$6x^2y^2-12xy^3+6y^4$ and $x^4-4x^3y+6x^2y^2-4xy^3+y^4$.", "markdown": "Add $4xy^3-4y^4$, $4x^3y-12x^2y^2+12xy^3-4y^4$, $6x^2y^2-12xy^3+6y^4$ and $x^4-4x^3y+6x^2y^2-4xy^3+y^4$.", "answer_latex": [ "$x^4 - y^4$." ], "answer_markdown": [ "$x^4 - y^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*x*y**3 - 4*y**4) + (4*x**3*y - 12*x**2*y**2 + 12*x*y**3 - 4*y**4) + (6*x**2*y**2 - 12*x*y**3 + 6*y**4) + (x**4 - 4*x**3*y + 6*x**2*y**2 - 4*x*y**3 + y**4)", "answer_expr": "x**4 - y**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**4 + x**4" ], "shape": [ "identity: -a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/16", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 16", "problem_latex": "A man weighs 36 pounds more than his wife, and the sum of\ntheir weights is 317 pounds. What is the weight of each?", "markdown": "A man weighs 36 pounds more than his wife, and the sum of their weights is 317 pounds. What is the weight of each?", "answer_latex": [ "$176\\frac{1}{2}$ lbs.; $140\\frac{1}{2}$ lbs." ], "answer_markdown": [ "$176\\frac{1}{2}$ lbs.; $140\\frac{1}{2}$ lbs." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{m: 353/2, w: 281/2}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(x, a + 36), Eq(a + x, 317))" ], "shape": [ "solve: (Eq(x, N + a), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/17", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 17", "problem_latex": "A watch and chain cost \\$350. What was the cost of each, if\nthe chain cost $\\frac{3}{4}$ as much as the watch?", "markdown": "A watch and chain cost $350. What was the cost of each, if the chain cost $\\frac{3}{4}$ as much as the watch?", "answer_latex": [ "watch, \\$200; chain, \\$150." ], "answer_markdown": [ "watch, $200; chain, $150." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{w: 200, c: 150}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a, 3*x/4), Eq(a + x, 350))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/18", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 18", "problem_latex": "Simplify $3x^2-2x+1-(x^2+2x+3)-(2x^2-6x-6)$.", "markdown": "Simplify $3x^2-2x+1-(x^2+2x+3)-(2x^2-6x-6)$.", "answer_latex": [ "$2x + 4$." ], "answer_markdown": [ "$2x + 4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "3*x**2 - 2*x + 1 - (x**2 + 2*x + 3) - (2*x**2 - 6*x - 6)", "answer_expr": "2*x + 4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*x + 4" ], "shape": [ "identity: N*x + N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/19", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 19", "problem_latex": "Simplify $(a + 2y)^2-(a-2y)^2$", "markdown": "Simplify $(a + 2y)^2-(a-2y)^2$", "answer_latex": [ "$8\\,ay$." ], "answer_markdown": [ "$8\\,ay$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a + 2*y)**2 - (a - 2*y)**2", "answer_expr": "8*a*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -(-2*a + x)**2 + (2*a + x)**2" ], "shape": [ "identity: 0" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/2", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 2", "problem_latex": "Multiply $b^4 - 2b^2$ by $b^4 + 2b^2 - 1$.", "markdown": "Multiply $b^4 - 2b^2$ by $b^4 + 2b^2 - 1$.", "answer_latex": [ "$b^8 - 2b^4 + 1$." ], "answer_markdown": [ "$b^8 - 2b^4 + 1$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-1.5078490076120942831", "0.051767081255093216896" ], "problem_expr": "(b**4 - 2*b**2)*(b**4 + 2*b**2 - 1)", "answer_expr": "b**8 - 2*b**4 + 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (x**4 - 2*x**2)*(x**4 + 2*x**2 - 1)" ], "shape": [ "identity: (N*x**N + x**N)*(N*x**N + x**N - 1)" ], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/20", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 20", "problem_latex": "What is the value of $1 + \\frac{1}{2}a + \\frac{1}{3}b$ times\n$1- \\frac{1}{2}a + \\frac{1}{3}b$ ?", "markdown": "What is the value of $1 + \\frac{1}{2}a + \\frac{1}{3}b$ times $1- \\frac{1}{2}a + \\frac{1}{3}b$ ?", "answer_latex": [ "$1 + \\frac{2}{3} b + \\frac{1}{9} b^2 - \\frac{1}{4} a^2$." ], "answer_markdown": [ "$1 + \\frac{2}{3} b + \\frac{1}{9} b^2 - \\frac{1}{4} a^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1 + Rational(1,2)*a + Rational(1,3)*b)*(1 - Rational(1,2)*a + Rational(1,3)*b)", "answer_expr": "1 + Rational(2,3)*b + Rational(1,9)*b**2 - Rational(1,4)*a**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/3 - x/2 + 1)*(a/3 + x/2 + 1)" ], "shape": [ "identity: (N*a + N*x + 1)**2" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/3", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 3", "problem_latex": "Simplify $11x^2 + 4y^2 - (2xy - 3y^2) + (2x^2 - 3xy) - (3x^2\n- 5xy)$.", "markdown": "Simplify $11x^2 + 4y^2 - (2xy - 3y^2) + (2x^2 - 3xy) - (3x^2 - 5xy)$.", "answer_latex": [ "$10x^2 + 7y^2$." ], "answer_markdown": [ "$10x^2 + 7y^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "11*x**2 + 4*y**2 - (2*x*y - 3*y**2) + (2*x**2 - 3*x*y) - (3*x**2 - 5*x*y)", "answer_expr": "10*x**2 + 7*y**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 7*a**2 + 10*x**2" ], "shape": [ "identity: N*a**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/4", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 4", "problem_latex": "Divide $\\$300$ among $A$, $B$, and $C$, so that $A$ shall\nhave twice as much as $B$, and $B$ $\\$20$ more than $C$.", "markdown": "Divide $\\$300$ among $A$, $B$, and $C$, so that $A$ shall have twice as much as $B$, and $B$ $$20$ more than $C$.", "answer_latex": [ "\\$160; \\$80; \\$60." ], "answer_markdown": [ "$160; $80; $60." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{A: 160, B: 80, C: 60}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(x, 2*a), Eq(a, b + 20), Eq(a + b + x, 300))" ], "shape": [ "solve: (Eq(x, N*a), Eq(a, N + b), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/5", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 5", "problem_latex": "Find two numbers differing by $8$ such that four times the\nless may exceed twice the greater by $10$.", "markdown": "Find two numbers differing by $8$ such that four times the less may exceed twice the greater by $10$.", "answer_latex": [ "13; 21." ], "answer_markdown": [ "13; 21." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 13, y: 21}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(4*x, 2*a + 10), Eq(a, x + 8))" ], "shape": [ "solve: (Eq(N*x, N*a + N), Eq(a, N + x))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/6", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 6", "problem_latex": "What must be added to $3a^3 - 4a^2 - 4$ to produce $5a^3 +\n6$?", "markdown": "What must be added to $3a^3 - 4a^2 - 4$ to produce $5a^3 + 6$?", "answer_latex": [ "$2a^3 + 4a^2 + 10$." ], "answer_markdown": [ "$2a^3 + 4a^2 + 10$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "5*a**3 + 6 - (3*a**3 - 4*a**2 - 4)", "answer_expr": "2*a**3 + 4*a**2 + 10" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*x**3 + 4*x**2 + 10" ], "shape": [ "identity: 2*N*x**N + N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/7", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 7", "problem_latex": "Add $\\frac{2}{3}a^2 - ab - \\frac{5}{4}b^2$, $\\frac{2}{3}a^2\n+ \\frac{1}{3}ab - \\frac{1}{4}b^2$, and $-a^2 -\\frac{2}{3}ab +\n2b^2$.", "markdown": "Add $\\frac{2}{3}a^2 - ab - \\frac{5}{4}b^2$, $\\frac{2}{3}a^2 + \\frac{1}{3}ab - \\frac{1}{4}b^2$, and $-a^2 -\\frac{2}{3}ab + 2b^2$.", "answer_latex": [ "$\\frac{1}{3} a^2 - \\frac{4}{3} ab + \\frac{1}{2} b^2$." ], "answer_markdown": [ "$\\frac{1}{3} a^2 - \\frac{4}{3} ab + \\frac{1}{2} b^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(2,3)*a**2 - a*b - Rational(5,4)*b**2) + (Rational(2,3)*a**2 + Rational(1,3)*a*b - Rational(1,4)*b**2) + (-a**2 - Rational(2,3)*a*b + 2*b**2)", "answer_expr": "Rational(1,3)*a**2 - Rational(4,3)*a*b + Rational(1,2)*b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**2/2 - 4*a*x/3 + x**2/3" ], "shape": [ "identity: N*a*x + N*a**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/8", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 8", "problem_latex": "Simplify $8ab^2c^4 \\times (-3a^4bc^2) \\times (-2a^2b^3c)$.", "markdown": "Simplify $8ab^2c^4 \\times (-3a^4bc^2) \\times (-2a^2b^3c)$.", "answer_latex": [ "$48a^7 b^6 c^7$." ], "answer_markdown": [ "$48a^7 b^6 c^7$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "8*a*b**2*c**4*(-3*a**4*b*c**2)*(-2*a**2*b**3*c)", "answer_expr": "48*a**7*b**6*c**7" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 48*a**6*b**7*x**7" ], "shape": [ "identity: N*a**N*b**N*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-23/9", "set": "boyden-first-book-in-algebra-1895/ex-23", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 23, problem 9", "problem_latex": "Expand $\\left(-\\frac{2}{3}xy^2z^3\\right)^4$.", "markdown": "Expand $\\left(-\\frac{2}{3}xy^2z^3\\right)^4$.", "answer_latex": [ "$\\frac{16}{81}x^4 y^8 z^{12}$." ], "answer_markdown": [ "$\\frac{16}{81}x^4 y^8 z^{12}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-Rational(2,3)*x*y**2*z**3)**4", "answer_expr": "Rational(16,81)*x**4*y**8*z**12" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 16*a**8*b**12*x**4/81" ], "shape": [ "identity: N*a**N*b**N*x**N" ], "same_problem_in": [], "needs": [ "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/1", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 1", "problem_latex": "$15x^2 y$ by $3x$.", "markdown": "$15x^2 y$ by $3x$.", "answer_latex": [ "$5xy$." ], "answer_markdown": [ "$5xy$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(15*x**2*y)/(3*x)", "answer_expr": "5*x*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 5*a*b" ], "shape": [ "identity: N*a*b" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/10", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 10", "problem_latex": "$\\frac{1}{5} x^3 y^4$ by $-\\frac{1}{15} xy^3$.", "markdown": "$\\frac{1}{5} x^3 y^4$ by $-\\frac{1}{15} xy^3$.", "answer_latex": [ "$-3x^2y$." ], "answer_markdown": [ "$-3x^2y$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(1,5)*x**3*y**4)/(-Rational(1,15)*x*y**3)", "answer_expr": "-3*x**2*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -3*a**2*b" ], "shape": [ "identity: N*a**N*b" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/11", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 11", "problem_latex": "$-45x^5 y^7 z$ by $9x^2 y^4 z$.", "markdown": "$-45x^5 y^7 z$ by $9x^2 y^4 z$.", "answer_latex": [ "$-5x^3 y^3$." ], "answer_markdown": [ "$-5x^3 y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-45*x**5*y**7*z)/(9*x**2*y**4*z)", "answer_expr": "-5*x**3*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -5*a**3*b**3" ], "shape": [ "identity: N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/12", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 12", "problem_latex": "$60a^4 bc^{11}$ by $-4ab^2 c^7$.", "markdown": "$60a^4 bc^{11}$ by $-4ab^2 c^7$.", "answer_latex": [ "$-5a^2 c^4$." ], "answer_markdown": [ "$-5a^2 c^4$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-0.33806233009728411852", "-1.0690079086860065369" ], "problem_expr": "(60*a**4*b*c**11)/(-4*a*b**2*c**7)", "answer_expr": "-5*a**2*c**4" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: -15*a**3*c**4/b" ], "shape": [ "identity: N*a**N*c**N/b" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/13", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 13", "problem_latex": "$-\\frac{2}{3} x^7 y^2$ by $-\\frac{5}{6} x^4 y$.", "markdown": "$-\\frac{2}{3} x^7 y^2$ by $-\\frac{5}{6} x^4 y$.", "answer_latex": [ "$\\frac{4}{5} x^3y$." ], "answer_markdown": [ "$\\frac{4}{5} x^3y$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-Rational(2,3)*x**7*y**2)/(-Rational(5,6)*x**4*y)", "answer_expr": "Rational(4,5)*x**3*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*a**3*b/5" ], "shape": [ "identity: N*a**N*b" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/14", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 14", "problem_latex": "$\\frac{3}{4} a^5 m^4 n^3$ by $-\\frac{1}{4} a^2 mn^3$.", "markdown": "$\\frac{3}{4} a^5 m^4 n^3$ by $-\\frac{1}{4} a^2 mn^3$.", "answer_latex": [ "$-3a^3 m^3$." ], "answer_markdown": [ "$-3a^3 m^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(3,4)*a**5*m**4*n**3)/(-Rational(1,4)*a**2*m*n**3)", "answer_expr": "-3*a**3*m**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -3*a**3*b**3" ], "shape": [ "identity: N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/15", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 15", "problem_latex": "$5m^4 n^2 x^5$ by $\\frac{5}{8} mn^2 x$.", "markdown": "$5m^4 n^2 x^5$ by $\\frac{5}{8} mn^2 x$.", "answer_latex": [ "$8m^3 x^4$." ], "answer_markdown": [ "$8m^3 x^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(5*m**4*n**2*x**5)/(Rational(5,8)*m*n**2*x)", "answer_expr": "8*m**3*x**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 8*a**3*b**4" ], "shape": [ "identity: N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/16", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 16", "problem_latex": "$4x^3 y^2 z^8$ by $-\\frac{2}{3} xz^5$.", "markdown": "$4x^3 y^2 z^8$ by $-\\frac{2}{3} xz^5$.", "answer_latex": [ "$-6x^2 y^2 z^3$." ], "answer_markdown": [ "$-6x^2 y^2 z^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*x**3*y**2*z**8)/(-Rational(2,3)*x*z**5)", "answer_expr": "-6*x**2*y**2*z**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -6*a**2*b**2*c**3" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/17", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 17", "problem_latex": "$10(x + y)^4 z^3$ by $5(x + y)^2 z$.", "markdown": "$10(x + y)^4 z^3$ by $5(x + y)^2 z$.", "answer_latex": [ "$2(x + y)^2 z^2$." ], "answer_markdown": [ "$2(x + y)^2 z^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(10*(x + y)**4*z**3)/(5*(x + y)**2*z)", "answer_expr": "2*(x + y)**2*z**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*c**2*(a + b)**2" ], "shape": [ "identity: N*c**N*(a + b)**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/18", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 18", "problem_latex": "$15(a - b)^3 x^2$ by $3(a - b)x$.", "markdown": "$15(a - b)^3 x^2$ by $3(a - b)x$.", "answer_latex": [ "$5(a - b)^2 x$." ], "answer_markdown": [ "$5(a - b)^2 x$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(15*(a - b)**3*x**2)/(3*(a - b)*x)", "answer_expr": "5*(a - b)**2*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 15*c*(a - b)**3/(3*a - 3*b)" ], "shape": [ "identity: N*c*(a - b)**N/(N*a + N*b)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/19", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 19", "problem_latex": "Simplify $(-x^{2}y^{3}z^{2}) \\times (-x^{4}y^{5}z^{4}) \\div 2x^{3}y^{3}z^{4}$.", "markdown": "Simplify $(-x^{2}y^{3}z^{2}) \\times (-x^{4}y^{5}z^{4}) \\div 2x^{3}y^{3}z^{4}$.", "answer_latex": [ "$\\frac{1}{2} x^3 y^3 z^2$." ], "answer_markdown": [ "$\\frac{1}{2} x^3 y^3 z^2$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "1.2631421041255377016", "5.8001423148621629153" ], "problem_expr": "(-x**2*y**3*z**2)*(-x**4*y**5*z**4)/(2*x**3*y**3*z**4)", "answer_expr": "Rational(1,2)*x**3*y**3*z**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: a**3*b**5*c**2/2" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/2", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 2", "problem_latex": "$39a b^2$ by $3b$.", "markdown": "$39a b^2$ by $3b$.", "answer_latex": [ "$13ab$." ], "answer_markdown": [ "$13ab$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(39*a*b**2)/(3*b)", "answer_expr": "13*a*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 13*a*b" ], "shape": [ "identity: N*a*b" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/20", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 20", "problem_latex": "Simplify $a^{5}b^{2}c \\times (-a^{3}b^{3}c^{3}) \\div 3(a^{3}bc^{2})^{2}$.", "markdown": "Simplify $a^{5}b^{2}c \\times (-a^{3}b^{3}c^{3}) \\div 3(a^{3}bc^{2})^{2}$.", "answer_latex": [ "$-\\frac{1}{3} a^2 b^3$." ], "answer_markdown": [ "$-\\frac{1}{3} a^2 b^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**5*b**2*c*(-a**3*b**3*c**3))/(3*(a**3*b*c**2)**2)", "answer_expr": "-Rational(1,3)*a**2*b**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**2*b**3/3" ], "shape": [ "identity: N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/21", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 21", "problem_latex": "Expand $(x^{3}y^{2}-3xy)^{3}$.", "markdown": "Expand $(x^{3}y^{2}-3xy)^{3}$.", "answer_latex": [ "$x^9 y^6 - 9x^7 y^5 + 27x^5 y^4 - 27 x^3 y^3$." ], "answer_markdown": [ "$x^9 y^6 - 9x^7 y^5 + 27x^5 y^4 - 27 x^3 y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**3*y**2 - 3*x*y)**3", "answer_expr": "x**9*y**6 - 9*x**7*y**5 + 27*x**5*y**4 - 27*x**3*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3*b**2 - 3*a*b)**3" ], "shape": [ "identity: (N*a*b + a**N*b**N)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/22", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 22", "problem_latex": "If a man can ride one mile for $a$ cents, how far can\ntwo men ride for $b$ cents?", "markdown": "If a man can ride one mile for $a$ cents, how far can two men ride for $b$ cents?", "answer_latex": [ "$\\frac{b}{2a}$ miles." ], "answer_markdown": [ "$\\frac{b}{2a}$ miles." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "b/(2*a)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(2*a*x, b)" ], "shape": [ "solve: Eq(N*a*x, b)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/23", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 23", "problem_latex": "In how many days can $x$ men earn as much as 8\nmen in $y$ days?", "markdown": "In how many days can $x$ men earn as much as 8 men in $y$ days?", "answer_latex": [ "$\\frac{8y}{x}$ days." ], "answer_markdown": [ "$\\frac{8y}{x}$ days." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "8*y/x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(a*x, 8*b)" ], "shape": [ "solve: Eq(a*x, N*b)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/24", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 24", "problem_latex": "$a$ times $b$ is how many times $c$?", "markdown": "$a$ times $b$ is how many times $c$?", "answer_latex": [ "$\\frac{ab}{c}$." ], "answer_markdown": [ "$\\frac{ab}{c}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "a*b/c" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(c*x, a*b)" ], "shape": [ "solve: Eq(c*x, a*b)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/3", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 3", "problem_latex": "$27a^3 b^3 c$ by $9ab^2 c$.", "markdown": "$27a^3 b^3 c$ by $9ab^2 c$.", "answer_latex": [ "$3a^2$." ], "answer_markdown": [ "$3a^2$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "8.0679863368862916169", "5.2204617473970122227" ], "problem_expr": "(27*a**3*b**3*c)/(9*a*b**2*c)", "answer_expr": "3*a**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: 3*a**2*b" ], "shape": [ "identity: N*a**N*b" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/4", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 4", "problem_latex": "$35x^4 y^4 z$ by $7x^2 yz$.", "markdown": "$35x^4 y^4 z$ by $7x^2 yz$.", "answer_latex": [ "$5x^2 y^3$." ], "answer_markdown": [ "$5x^2 y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(35*x**4*y**4*z)/(7*x**2*y*z)", "answer_expr": "5*x**2*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 5*a**2*b**3" ], "shape": [ "identity: N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/5", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 5", "problem_latex": "$-51cx^3 y$ by $3cyx^2$.", "markdown": "$-51cx^3 y$ by $3cyx^2$.", "answer_latex": [ "$-17x$." ], "answer_markdown": [ "$-17x$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-51*c*x**3*y)/(3*c*y*x**2)", "answer_expr": "-17*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -17*a" ], "shape": [ "identity: N*a" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/6", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 6", "problem_latex": "$121x^3 y^3 z$ by $-11y^2 z$.", "markdown": "$121x^3 y^3 z$ by $-11y^2 z$.", "answer_latex": [ "$-11x^3 y$." ], "answer_markdown": [ "$-11x^3 y$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(121*x**3*y**3*z)/(-11*y**2*z)", "answer_expr": "-11*x**3*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -11*a**3*b" ], "shape": [ "identity: N*a**N*b" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/7", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 7", "problem_latex": "$-28x^2 y^2 z^2$ by $-7x y^2$.", "markdown": "$-28x^2 y^2 z^2$ by $-7x y^2$.", "answer_latex": [ "$4xz^2$." ], "answer_markdown": [ "$4xz^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-28*x**2*y**2*z**2)/(-7*x*y**2)", "answer_expr": "4*x*z**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*a*b**2" ], "shape": [ "identity: N*a*b**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/8", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 8", "problem_latex": "$-36a^3 b^2 c^4$ by $-4a b^2 c^2$.", "markdown": "$-36a^3 b^2 c^4$ by $-4a b^2 c^2$.", "answer_latex": [ "$9a^2c^2$." ], "answer_markdown": [ "$9a^2c^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-36*a**3*b**2*c**4)/(-4*a*b**2*c**2)", "answer_expr": "9*a**2*c**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 9*a**2*b**2" ], "shape": [ "identity: N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-24/9", "set": "boyden-first-book-in-algebra-1895/ex-24", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 24, problem 9", "problem_latex": "$\\frac{1}{3} a^4 b^5$ by $\\frac{1}{6} a^2 b^2$.", "markdown": "$\\frac{1}{3} a^4 b^5$ by $\\frac{1}{6} a^2 b^2$.", "answer_latex": [ "$2a^2 b^3$." ], "answer_markdown": [ "$2a^2 b^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(1,3)*a**4*b**5)/(Rational(1,6)*a**2*b**2)", "answer_expr": "2*a**2*b**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a**2*b**3" ], "shape": [ "identity: N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/1", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 1", "problem_latex": "$18a^{4}b^{3}-42a^{3}b^{2}+90a^{6}bx$ by $6a^{3}b$.", "markdown": "$18a^{4}b^{3}-42a^{3}b^{2}+90a^{6}bx$ by $6a^{3}b$.", "answer_latex": [ "$3ab^2 - 7b + 15a^3 x$." ], "answer_markdown": [ "$3ab^2 - 7b + 15a^3 x$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(18*a**4*b**3 - 42*a**3*b**2 + 90*a**6*b*x)/(6*a**3*b)", "answer_expr": "3*a*b**2 - 7*b + 15*a**3*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (18*a**3*x**4 - 42*a**2*x**3 + 90*a*b*x**6)/(6*a*x**3)" ], "shape": [ "identity: N*x**N*(N*a*b*x**N + 2*N*a**N*x**N)/a" ], "same_problem_in": [], "needs": [ "cas.cancel" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/10", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 10", "problem_latex": "$24y^{3}+32y^{7}-48y^{6}$ by $3y^{3}$.", "markdown": "$24y^{3}+32y^{7}-48y^{6}$ by $3y^{3}$.", "answer_latex": [ "$8 + \\frac{32}{3} y^4 - 16y^3$." ], "answer_markdown": [ "$8 + \\frac{32}{3} y^4 - 16y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(24*y**3 + 32*y**7 - 48*y**6)/(3*y**3)", "answer_expr": "8 + Rational(32,3)*y**4 - 16*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (32*x**7 - 48*x**6 + 24*x**3)/(3*x**3)" ], "shape": [ "identity: 3*N**2*x**(2*N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/11", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 11", "problem_latex": "$\\frac{1}{4}a^2x-\\frac{1}{16}abx - \\frac{3}{8}acx$ by $\\frac{3}{8}ax$.", "markdown": "$\\frac{1}{4}a^2x-\\frac{1}{16}abx - \\frac{3}{8}acx$ by $\\frac{3}{8}ax$.", "answer_latex": [ "$\\frac{2}{3} a - \\frac{1}{6} b - c$." ], "answer_markdown": [ "$\\frac{2}{3} a - \\frac{1}{6} b - c$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(1,4)*a**2*x - Rational(1,16)*a*b*x - Rational(3,8)*a*c*x)/(Rational(3,8)*a*x)", "answer_expr": "Rational(2,3)*a - Rational(1,6)*b - c" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 8*(-a*c*x/16 - 3*b*c*x/8 + c*x**2/4)/(3*c*x)" ], "shape": [ "identity: N*(N*a*c*x + N*b*c*x + N*c*x**N)/(c*x)" ], "same_problem_in": [], "needs": [ "cas.cancel", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/12", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 12", "problem_latex": "$-\\frac{5}{2}x^2+\\frac{5}{3}xy+\\frac{10}{3}x$ by $-\\frac{5}{6}x$.", "markdown": "$-\\frac{5}{2}x^2+\\frac{5}{3}xy+\\frac{10}{3}x$ by $-\\frac{5}{6}x$.", "answer_latex": [ "$3x - 2y - 4$." ], "answer_markdown": [ "$3x - 2y - 4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-Rational(5,2)*x**2 + Rational(5,3)*x*y + Rational(10,3)*x)/(-Rational(5,6)*x)", "answer_expr": "3*x - 2*y - 4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -6*(5*a*x/3 - 5*x**2/2 + 10*x/3)/(5*x)" ], "shape": [ "identity: N*(N*a*x + N*x + N*x**N)/x" ], "same_problem_in": [], "needs": [ "cas.cancel", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/13", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 13", "problem_latex": "An army was drawn up with $x$ men in front and $y$\nmen deep. How many men were there in the army?", "markdown": "An army was drawn up with $x$ men in front and $y$ men deep. How many men were there in the army?", "answer_latex": [ "$xy$ men." ], "answer_markdown": [ "$xy$ men." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/14", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 14", "problem_latex": "In how many minutes will a train go $x$ miles at\nthe rate of $a$ miles an hour?", "markdown": "In how many minutes will a train go $x$ miles at the rate of $a$ miles an hour?", "answer_latex": [ "$\\frac{60x}{a}$ minutes." ], "answer_markdown": [ "$\\frac{60x}{a}$ minutes." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(a*T/60, x)", "answer_expr": "60*x/a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(a*x/60, b)" ], "shape": [ "solve: Eq(N*a*x, b)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/15", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 15", "problem_latex": "How many apples at $x$ cents apiece can be bought\nfor $b$ dollars?", "markdown": "How many apples at $x$ cents apiece can be bought for $b$ dollars?", "answer_latex": [ "$\\frac{100b}{x}$ apples." ], "answer_markdown": [ "$\\frac{100b}{x}$ apples." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(n*x, 100*b)", "answer_expr": "100*b/x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(b*x, 100*a)" ], "shape": [ "solve: Eq(b*x, N*a)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/2", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 2", "problem_latex": "$10x^{5}y^{2}+6x^{3}y^{2}-18x^{4}y^{4}$ by $2x^{3}y$.", "markdown": "$10x^{5}y^{2}+6x^{3}y^{2}-18x^{4}y^{4}$ by $2x^{3}y$.", "answer_latex": [ "$5x^2 y + 3y - 9xy^3$." ], "answer_markdown": [ "$5x^2 y + 3y - 9xy^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(10*x**5*y**2 + 6*x**3*y**2 - 18*x**4*y**4)/(2*x**3*y)", "answer_expr": "5*x**2*y + 3*y - 9*x*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-18*a**4*x**4 + 10*a**2*x**5 + 6*a**2*x**3)/(2*a*x**3)" ], "shape": [ "identity: 3*N**2*a**N*x**(2*N)/a" ], "same_problem_in": [], "needs": [ "cas.cancel" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/3", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 3", "problem_latex": "$72x^{5}y^{6}-36x^{4}y^{3}-18x^{2}y^{2}$ by $9x^{2}y$.", "markdown": "$72x^{5}y^{6}-36x^{4}y^{3}-18x^{2}y^{2}$ by $9x^{2}y$.", "answer_latex": [ "$8x^3 y^5 - 4x^2 y^2 - 2y$." ], "answer_markdown": [ "$8x^3 y^5 - 4x^2 y^2 - 2y$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(72*x**5*y**6 - 36*x**4*y**3 - 18*x**2*y**2)/(9*x**2*y)", "answer_expr": "8*x**3*y**5 - 4*x**2*y**2 - 2*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (72*a**6*x**5 - 36*a**3*x**4 - 18*a**2*x**2)/(9*a*x**2)" ], "shape": [ "identity: 3*N**2*a**N*x**(2*N)/a" ], "same_problem_in": [], "needs": [ "cas.cancel" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/4", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 4", "problem_latex": "$169a^{4}b-117a^{3}b^{2}+91a^{2}b$ by $13a^{2}$.", "markdown": "$169a^{4}b-117a^{3}b^{2}+91a^{2}b$ by $13a^{2}$.", "answer_latex": [ "$13a^2 b - 9ab^2 + 7b$." ], "answer_markdown": [ "$13a^2 b - 9ab^2 + 7b$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(169*a**4*b - 117*a**3*b**2 + 91*a**2*b)/(13*a**2)", "answer_expr": "13*a**2*b - 9*a*b**2 + 7*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-117*a**2*x**3 + 169*a*x**4 + 91*a*x**2)/(13*x**2)" ], "shape": [ "identity: N*x**N*(2*N*a*x**N + N*a**N*x**N)" ], "same_problem_in": [], "needs": [ "cas.cancel" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/5", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 5", "problem_latex": "$-2a^{5}x^{3}+\\frac{7}{2}a^{4}x^{4}$ by $\\frac{7}{3}a^{3}x$.", "markdown": "$-2a^{5}x^{3}+\\frac{7}{2}a^{4}x^{4}$ by $\\frac{7}{3}a^{3}x$.", "answer_latex": [ "$-\\frac{6}{7} a^2x^2 + \\frac{3}{2} ax^3$." ], "answer_markdown": [ "$-\\frac{6}{7} a^2x^2 + \\frac{3}{2} ax^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-2*a**5*x**3 + Rational(7,2)*a**4*x**4)/(Rational(7,3)*a**3*x)", "answer_expr": "-Rational(6,7)*a**2*x**2 + Rational(3,2)*a*x**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*(7*a**4*x**4/2 - 2*a**3*x**5)/(7*a*x**3)" ], "shape": [ "identity: 2*N**2*a**N*x**(2*N)/a" ], "same_problem_in": [], "needs": [ "cas.cancel", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/6", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 6", "problem_latex": "$\\frac{1}{2}x^{5}y^{2}-3x^{3}y^{4}$ by $-\\frac{3}{2}x^3y^{2}$.", "markdown": "$\\frac{1}{2}x^{5}y^{2}-3x^{3}y^{4}$ by $-\\frac{3}{2}x^3y^{2}$.", "answer_latex": [ "$-\\frac{1}{3} x^2 + 2y^2$." ], "answer_markdown": [ "$-\\frac{1}{3} x^2 + 2y^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(1,2)*x**5*y**2 - 3*x**3*y**4)/(-Rational(3,2)*x**3*y**2)", "answer_expr": "-Rational(1,3)*x**2 + 2*y**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -2*(-3*a**4*x**3 + a**2*x**5/2)/(3*a**2*x**3)" ], "shape": [ "identity: 2*N**2*a**(2*N)*x**(2*N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/7", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 7", "problem_latex": "$32x^{3}y^{4}z^{6}-24x^{5}y^{4}z^{4}+8x^{4}y^{2}$ by $-8x^{3}y$.", "markdown": "$32x^{3}y^{4}z^{6}-24x^{5}y^{4}z^{4}+8x^{4}y^{2}$ by $-8x^{3}y$.", "answer_latex": [ "$-4y^3 z^3 + 3x^2 y^3 z^4 - xy$." ], "answer_markdown": [ "$-4y^3 z^3 + 3x^2 y^3 z^4 - xy$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-45.793357622608566221", "-14.962966300719947223" ], "problem_expr": "(32*x**3*y**4*z**6 - 24*x**5*y**4*z**4 + 8*x**4*y**2)/(-8*x**3*y)", "answer_expr": "-4*y**3*z**3 + 3*x**2*y**3*z**4 - x*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: -(32*a**4*b**6*x**3 - 24*a**4*b**4*x**5 + 8*a**2*x**4)/(8*a*x**3)" ], "shape": [ "identity: N*x**N*(2*N*a**N*b**N*x**N + N*a**N*x**N)/a" ], "same_problem_in": [], "needs": [ "cas.cancel" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/8", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 8", "problem_latex": "$120a^{4}b^{3}c^{5}-186a^{5}b^{7}c^{6}$ by $6a^{3}b^{3}c^{4}$.", "markdown": "$120a^{4}b^{3}c^{5}-186a^{5}b^{7}c^{6}$ by $6a^{3}b^{3}c^{4}$.", "answer_latex": [ "$20ac - 31a^2 b^4 c^2$." ], "answer_markdown": [ "$20ac - 31a^2 b^4 c^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(120*a**4*b**3*c**5 - 186*a**5*b**7*c**6)/(6*a**3*b**3*c**4)", "answer_expr": "20*a*c - 31*a**2*b**4*c**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-186*a**7*b**6*x**5 + 120*a**3*b**5*x**4)/(6*a**3*b**4*x**3)" ], "shape": [ "identity: 2*N**2*a**(2*N)*b**(2*N)*x**(2*N)" ], "same_problem_in": [], "needs": [ "cas.cancel" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-25/9", "set": "boyden-first-book-in-algebra-1895/ex-25", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 25, problem 9", "problem_latex": "$4x^{8}-10x^{5}+2x^{6}-16x^{3}-6x^{4}$ by $4x^{2}$.", "markdown": "$4x^{8}-10x^{5}+2x^{6}-16x^{3}-6x^{4}$ by $4x^{2}$.", "answer_latex": [ "$x^6 - \\frac{5}{2} x^3 + \\frac{1}{2} x^4 - 4x - \\frac {3}{2}\nx^2$." ], "answer_markdown": [ "$x^6 - \\frac{5}{2} x^3 + \\frac{1}{2} x^4 - 4x - \\frac {3}{2} x^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*x**8 - 10*x**5 + 2*x**6 - 16*x**3 - 6*x**4)/(4*x**2)", "answer_expr": "x**6 - Rational(5,2)*x**3 + Rational(1,2)*x**4 - 4*x - Rational(3,2)*x**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (4*x**8 + 2*x**6 - 10*x**5 - 6*x**4 - 16*x**3)/(4*x**2)" ], "shape": [ "identity: 5*N**2*x**(2*N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/1", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 1", "problem_latex": "$x^2+8x-105$ by $x+15$.", "markdown": "$x^2+8x-105$ by $x+15$.", "answer_latex": [ "$x - 7$." ], "answer_markdown": [ "$x - 7$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2 + 8*x - 105)/(x + 15)", "answer_expr": "x - 7" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**2 + 8*x - 105)/(x + 15)" ], "shape": [ "identity: (N*x + N + x**N)/(N + x)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/10", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 10", "problem_latex": "$81x^8-y^4$ by $3x^2-y$.", "markdown": "$81x^8-y^4$ by $3x^2-y$.", "answer_latex": [ "$27x^5 + 9x^4y + 3x^2y^2 + y^3$." ], "answer_markdown": [ "$27x^5 + 9x^4y + 3x^2y^2 + y^3$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "3.73733230892450119", "3.9565717718705049891" ], "problem_expr": "(81*x**8 - y**4)/(3*x**2 - y)", "answer_expr": "27*x**5 + 9*x**4*y + 3*x**2*y**2 + y**3" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (-a**4 + 81*x**8)/(-a + 3*x**2)" ], "shape": [ "identity: (N*x**N - a**N)/(N*x**N - a)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/11", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 11", "problem_latex": "$x^5-x^4y-2x^3y^2-5x^2y^3-17xy^4-12y^5$ by $x^2-2xy-3y^2$.", "markdown": "$x^5-x^4y-2x^3y^2-5x^2y^3-17xy^4-12y^5$ by $x^2-2xy-3y^2$.", "answer_latex": [ "$x^3 + x^2y + 3xy^2 + 4y^3$." ], "answer_markdown": [ "$x^3 + x^2y + 3xy^2 + 4y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**5 - x**4*y - 2*x**3*y**2 - 5*x**2*y**3 - 17*x*y**4 - 12*y**5)/(x**2 - 2*x*y - 3*y**2)", "answer_expr": "x**3 + x**2*y + 3*x*y**2 + 4*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-12*a**5 - 17*a**4*x - 5*a**3*x**2 - 2*a**2*x**3 - a*x**4 + x**5)/(-3*a**2 - 2*a*x + x**2)" ], "shape": [ "identity: (N*a**N*x + 2*N*a**N*x**N + N*a**N - a*x**N + x**N)/(N*a*x + N*a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/12", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 12", "problem_latex": "$a^5+a^4b-14a^3b^2+15a^2b^3-4b^3$ by $a^2-3ab+2b^2$.", "markdown": "$a^5+a^4b-14a^3b^2+15a^2b^3-4b^3$ by $a^2-3ab+2b^2$.", "answer_latex": [ "$a^3 + 4a^2b - 3ab^2 - 2b^3$." ], "answer_markdown": [ "$a^3 + 4a^2b - 3ab^2 - 2b^3$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "37.130228216586436481", "-18.343395999714503958" ], "problem_expr": "(a**5 + a**4*b - 14*a**3*b**2 + 15*a**2*b**3 - 4*b**3)/(a**2 - 3*a*b + 2*b**2)", "answer_expr": "a**3 + 4*a**2*b - 3*a*b**2 - 2*b**3" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (15*a**3*x**2 - 4*a**3 - 14*a**2*x**3 + a*x**4 + x**5)/(2*a**2 - 3*a*x + x**2)" ], "shape": [ "identity: (2*N*a**N*x**N + N*a**N + a*x**N + x**N)/(N*a*x + N*a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/13", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 13", "problem_latex": "$x^6 - 5x^3 + 3 + 5x^4 - 10x - x^5 + 10x^2$ by $x^2 + 3 -\nx$.", "markdown": "$x^6 - 5x^3 + 3 + 5x^4 - 10x - x^5 + 10x^2$ by $x^2 + 3 - x$.", "answer_latex": [ "$x^4 + 2x^2 - 3x + 1.$" ], "answer_markdown": [ "$x^4 + 2x^2 - 3x + 1.$" ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**6 - 5*x**3 + 3 + 5*x**4 - 10*x - x**5 + 10*x**2)/(x**2 + 3 - x)", "answer_expr": "x**4 + 2*x**2 - 3*x + 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**6 - x**5 + 5*x**4 - 5*x**3 + 10*x**2 - 10*x + 3)/(x**2 - x + 3)" ], "shape": [ "identity: (N*x + 3*N*x**N + N)/(N - x + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/14", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 14", "problem_latex": "$x^6 - 2x^3 - 2 + x - 3x^5 + 2x^4 - 5x^2$ by $x^3 + 2 + x$.", "markdown": "$x^6 - 2x^3 - 2 + x - 3x^5 + 2x^4 - 5x^2$ by $x^3 + 2 + x$.", "answer_latex": [ "$x^3 - 3x^2 + x - 1$." ], "answer_markdown": [ "$x^3 - 3x^2 + x - 1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**6 - 2*x**3 - 2 + x - 3*x**5 + 2*x**4 - 5*x**2)/(x**3 + 2 + x)", "answer_expr": "x**3 - 3*x**2 + x - 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**6 - 3*x**5 + 2*x**4 - 2*x**3 - 5*x**2 + x - 2)/(x**3 + x + 2)" ], "shape": [ "identity: (4*N*x**N + N + x + x**N)/(N + x + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/15", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 15", "problem_latex": "$a^5 - a - 2a^2 - a^3$ by $a + a^3 + a^2$.", "markdown": "$a^5 - a - 2a^2 - a^3$ by $a + a^3 + a^2$.", "answer_latex": [ "$a^2 - a - 1$." ], "answer_markdown": [ "$a^2 - a - 1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**5 - a - 2*a**2 - a**3)/(a + a**3 + a**2)", "answer_expr": "a**2 - a - 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**5 - x**3 - 2*x**2 - x)/(x**3 + x**2 + x)" ], "shape": [ "identity: (N*x**N - x)/(x + 2*x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/16", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 16", "problem_latex": "$x^6 - 2x^3 - x^2 - x^4$ by $1 + xx^2 + x$.", "markdown": "$x^6 - 2x^3 - x^2 - x^4$ by $1 + xx^2 + x$.", "answer_latex": [ "$x^4 - x^3 - x^2$." ], "answer_markdown": [ "$x^4 - x^3 - x^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**6 - 2*x**3 - x**2 - x**4)/(1 + x**2 + x)", "answer_expr": "x**4 - x**3 - x**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**6 - x**4 - 2*x**3 - x**2)/(x**2 + x + 1)" ], "shape": [ "identity: (N*x**N - x**N)/(x + x**N + 1)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/17", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 17", "problem_latex": "$a^{11} - a^2$ by $a^3 - 1$.", "markdown": "$a^{11} - a^2$ by $a^3 - 1$.", "answer_latex": [ "$a^8 + a^5 + a^2$." ], "answer_markdown": [ "$a^8 + a^5 + a^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**11 - a**2)/(a**3 - 1)", "answer_expr": "a**8 + a**5 + a**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**11 - x**2)/(x**3 - 1)" ], "shape": [ "identity: 0" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/18", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 18", "problem_latex": "$a^{12} - a^4$ by $a^2 + 1$.", "markdown": "$a^{12} - a^4$ by $a^2 + 1$.", "answer_latex": [ "$a^10 - a^8 + a^6 - a^4$." ], "answer_markdown": [ "$a^10 - a^8 + a^6 - a^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**12 - a**4)/(a**2 + 1)", "answer_expr": "a**10 - a**8 + a**6 - a**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**12 - x**4)/(x**2 + 1)" ], "shape": [ "identity: 0" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/19", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 19", "problem_latex": "$x^4 + 4y^4$ by $x^2 - 2xy + y^2$.", "markdown": "$x^4 + 4y^4$ by $x^2 - 2xy + y^2$.", "answer_latex": [ "$x^2 + 2xy + 2y^2$." ], "answer_markdown": [ "$x^2 + 2xy + 2y^2$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "22842.774352294922634", "45.501374441743456385" ], "problem_expr": "(x**4 + 4*y**4)/(x**2 - 2*x*y + y**2)", "answer_expr": "x**2 + 2*x*y + 2*y**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (4*a**4 + x**4)/(a**2 - 2*a*x + x**2)" ], "shape": [ "identity: (N*a**N + x**N)/(N*a*x + a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/2", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 2", "problem_latex": "$x^2+8x-33$ by $x+11$.", "markdown": "$x^2+8x-33$ by $x+11$.", "answer_latex": [ "$x - 3$." ], "answer_markdown": [ "$x - 3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2 + 8*x - 33)/(x + 11)", "answer_expr": "x - 3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**2 + 8*x - 33)/(x + 11)" ], "shape": [ "identity: (N*x + N + x**N)/(N + x)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/20", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 20", "problem_latex": "$4a^4 + 81b^4$ by $2a^2 + 6ab + 9b^2$.", "markdown": "$4a^4 + 81b^4$ by $2a^2 + 6ab + 9b^2$.", "answer_latex": [ "$2a^2 - 6ab + 9b^2$." ], "answer_markdown": [ "$2a^2 - 6ab + 9b^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*a**4 + 81*b**4)/(2*a**2 + 6*a*b + 9*b**2)", "answer_expr": "2*a**2 - 6*a*b + 9*b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (81*a**4 + 4*x**4)/(9*a**2 + 6*a*x + 2*x**2)" ], "shape": [ "identity: (N*a**N + N*x**N)/(N*a*x + N*a**N + N*x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/21", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 21", "problem_latex": "$\\frac{1}{2}x^4 + \\frac{3}{4}x^3y - \\frac{1}{3}x^2y^2\n + \\frac{7}{6}xy^3 - \\frac{1}{3}y^4$\n by $x^2 - \\frac{1}{2}xy + y^2$.", "markdown": "$\\frac{1}{2}x^4 + \\frac{3}{4}x^3y - \\frac{1}{3}x^2y^2 + \\frac{7}{6}xy^3 - \\frac{1}{3}y^4$ by $x^2 - \\frac{1}{2}xy + y^2$.", "answer_latex": [ "$\\frac{1}{2} x^2 + xy - \\frac{1}{3} y^2$." ], "answer_markdown": [ "$\\frac{1}{2} x^2 + xy - 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\\frac{5}{36}x^2y + \\frac{1}{6}xy^2 +\n\\frac{1}{6}x^3$\n by $\\frac{1}{2}x + \\frac{1}{3}y$.", "markdown": "$\\frac{2}{9}y^3 - \\frac{5}{36}x^2y + \\frac{1}{6}xy^2 + \\frac{1}{6}x^3$ by $\\frac{1}{2}x + \\frac{1}{3}y$.", "answer_latex": [ "$\\frac{1}{3} x^2 - \\frac{1}{2} xy + \\frac {2}{3} y^2$." ], "answer_markdown": [ "$\\frac{1}{3} x^2 - \\frac{1}{2} xy + \\frac {2}{3} y^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(2,9)*y**3 - Rational(5,36)*x**2*y + Rational(1,6)*x*y**2 + Rational(1,6)*x**3)/(Rational(1,2)*x + Rational(1,3)*y)", "answer_expr": "Rational(1,3)*x**2 - Rational(1,2)*x*y + Rational(2,3)*y**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a**3/9 + a**2*x/6 - 5*a*x**2/36 + x**3/6)/(a/3 + x/2)" ], "shape": [ "identity: (N*a*x**N + N*a**N*x + N*a**N + N*x**N)/(N*a + N*x)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/23", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 23", "problem_latex": "$\\frac{1}{4}(x - y)^5 - (x - y)^3 - \\frac{1}{2}(x - y)^2 -\n\\frac{1}{16}(x - y)$\n by $\\frac{1}{2}(x - y)^2 + (x - y) +\\frac{1}{4}$.", "markdown": "$\\frac{1}{4}(x - y)^5 - (x - y)^3 - \\frac{1}{2}(x - y)^2 - \\frac{1}{16}(x - y)$ by $\\frac{1}{2}(x - y)^2 + (x - y) +\\frac{1}{4}$.", "answer_latex": [ "$\\frac{1}{2}\\left(x - y\\right)^3 - \\left(x - y\\right)^2\n- \\frac{1}{4}(x - y)$." ], "answer_markdown": [ "$\\frac{1}{2}\\left(x - y\\right)^3 - \\left(x - y\\right)^2 - \\frac{1}{4}(x - y)$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(Rational(1,4)*(x - y)**5 - (x - y)**3 - Rational(1,2)*(x - y)**2 - Rational(1,16)*(x - y))/(Rational(1,2)*(x - y)**2 + (x - y) + Rational(1,4))", "answer_expr": "Rational(1,2)*(x - y)**3 - (x - y)**2 - Rational(1,4)*(x - y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/16 - x/16 + (-a + x)**5/4 - (-a + x)**3 - (-a + x)**2/2)/(-a + x + (-a + x)**2/2 + 1/4)" ], "shape": [ "identity: (N*a + N*x + 2*N*(-a + x)**N - (-a + x)**N)/(N*(-a + x)**N + N - a + x)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/24", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 24", "problem_latex": "$16x^8 - 81y^4$ by $27y^3 + 18x^2y^2 + 8x^6 + 12x^4y$.", "markdown": "$16x^8 - 81y^4$ by $27y^3 + 18x^2y^2 + 8x^6 + 12x^4y$.", "answer_latex": [ "$2x^2 - 3y$." ], "answer_markdown": [ "$2x^2 - 3y$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(16*x**8 - 81*y**4)/(27*y**3 + 18*x**2*y**2 + 8*x**6 + 12*x**4*y)", "answer_expr": "2*x**2 - 3*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-81*a**4 + 16*x**8)/(27*a**3 + 18*a**2*x**2 + 12*a*x**4 + 8*x**6)" ], "shape": [ "identity: (N*a**N + N*x**N)/(N*a*x**N + N*a**N*x**N + N*a**N + N*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/25", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 25", "problem_latex": "$4x^4 - 10x^2 + 6$ by $x + 1$.", "markdown": "$4x^4 - 10x^2 + 6$ by $x + 1$.", "answer_latex": [ "$4x^3 - 4x^2 - 6x + 6$." ], "answer_markdown": [ "$4x^3 - 4x^2 - 6x + 6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*x**4 - 10*x**2 + 6)/(x + 1)", "answer_expr": "4*x**3 - 4*x**2 - 6*x + 6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (4*x**4 - 10*x**2 + 6)/(x + 1)" ], "shape": [ "identity: (2*N*x**N + N)/(x + 1)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/26", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 26", "problem_latex": "$4a^4 - 5a^2b^2 + b^4$ by $2a - b$.", "markdown": "$4a^4 - 5a^2b^2 + b^4$ by $2a - b$.", "answer_latex": [ "$2a^3 + a^2b - 2ab^2 - b^3$." ], "answer_markdown": [ "$2a^3 + a^2b - 2ab^2 - b^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*a**4 - 5*a**2*b**2 + b**4)/(2*a - b)", "answer_expr": "2*a**3 + a**2*b - 2*a*b**2 - b**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**4 - 5*a**2*x**2 + 4*x**4)/(-a + 2*x)" ], "shape": [ "identity: (N*a**N*x**N + N*x**N + a**N)/(N*x - a)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/27", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 27", "problem_latex": "$a^6 - b^6 + a^4 + b^4 + a^2b^2$ by $a^2 - b^2 + 1$.", "markdown": "$a^6 - b^6 + a^4 + b^4 + a^2b^2$ by $a^2 - b^2 + 1$.", "answer_latex": [ "$a^4 + a^2b^2 + b^4$." ], "answer_markdown": [ "$a^4 + a^2b^2 + b^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**6 - b**6 + a**4 + b**4 + a**2*b**2)/(a**2 - b**2 + 1)", "answer_expr": "a**4 + a**2*b**2 + b**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a**6 + a**4 + a**2*x**2 + x**6 + x**4)/(-a**2 + x**2 + 1)" ], "shape": [ "identity: (a**N*x**N + 2*x**N)/(-a**N + x**N + 1)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/28", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 28", "problem_latex": "$x^6 - y^6 - x^4 - y^4 - x^2y^2$ by $x^2 - y^2 - 1$.", "markdown": "$x^6 - y^6 - x^4 - y^4 - x^2y^2$ by $x^2 - y^2 - 1$.", "answer_latex": [ "$x^4 + x^2y^2 + y^4$." ], "answer_markdown": [ "$x^4 + x^2y^2 + y^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**6 - y**6 - x**4 - y**4 - x**2*y**2)/(x**2 - y**2 - 1)", "answer_expr": "x**4 + x**2*y**2 + y**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a**6 - a**4 - a**2*x**2 + x**6 - x**4)/(-a**2 + x**2 - 1)" ], "shape": [ "identity: (-a**N*x**N - 2*a**N)/(-a**N + x**N - 1)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/29", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 29", "problem_latex": "$81a^{12} - 16b^8$ by $12a^3b^4 - 8b^6 - 18a^6b^2 + 27a^9$.", "markdown": "$81a^{12} - 16b^8$ by $12a^3b^4 - 8b^6 - 18a^6b^2 + 27a^9$.", "answer_latex": [ "$3a^3 + 2b^2$." ], "answer_markdown": [ "$3a^3 + 2b^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(81*a**12 - 16*b**8)/(12*a**3*b**4 - 8*b**6 - 18*a**6*b**2 + 27*a**9)", "answer_expr": "3*a**3 + 2*b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-16*a**8 + 81*x**12)/(-8*a**6 + 12*a**4*x**3 - 18*a**2*x**6 + 27*x**9)" ], "shape": [ "identity: (N*a**N + N*x**N)/(2*N*a**N*x**N + N*a**N + N*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/3", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 3", "problem_latex": "$x^4+x^2-20$ by $x^2-4$.", "markdown": "$x^4+x^2-20$ by $x^2-4$.", "answer_latex": [ "$x^2 + 5$." ], "answer_markdown": [ "$x^2 + 5$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**4 + x**2 - 20)/(x**2 - 4)", "answer_expr": "x**2 + 5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**4 + x**2 - 20)/(x**2 - 4)" ], "shape": [ "identity: (N + 2*x**N)/(N + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/30", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 30", "problem_latex": "$1 + 3x$ by $1 + x$ to four terms of quotient.", "markdown": "$1 + 3x$ by $1 + x$ to four terms of quotient.", "answer_latex": [ "$1 + 2x - 2x^2 + 2x^3 - \\text{etc}$." ], "answer_markdown": [ "$1 + 2x - 2x^2 + 2x^3 - \\text{etc}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.series" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/31", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 31, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 31", "problem_latex": "$1 - 2a$ by $1 - a$ to four terms of quotient.", "markdown": "$1 - 2a$ by $1 - a$ to four terms of quotient.", "answer_latex": [ "$1 - a - a^2 - a^3 - \\text{etc}$." ], "answer_markdown": [ "$1 - a - a^2 - a^3 - \\text{etc}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.series" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/32", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 32, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 32", "problem_latex": "$4 + a$ by $2 - a$ to four terms.", "markdown": "$4 + a$ by $2 - a$ to four terms.", "answer_latex": [ "$2 + \\frac{3}{2} a + \\frac{3}{4} a^2 + \\frac{3}{8} a^3 +\n\\text{etc}$." ], "answer_markdown": [ "$2 + \\frac{3}{2} a + \\frac{3}{4} a^2 + \\frac{3}{8} a^3 + \\text{etc}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.series" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/33", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 33, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 33", "problem_latex": "$9 - x$ by $3 + x$ to four terms.", "markdown": "$9 - x$ by $3 + x$ to four terms.", "answer_latex": [ "$3 - \\frac{4}{3} x + \\frac{4}{9} x^2 - \\frac{4}{27} x^3\n+ \\text{etc}$." ], "answer_markdown": [ "$3 - \\frac{4}{3} x + \\frac{4}{9} x^2 - \\frac{4}{27} x^3 + \\text{etc}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.series" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/34", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 34, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 34", "problem_latex": "If a boy can do a piece of work in $x$ minutes, how many\nhours would it take him to perform $12$ times as much work?", "markdown": "If a boy can do a piece of work in $x$ minutes, how many hours would it take him to perform $12$ times as much work?", "answer_latex": [ "$\\displaystyle \\frac{x}{5}$ hrs." ], "answer_markdown": [ "$\\displaystyle \\frac{x}{5}$ hrs." ], "checks": [ { "task": "identity", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "12*x/60", "answer_expr": "x/5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "identity: x/5" ], "shape": [ "identity: N*x" ], "same_problem_in": [], "needs": [ "core.frac", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/35", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 35, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 35", "problem_latex": "A man has $x$ dollars, $y$ acres of land worth $m$ dollars\nan acre, and $c$ houses each worth $b$ dollars. What is my share\nif I am one of $n$ heirs?", "markdown": "A man has $x$ dollars, $y$ acres of land worth $m$ dollars an acre, and $c$ houses each worth $b$ dollars. What is my share if I am one of $n$ heirs?", "answer_latex": [ "$\\displaystyle \\frac{x + my + bc}{n}$ dols." ], "answer_markdown": [ "$\\displaystyle \\frac{x + my + bc}{n}$ dols." ], "checks": [ { "task": "identity", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "(x + y*m + c*b)/n", "answer_expr": "(x + m*y + b*c)/n" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "identity: (a*b + c*e + x)/d" ], "shape": [ "identity: (a*b + c*e + x)/d" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/36", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 36, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 36", "problem_latex": "A storekeeper mixed $m$ pounds of coffee worth $a$ cents a\npound with $p$ pounds worth $b$ cents a pound. How much is the\nmixture worth per pound?", "markdown": "A storekeeper mixed $m$ pounds of coffee worth $a$ cents a pound with $p$ pounds worth $b$ cents a pound. How much is the mixture worth per pound?", "answer_latex": [ "$\\displaystyle \\frac{am + bp}{m + p}$ cts." ], "answer_markdown": [ "$\\displaystyle \\frac{am + bp}{m + p}$ cts." ], "checks": [ { "task": "identity", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "(m*a + p*b)/(m + p)", "answer_expr": "(a*m + b*p)/(m + p)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "identity: (a*x + b*c)/(c + x)" ], "shape": [ "identity: (a*x + b*c)/(c + x)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/37", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 37, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 37", "problem_latex": "If John is $y$ years old, how old was he 11 years ago?", "markdown": "If John is $y$ years old, how old was he 11 years ago?", "answer_latex": [ "$y - 11$ yrs." ], "answer_markdown": [ "$y - 11$ yrs." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/4", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 4", "problem_latex": "$y^4-y^2-30$ by $y^2+5$.", "markdown": "$y^4-y^2-30$ by $y^2+5$.", "answer_latex": [ "$y^2 - 6$." ], "answer_markdown": [ "$y^2 - 6$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(y**4 - y**2 - 30)/(y**2 + 5)", "answer_expr": "y**2 - 6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**4 - x**2 - 30)/(x**2 + 5)" ], "shape": [ "identity: N/(N + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/5", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 5", "problem_latex": "$x^4-31x^2+9$ by $x^2+5x-3$.", "markdown": "$x^4-31x^2+9$ by $x^2+5x-3$.", "answer_latex": [ "$x^2 - 5x - 3$." ], "answer_markdown": [ "$x^2 - 5x - 3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**4 - 31*x**2 + 9)/(x**2 + 5*x - 3)", "answer_expr": "x**2 - 5*x - 3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**4 - 31*x**2 + 9)/(x**2 + 5*x - 3)" ], "shape": [ "identity: (N*x**N + N + x**N)/(N*x + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/6", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 6", "problem_latex": "$a^4-12a^2+16$ by $a^2-2a-4$.", "markdown": "$a^4-12a^2+16$ by $a^2-2a-4$.", "answer_latex": [ "$a^2 + 2a - 4$." ], "answer_markdown": [ "$a^2 + 2a - 4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**4 - 12*a**2 + 16)/(a**2 - 2*a - 4)", "answer_expr": "a**2 + 2*a - 4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**4 - 12*x**2 + 16)/(x**2 - 2*x 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[] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/8", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 8", "problem_latex": "$a^3+b^3$ by $a+b$.", "markdown": "$a^3+b^3$ by $a+b$.", "answer_latex": [ "$a^2 - ab + b^2$." ], "answer_markdown": [ "$a^2 - ab + b^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**3 + b**3)/(a + b)", "answer_expr": "a**2 - a*b + b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3 + x**3)/(a + x)" ], "shape": [ "identity: (a**N + x**N)/(a + x)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-26/9", "set": "boyden-first-book-in-algebra-1895/ex-26", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 26, problem 9", "problem_latex": "$16a^4-81b^4$ by $2a-3b$.", "markdown": "$16a^4-81b^4$ by $2a-3b$.", "answer_latex": [ "$8a^3 + 12a^2 b + 18ab^2 + 27b^3$." ], "answer_markdown": [ "$8a^3 + 12a^2 b + 18ab^2 + 27b^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(16*a**4 - 81*b**4)/(2*a - 3*b)", "answer_expr": "8*a**3 + 12*a**2*b + 18*a*b**2 + 27*b**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-81*a**4 + 16*x**4)/(-3*a + 2*x)" ], "shape": [ "identity: (N*a**N + N*x**N)/(N*a + N*x)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/1", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 1", "problem_latex": "$\\sqrt{16 a^{2} b^{6}}$.", "markdown": "$\\sqrt{16 a^{2} b^{6}}$.", "answer_latex": [ "$4ab^3$." ], "answer_markdown": [ "$4ab^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "sqrt(16*a**2*b**6)", "answer_expr": "4*a*b**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*b**2*Abs(a)*Abs(b)" ], "shape": [ "identity: N*b**N*Abs(a)*Abs(b)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/10", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 10", "problem_latex": "$\\sqrt[3]{\\frac{8}{27} a^{9} b^{6}}$.", "markdown": "$\\sqrt[3]{\\frac{8}{27} a^{9} b^{6}}$.", "answer_latex": [ "$\\frac(2)(3) a^3b^2$." ], "answer_markdown": [ "$\\frac(2)(3) a^3b^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "root(Rational(8,27)*a**9*b**6, 3)", "answer_expr": "Rational(2,3)*a**3*b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*b**2*(a**9)**(1/3)/3" ], "shape": [ "identity: N*b**N*(a**N)**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/11", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 11", "problem_latex": "$\\sqrt[3]{-\\frac{27}{64} x^{9} y^{12}}$.", "markdown": "$\\sqrt[3]{-\\frac{27}{64} x^{9} y^{12}}$.", "answer_latex": [ "$- \\frac{3}{4} x^3y^4$." ], "answer_markdown": [ "$- \\frac{3}{4} x^3y^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "real_root(-Rational(27,64)*x**9*y**12, 3)", "answer_expr": "-Rational(3,4)*x**3*y**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*b**4*(-a**9)**(1/3)/4", "identity: -3*a**2*b**4*Abs(a)*sign(a**9*b**12)/4" ], "shape": [ "identity: N*a**N*b**N*Abs(a)*sign(a**N*b**N)", "identity: N*b**N*(-a**N)**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/12", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 12", "problem_latex": "$\\sqrt[5]{-\\frac{32}{243} a^{5} b^{15}}$.", "markdown": "$\\sqrt[5]{-\\frac{32}{243} a^{5} b^{15}}$.", "answer_latex": [ "$- \\frac{2}{3} ab^3$." ], "answer_markdown": [ "$- \\frac{2}{3} ab^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "real_root(-Rational(32,243)*a**5*b**15, 5)", "answer_expr": "-Rational(2,3)*a*b**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*(-a**5*b**15)**(1/5)/3", "identity: -2*b**2*Abs(a)*Abs(b)*sign(a**5*b**15)/3" ], "shape": [ "identity: N*(-a**N*b**N)**N", "identity: N*b**N*Abs(a)*Abs(b)*sign(a**N*b**N)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/13", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 13", "problem_latex": "$\\sqrt[6]{x^{12} \\left(a - b \\right)^{6}}$.", "markdown": "$\\sqrt[6]{x^{12} \\left(a - b \\right)^{6}}$.", "answer_latex": [ "$x^2(a - b)$." ], "answer_markdown": [ "$x^2(a - b)$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "root(x**12*(a - b)**6, 6)", "answer_expr": "x**2*(a - b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: c**2*Abs(a - b)" ], "shape": [ "identity: c**N*Abs(a - b)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/14", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 14", "problem_latex": "$\\sqrt[3]{a^9 \\left(x^{2} + y^{2} \\right)^{3}}$.", "markdown": "$\\sqrt[3]{a^9 \\left(x^{2} + y^{2} \\right)^{3}}$.", "answer_latex": [ "$a^3(x^2 + y^2)$." ], "answer_markdown": [ "$a^3(x^2 + y^2)$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "root(a**9*(x**2 + y**2)**3, 3)", "answer_expr": "a**3*(x**2 + y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (b**2 + c**2)*(a**9)**(1/3)" ], "shape": [ "identity: (b**N + c**N)*(a**N)**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/15", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 15", "problem_latex": "$\\sqrt{4 a^{2} b^{6} \\left(x^{2} - y \\right)^{4}}$.", "markdown": "$\\sqrt{4 a^{2} b^{6} \\left(x^{2} - y \\right)^{4}}$.", "answer_latex": [ "$2ab^3\\left(x^2 - y\\right)^2$." ], "answer_markdown": [ "$2ab^3\\left(x^2 - y\\right)^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "sqrt(4*a**2*b**6*(x**2 - y)**4)", "answer_expr": "2*a*b**3*(x**2 - y)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*b**2*(c**2 - d)**2*Abs(a)*Abs(b)" ], "shape": [ "identity: N*b**N*(c**N - d)**N*Abs(a)*Abs(b)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/16", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 16", "problem_latex": "$\\sqrt{16 x^{4} y^{2} \\left(m^{3} + y \\right)^{6}}$.", "markdown": "$\\sqrt{16 x^{4} y^{2} \\left(m^{3} + y \\right)^{6}}$.", "answer_latex": [ "$4x^2y\\left(m^3 + y\\right)^3$." ], "answer_markdown": [ "$4x^2y\\left(m^3 + y\\right)^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "sqrt(16*x**4*y**2*(m**3 + y)**6)", "answer_expr": "4*x**2*y*(m**3 + y)**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*b**2*(a**3 + c)**2*Abs(c)*Abs(a**3 + c)" ], "shape": [ "identity: N*b**N*(a**N + c)**N*Abs(c)*Abs(a**N + c)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/17", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 17", "problem_latex": "$\\sqrt{\\frac{1}{9} a^{4} b^{6}} - \\sqrt[3]{\\frac{1}{8} a^{6}\nb^{9}} - \\sqrt[5]{\\frac{32}{243} a^{10} b^{15}} + \\sqrt[3]{a^{6}\nb^{9}}$.", 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"identity: -a**2*(-b**3)**(1/3) + a**2*(-b**5)**(1/5)/2 + a**2*(b**3)**(1/3)/2 - a**2*Abs(b)/2", "identity: 3*a**2*Abs(b)*sign(a**6*b**3)/2 - a**2*Abs(b)*sign(a**10*b**5)/2 - a**2*Abs(b)/2" ], "shape": [ "identity: 2*N*a**N*Abs(b)*sign(a**N*b**N) + N*a**N*Abs(b)", "identity: N*a**N*(-b**N)**N + N*a**N*(b**N)**N + N*a**N*Abs(b) - a**N*(-b**N)**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/19", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 19", "problem_latex": "Multiply $\\sqrt{25 a^{4} b^{2} c^{2}}$ by $-\\sqrt[3]{-8\na^{3} b^{6} c^{9}}$.", "markdown": "Multiply $\\sqrt{25 a^{4} b^{2} c^{2}}$ by $-\\sqrt[3]{-8 a^{3} b^{6} c^{9}}$.", "answer_latex": [ "$10a^3b^3c^4$." ], "answer_markdown": [ "$10a^3b^3c^4$." ], "checks": [ { "task": "identity", "verdict": "FLAG-DOMAIN", "judge_why": "not enough points inside the domain", "problem_expr": "sqrt(25*a**4*b**2*c**2)*(-root(-8*a**3*b**6*c**9, 3))", "answer_expr": "10*a**3*b**3*c**4" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-DOMAIN" ] }, "form": [ "identity: -10*a**2*b**2*(-a**3*c**9)**(1/3)*Abs(b)*Abs(c)" ], "shape": [ "identity: N*a**N*b**N*(-a**N*c**N)**N*Abs(b)*Abs(c)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/2", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 2", "problem_latex": "$\\sqrt[4]{81 x^{4} y^{8}}$.", "markdown": "$\\sqrt[4]{81 x^{4} y^{8}}$.", "answer_latex": [ "$3xy^2$." ], "answer_markdown": [ "$3xy^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "root(81*x**4*y**8, 4)", "answer_expr": "3*x*y**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*b**2*Abs(a)" ], "shape": [ "identity: N*b**N*Abs(a)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/20", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 20", "problem_latex": "Divide $\\sqrt{144 x^{4} y^{4}}$ by $\\sqrt[5]{243 x^{10}\n y^{5}}$.", "markdown": "Divide $\\sqrt{144 x^{4} y^{4}}$ by $\\sqrt[5]{243 x^{10} y^{5}}$.", "answer_latex": [ "$4y$." ], "answer_markdown": [ "$4y$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "sqrt(144*x**4*y**4)/root(243*x**10*y**5, 5)", "answer_expr": "4*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*a**2/(a**5)**(1/5)" ], "shape": [ "identity: N*a**N*(a**N)**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/21", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 21", "problem_latex": "Multiply $-\\sqrt[3]{-125 x^{3} y^{6} z^{6}}$ by $\\sqrt{9\nx^{4} y^{2} z^{6}}$.", "markdown": "Multiply $-\\sqrt[3]{-125 x^{3} y^{6} z^{6}}$ by $\\sqrt{9 x^{4} y^{2} z^{6}}$.", "answer_latex": [ "$15x^3y^3z^5$." ], "answer_markdown": [ "$15x^3y^3z^5$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-real_root(-125*x**3*y**6*z**6, 3))*sqrt(9*x**4*y**2*z**6)", "answer_expr": "15*x**3*y**3*z**5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -15*a**2*b**2*c**4*(-a**3)**(1/3)*Abs(b)*Abs(c)", "identity: 15*a**2*b**2*c**4*Abs(a)*Abs(b)*Abs(c)*sign(a**3*b**6*c**6)" ], "shape": [ "identity: N*a**N*b**N*c**N*(-a**N)**N*Abs(b)*Abs(c)", "identity: N*a**N*b**N*c**N*Abs(a)*Abs(b)*Abs(c)*sign(a**N*b**N*c**N)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/22", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 22", "problem_latex": "Divide $\\sqrt{100 a^{6} b^{12}}$ by $\\sqrt[5]{32 a^{15}\n b^{25}}$.", "markdown": "Divide $\\sqrt{100 a^{6} b^{12}}$ by $\\sqrt[5]{32 a^{15} b^{25}}$.", "answer_latex": [ "$5b$." ], "answer_markdown": [ "$5b$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "sqrt(100*a**6*b**12)/root(32*a**15*b**25, 5)", "answer_expr": "5*b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 5*a**2*b**6*Abs(a)/(a**15*b**25)**(1/5)" ], "shape": [ "identity: N*a**N*b**N*(a**N*b**N)**N*Abs(a)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/23", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 23", "problem_latex": "From two cities $a$ miles apart two trains start toward each\nother, the one going $x$ miles an hour, and the other $y$ miles an\nhour. How long before they will meet? How far will each train have\ngone?", "markdown": "From two cities $a$ miles apart two trains start toward each other, the one going $x$ miles an hour, and the other $y$ miles an hour. How long before they will meet? How far will each train have gone?", "answer_latex": [ "$\\displaystyle \\frac{a}{x + y}$ hrs.; $\\displaystyle\n\\frac{ax}{x + y}$ miles.; $\\displaystyle \\frac{ay}{x + y}$ miles." ], "answer_markdown": [ "$\\displaystyle \\frac{a}{x + y}$ hrs.; $\\displaystyle \\frac{ax}{x + y}$ miles.; $\\displaystyle \\frac{ay}{x + y}$ miles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{t: a/(x + y), d1: a*x/(x + y), d2: a*y/(x + y)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, d*x), Eq(c, e*x), Eq(b + c, a))" ], "shape": [ "solve: (Eq(b, d*x), Eq(c, e*x), Eq(b + c, a))" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/24", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 24", "problem_latex": "What number is that whose double exceeds its half by 39?", "markdown": "What number is that whose double exceeds its half by 39?", "answer_latex": [ "$26$." ], "answer_markdown": [ "$26$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{n: 26}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*x/2, 39)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "39 ENTER 2 ENTER 2 1/x −", "÷" ], "constants": [ { "value": "2", "source": "the 2 in 'whose double' (2n), and the 2 in 'its half' (n/2 = n ÷ 2, entered as 1/x of 2)" } ], "calculator_value": "+26E+0", "printed_value": "26", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/25", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 25", "problem_latex": "Mr. A. is $m$ years old, and 6 years ago he was one-half as\nold as Mr. B. How old was Mr. B. then? How old is Mr. B. now?", "markdown": "Mr. A. is $m$ years old, and 6 years ago he was one-half as old as Mr. B. How old was Mr. B. then? How old is Mr. B. now?", "answer_latex": [ "$2(m - 6)$; $2m - 6$." ], "answer_markdown": [ "$2(m - 6)$; $2m - 6$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{b_then: 2*(m - 6), b_now: 2*m - 6}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, a - 6), Eq(b - 6, x/2))" ], "shape": [ "solve: (Eq(x, N + a), Eq(N + b, N*x))" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/3", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 3", "problem_latex": "$\\sqrt[3]{-8 x^{6} y^{3}}$.", "markdown": "$\\sqrt[3]{-8 x^{6} y^{3}}$.", "answer_latex": [ "$- 2x^2y$." ], "answer_markdown": [ "$- 2x^2y$." ], "checks": [ { "task": "identity", "verdict": "FLAG-DOMAIN", "judge_why": "not enough points inside the domain", "problem_expr": "root(-8*x**6*y**3, 3)", "answer_expr": "-2*x**2*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-DOMAIN" ] }, "form": [ "identity: 2*a**2*(-b**3)**(1/3)" ], "shape": [ "identity: N*a**N*(-b**N)**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/4", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 4", "problem_latex": "$\\sqrt[5]{-32 a^{10} b^{15}}$.", "markdown": "$\\sqrt[5]{-32 a^{10} b^{15}}$.", "answer_latex": [ "$- 2a^2b^3$." ], "answer_markdown": [ "$- 2a^2b^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "real_root(-32*a**10*b**15, 5)", "answer_expr": "-2*a**2*b**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a**2*(-b**15)**(1/5)", "identity: -2*a**2*b**2*Abs(b)*sign(a**10*b**15)" ], "shape": [ "identity: N*a**N*(-b**N)**N", "identity: N*a**N*b**N*Abs(b)*sign(a**N*b**N)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/5", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 5", "problem_latex": "$\\sqrt[5]{243 a^{5} b^{10}}$.", "markdown": "$\\sqrt[5]{243 a^{5} b^{10}}$.", "answer_latex": [ "$3ab^2$." ], "answer_markdown": [ "$3ab^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "root(243*a**5*b**10, 5)", "answer_expr": "3*a*b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*b**2*(a**5)**(1/5)" ], "shape": [ "identity: N*b**N*(a**N)**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/6", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 6", "problem_latex": "$\\sqrt[3]{27 x^{3} y^{9}}$.", "markdown": "$\\sqrt[3]{27 x^{3} y^{9}}$.", "answer_latex": [ "$3xy^3$." ], "answer_markdown": [ "$3xy^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "root(27*x**3*y**9, 3)", "answer_expr": "3*x*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*(a**3*b**9)**(1/3)" ], "shape": [ "identity: N*(a**N*b**N)**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/7", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 7", "problem_latex": "$\\sqrt[4]{16 x^{8} y^{4}}$.", "markdown": "$\\sqrt[4]{16 x^{8} y^{4}}$.", "answer_latex": [ "$2x^2y$." ], "answer_markdown": [ "$2x^2y$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "root(16*x**8*y**4, 4)", "answer_expr": "2*x**2*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a**2*Abs(b)" ], "shape": [ "identity: N*a**N*Abs(b)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/8", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 8", "problem_latex": "$\\sqrt{9 x^{8} y^{6}}$.", "markdown": "$\\sqrt{9 x^{8} y^{6}}$.", "answer_latex": [ "$3x^4y^3$." ], "answer_markdown": [ "$3x^4y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "sqrt(9*x**8*y**6)", "answer_expr": "3*x**4*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*a**4*b**2*Abs(b)" ], "shape": [ "identity: N*a**N*b**N*Abs(b)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-27/9", "set": "boyden-first-book-in-algebra-1895/ex-27", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 27, problem 9", "problem_latex": "$\\sqrt{\\frac{4}{9} m^{6} y^{4}}$.", "markdown": "$\\sqrt{\\frac{4}{9} m^{6} y^{4}}$.", "answer_latex": [ "$\\frac{2}{3} m^3y^2$." ], "answer_markdown": [ "$\\frac{2}{3} m^3y^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "sqrt(Rational(4,9)*m**6*y**4)", "answer_expr": "Rational(2,3)*m**3*y**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a**2*b**2*Abs(a)/3" ], "shape": [ "identity: N*a**N*b**N*Abs(a)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/1", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 1", "problem_latex": "$4x^2-12xy+9y^2$.", "markdown": "$4x^2-12xy+9y^2$.", "answer_latex": [ "$2x - 3y$." ], "answer_markdown": [ "$2x - 3y$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "4*x**2 - 12*x*y + 9*y**2", "answer_expr": "2*x - 3*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/10", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 10", "problem_latex": "$x^6+2x^5-x^4+3x^2-2x+1$.", "markdown": "$x^6+2x^5-x^4+3x^2-2x+1$.", "answer_latex": [ "$x^3 + x^2 - x + 1$." ], "answer_markdown": [ "$x^3 + x^2 - x + 1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "x**6 + 2*x**5 - x**4 + 3*x**2 - 2*x + 1", "answer_expr": "x**3 + x**2 - x + 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/11", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 11", "problem_latex": "$6x^4-4x^3+4x^5-15x^2-8x+x^6+16$.", "markdown": "$6x^4-4x^3+4x^5-15x^2-8x+x^6+16$.", "answer_latex": [ "$x^3 + 2x^2 + x - 4$." ], "answer_markdown": [ "$x^3 + 2x^2 + x - 4$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "6*x**4 - 4*x**3 + 4*x**5 - 15*x**2 - 8*x + x**6 + 16", "answer_expr": "x**3 + 2*x**2 + x - 4" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/12", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 12", "problem_latex": "$7x^2-6x-11x^4+10x^3-4x^5+1+4x^6$.", "markdown": "$7x^2-6x-11x^4+10x^3-4x^5+1+4x^6$.", "answer_latex": [ "$2x^3 - x^2 - 3x + 1$." ], "answer_markdown": [ "$2x^3 - x^2 - 3x + 1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "7*x**2 - 6*x - 11*x**4 + 10*x**3 - 4*x**5 + 1 + 4*x**6", "answer_expr": "2*x**3 - x**2 - 3*x + 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/13", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 13", "problem_latex": "A is $x$ years old. If his age is as much above 50 as B's\nage is below 40, what is B's age?", "markdown": "A is $x$ years old. If his age is as much above 50 as B’s age is below 40, what is B’s age?", "answer_latex": [ "$90 - x$." ], "answer_markdown": [ "$90 - x$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x - 50, 40 - b)", "answer_expr": "90 - x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a - 50, -x + 40)" ], "shape": [ "solve: Eq(N + a, N - x)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/14", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 14", "problem_latex": "If $x$ represents the first digit, and $y$ the second digit,\nof a number, what will represent the number?", "markdown": "If $x$ represents the first digit, and $y$ the second digit, of a number, what will represent the number?", "answer_latex": [ "$10x + y$." ], "answer_markdown": [ "$10x + y$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "10*x + y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:expression_from_words" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/2", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 2", "problem_latex": "$x^4+10x^3y^3+25x^2y^6$.", "markdown": "$x^4+10x^3y^3+25x^2y^6$.", "answer_latex": [ "$x^2 + 5xy^3$." ], "answer_markdown": [ "$x^2 + 5xy^3$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "x**4 + 10*x**3*y**3 + 25*x**2*y**6", "answer_expr": "x**2 + 5*x*y**3" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/3", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 3", "problem_latex": "$16a^2b^2c^4-56abc^2xy^2z+49x^2y^4z^2$.", "markdown": "$16a^2b^2c^4-56abc^2xy^2z+49x^2y^4z^2$.", "answer_latex": [ "$4abc^2 - 7xy^2z$." ], "answer_markdown": [ "$4abc^2 - 7xy^2z$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "16*a**2*b**2*c**4 - 56*a*b*c**2*x*y**2*z + 49*x**2*y**4*z**2", "answer_expr": "4*a*b*c**2 - 7*x*y**2*z" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/4", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 4", "problem_latex": "$\\frac{1}{4}x^2-xy^2z+y^4z^2$.", "markdown": "$\\frac{1}{4}x^2-xy^2z+y^4z^2$.", "answer_latex": [ "$\\frac{1}{2} x - y^2z$." ], "answer_markdown": [ "$\\frac{1}{2} x - y^2z$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "x**2/4 - x*y**2*z + y**4*z**2", "answer_expr": "x/2 - y**2*z" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/5", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 5", "problem_latex": "$a^2b^6+\\frac{2}{3}ab^3c^4+\\frac{1}{9}c^8$.", "markdown": "$a^2b^6+\\frac{2}{3}ab^3c^4+\\frac{1}{9}c^8$.", "answer_latex": [ "$ab^3 + \\frac{1}{3}c^4$." ], "answer_markdown": [ "$ab^3 + \\frac{1}{3}c^4$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "a**2*b**6 + 2*a*b**3*c**4/3 + c**8/9", "answer_expr": "a*b**3 + c**4/3" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/6", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 6", "problem_latex": "$x^4-4x^3+2x^2+4x+1$.", "markdown": "$x^4-4x^3+2x^2+4x+1$.", "answer_latex": [ "$x^2 - 2x - 1$." ], "answer_markdown": [ "$x^2 - 2x - 1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "x**4 - 4*x**3 + 2*x**2 + 4*x + 1", "answer_expr": "x**2 - 2*x - 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/7", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 7", "problem_latex": "$x^4+6x^3+17x^2+24x+16$.", "markdown": "$x^4+6x^3+17x^2+24x+16$.", "answer_latex": [ "$x^2 + 3x + 4$." ], "answer_markdown": [ "$x^2 + 3x + 4$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "x**4 + 6*x**3 + 17*x**2 + 24*x + 16", "answer_expr": "x**2 + 3*x + 4" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/8", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 8", "problem_latex": "$4x^4+9x^2+4-4x-4x^3$.", "markdown": "$4x^4+9x^2+4-4x-4x^3$.", "answer_latex": [ "$2x^2 - x + 2$." ], "answer_markdown": [ "$2x^2 - x + 2$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "4*x**4 + 9*x**2 + 4 - 4*x - 4*x**3", "answer_expr": "2*x**2 - x + 2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-28/9", "set": "boyden-first-book-in-algebra-1895/ex-28", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 28, problem 9", "problem_latex": "$6x^3-5x^2+1-2x+9x^4$.", "markdown": "$6x^3-5x^2+1-2x+9x^4$.", "answer_latex": [ "$3x^2 + x - 1$." ], "answer_markdown": [ "$3x^2 + x - 1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "6*x**3 - 5*x**2 + 1 - 2*x + 9*x**4", "answer_expr": "3*x**2 + x - 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "other:polynomial_square_root" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/1", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 1", "problem_latex": "$27 x^{3} - 27 x^{2} y + 9 x y^2 - y^{3}$.", "markdown": "$27 x^{3} - 27 x^{2} y + 9 x y^2 - y^{3}$.", "answer_latex": [ "$3x-y$." ], "answer_markdown": [ "$3x-y$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "27*x**3 - 27*x**2*y + 9*x*y**2 - y**3", "answer_expr": "3*x - y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/10", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 10", "problem_latex": "$x^{9} - 7 x^{6} + x^{3} - 3 x^{4} - 3 x^{8} + 6 x^{7} + 6\nx^{5}$.", "markdown": "$x^{9} - 7 x^{6} + x^{3} - 3 x^{4} - 3 x^{8} + 6 x^{7} + 6 x^{5}$.", "answer_latex": [ "$x^3-x^2+x$." ], "answer_markdown": [ "$x^3-x^2+x$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "x**9 - 7*x**6 + x**3 - 3*x**4 - 3*x**8 + 6*x**7 + 6*x**5", "answer_expr": "x**3 - x**2 + x" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/11", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 11", "problem_latex": "$5 x^{3} - 3 x - 3 x^{5} - 1 + x^{6}$.", "markdown": "$5 x^{3} - 3 x - 3 x^{5} - 1 + x^{6}$.", "answer_latex": [ "$x^2-x-1$." ], "answer_markdown": [ "$x^2-x-1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "5*x**3 - 3*x - 3*x**5 - 1 + x**6", "answer_expr": "x**2 - x - 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/12", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 12", "problem_latex": "$\\frac{1}{8} a^{6} + \\frac{3}{2} a^{5} + 5 \\frac{1}{4} a^{4}\n + 2 a^{3} - 10 \\frac{1}{2} a^{2} + 6 a - 1$.", "markdown": "$\\frac{1}{8} a^{6} + \\frac{3}{2} a^{5} + 5 \\frac{1}{4} a^{4} + 2 a^{3} - 10 \\frac{1}{2} a^{2} + 6 a - 1$.", "answer_latex": [ "$\\frac{1}{2}a^2+2a-1$." ], "answer_markdown": [ "$\\frac{1}{2}a^2+2a-1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "Rational(1, 8)*a**6 + Rational(3, 2)*a**5 + Rational(21, 4)*a**4 + 2*a**3 - Rational(21, 2)*a**2 + 6*a - 1", "answer_expr": "Rational(1, 2)*a**2 + 2*a - 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/13", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 13", "problem_latex": "A board is $8 x$ inches long and $2 x$ inches wide. What is\nthe length of a square board having the same area?", "markdown": "A board is $8 x$ inches long and $2 x$ inches wide. What is the length of a square board having the same area?", "answer_latex": [ "$4x$ in." ], "answer_markdown": [ "$4x$ in." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{s: 4*x}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x**2, 16*a**2)" ], "shape": [ "solve: Eq(x**N, N*a**N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.arith", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/14", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 14", "problem_latex": "If $3 x$ represents the edge of a cubical box, what\nrepresents the cubical contents of the box?", "markdown": "If $3 x$ represents the edge of a cubical box, what represents the cubical contents of the box?", "answer_latex": [ "$27x^3$." ], "answer_markdown": [ "$27x^3$." ], "checks": [ { "task": "identity", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "(3*x)**3", "answer_expr": "27*x**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "identity: 27*a**3" ], "shape": [ "identity: N*a**N" ], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/15", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 15", "problem_latex": "If a cubical cistern contains $64y^3$ cubic feet, how long\nis one edge?", "markdown": "If a cubical cistern contains $64y^3$ cubic feet, how long is one edge?", "answer_latex": [ "$4y$ ft." ], "answer_markdown": [ "$4y$ ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{s: 4*y}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(exp(3), 64*a**3)", "solve: Eq(x**3, 64*a**3)" ], "shape": [ "solve: Eq(exp(N), N*a**N)", "solve: Eq(x**N, N*a**N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.arith", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/16a", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 16, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 16a", "problem_latex": "A man travels north $a$ miles, and then south $b$ miles. How\nfar is he from the starting-point? How far has he traveled?", "markdown": "A man travels north $a$ miles, and then south $b$ miles. How far is he from the starting-point? How far has he traveled?", "answer_latex": [ "$a-b$ miles north; $a+b$ miles." ], "answer_markdown": [ "$a-b$ miles north; $a+b$ miles." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "a - b" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/16b", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 16, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 16b", "problem_latex": "A man travels north $a$ miles, and then south $b$ miles. How\nfar is he from the starting-point? How far has he traveled?", "markdown": "A man travels north $a$ miles, and then south $b$ miles. How far is he from the starting-point? How far has he traveled?", "answer_latex": [ "$a-b$ miles north; $a+b$ miles." ], "answer_markdown": [ "$a-b$ miles north; $a+b$ miles." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "a + b" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/2", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 2", "problem_latex": "$15 x^{2} - 1 - 75 x^{4} + 125 x^{6}$.", "markdown": "$15 x^{2} - 1 - 75 x^{4} + 125 x^{6}$.", "answer_latex": [ "$5x^2-1$." ], "answer_markdown": [ "$5x^2-1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "15*x**2 - 1 - 75*x**4 + 125*x**6", "answer_expr": "5*x**2 - 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/3", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 3", "problem_latex": "$144 a^{2} b^{2} + 27 b^{6} + 108 a b^{4} + 64 a^{3}$.", "markdown": "$144 a^{2} b^{2} + 27 b^{6} + 108 a b^{4} + 64 a^{3}$.", "answer_latex": [ "$3b^2+4a$." ], "answer_markdown": [ "$3b^2+4a$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "144*a**2*b**2 + 27*b**6 + 108*a*b**4 + 64*a**3", "answer_expr": "3*b**2 + 4*a" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/4", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 4", "problem_latex": "$x^{6} - 8 y^{6} + 12 x^{2} y^{4} - 6 x^{4} y^{2}$.", "markdown": "$x^{6} - 8 y^{6} + 12 x^{2} y^{4} - 6 x^{4} y^{2}$.", "answer_latex": [ "$x^2-2y^2$." ], "answer_markdown": [ "$x^2-2y^2$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "x**6 - 8*y**6 + 12*x**2*y**4 - 6*x**4*y**2", "answer_expr": "x**2 - 2*y**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/5", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 5", "problem_latex": "$1 + 9 x + 27 x^{2} + 27 x{3}$.", "markdown": "$1 + 9 x + 27 x^{2} + 27 x{3}$.", "answer_latex": [ "$1+3x$." ], "answer_markdown": [ "$1+3x$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "1 + 9*x + 27*x**2 + 27*x**3", "answer_expr": "1 + 3*x" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/6", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 6", "problem_latex": "$1 - 21 m - 343 m^{3} + 147 m^{2}$.", "markdown": "$1 - 21 m - 343 m^{3} + 147 m^{2}$.", "answer_latex": [ "$1-7m$." ], "answer_markdown": [ "$1-7m$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "1 - 21*m - 343*m**3 + 147*m**2", "answer_expr": "1 - 7*m" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/7", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 7", "problem_latex": "$3 x^{2} + 64 x^{6} - 24 x^{4} - \\frac{1}{8}$.", "markdown": "$3 x^{2} + 64 x^{6} - 24 x^{4} - \\frac{1}{8}$.", "answer_latex": [ "$4x^2-\\frac{1}{2}$." ], "answer_markdown": [ "$4x^2-\\frac{1}{2}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "3*x**2 + 64*x**6 - 24*x**4 - Rational(1, 8)", "answer_expr": "4*x**2 - Rational(1, 2)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/8", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 8", "problem_latex": "$27 x^{9} + \\frac{1}{27} + x^{3} + 9 x^{6}$.", "markdown": "$27 x^{9} + \\frac{1}{27} + x^{3} + 9 x^{6}$.", "answer_latex": [ "$3x^3+\\frac{1}{3}$." ], "answer_markdown": [ "$3x^3+\\frac{1}{3}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "27*x**9 + Rational(1, 27) + x**3 + 9*x**6", "answer_expr": "3*x**3 + Rational(1, 3)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-29/9", "set": "boyden-first-book-in-algebra-1895/ex-29", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 29, problem 9", "problem_latex": "$8 a^{6} + 18 a^{4} + 9 a^{2} - 12 a^{5} - 13 a^{3} - 3 a +\n1$.", "markdown": "$8 a^{6} + 18 a^{4} + 9 a^{2} - 12 a^{5} - 13 a^{3} - 3 a + 1$.", "answer_latex": [ "$2a^2-a+1$." ], "answer_markdown": [ "$2a^2-a+1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "8*a**6 + 18*a**4 + 9*a**2 - 12*a**5 - 13*a**3 - 3*a + 1", "answer_expr": "2*a**2 - a + 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/1", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 1", "problem_latex": "In a class of 35 pupils there are 7 more girls than\nboys. How many are there of each?", "markdown": "In a class of 35 pupils there are 7 more girls than boys. How many are there of each?", "answer_latex": [ "14 boys; 21 girls." ], "answer_markdown": [ "14 boys; 21 girls." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{b: 14, g: 21}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, a + 7), Eq(a + b, 35))" ], "shape": [ "solve: (Eq(b, N + a), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/10", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 10", "problem_latex": "The sum of three numbers is 56; the second is 3\nmore than the first, and the third 5 more than the first.\nWhat are the numbers?", "markdown": "The sum of three numbers is 56; the second is 3 more than the first, and the third 5 more than the first. What are the numbers?", "answer_latex": [ "16; 19; 21." ], "answer_markdown": [ "16; 19; 21." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 16, b: 19, c: 21}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, a + 3), Eq(c, a + 5), Eq(a + b + c, 56))" ], "shape": [ "solve: (Eq(b, N + a), Eq(c, N + a), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/11", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 11", "problem_latex": "Divide 62 into three parts such that the first part\nis 4 more than the second, and the third 7 more than the\nsecond.", "markdown": "Divide 62 into three parts such that the first part is 4 more than the second, and the third 7 more than the second.", "answer_latex": [ "21; 17; 24." ], "answer_markdown": [ "21; 17; 24." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 21, b: 17, c: 24}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b + 4), Eq(c, b + 7), Eq(a + b + c, 62))" ], "shape": [ "solve: (Eq(a, N + b), Eq(c, N + b), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/12", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 12", "problem_latex": "Three men together received \\$34,200; if the second\nreceived \\$1500 more than the first, and the third \\$1200\nmore than the second, how much did each receive?", "markdown": "Three men together received $34,200; if the second received $1500 more than the first, and the third $1200 more than the second, how much did each receive?", "answer_latex": [ "\\$10,000; \\$11,500; \\$12,700." ], "answer_markdown": [ "$10,000; $11,500; $12,700." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 10000, b: 11500, c: 12700}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, a + 1500), Eq(c, b + 1200), Eq(a + b + c, 34200))" ], "shape": [ "solve: (Eq(b, N + a), Eq(c, N + b), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/13", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 13", "problem_latex": "Divide 65 into three parts such that the second part\nis 17 more than the first part, and the third 15 less than the\nfirst.", "markdown": "Divide 65 into three parts such that the second part is 17 more than the first part, and the third 15 less than the first.", "answer_latex": [ "21; 38; 6." ], "answer_markdown": [ "21; 38; 6." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 21, b: 38, c: 6}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, a + 17), Eq(c, a - 15), Eq(a + b + c, 65))" ], "shape": [ "solve: (Eq(b, N + a), Eq(c, N + a), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/14", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 14", "problem_latex": "A man had 95 sheep in three flocks. In the first\nflock there were 23 more than in the second, and in the\nthird flock 12 less than in the second. How many sheep\nin each flock?", "markdown": "A man had 95 sheep in three flocks. In the first flock there were 23 more than in the second, and in the third flock 12 less than in the second. How many sheep in each flock?", "answer_latex": [ "51; 28; 16 sheep." ], "answer_markdown": [ "51; 28; 16 sheep." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 51, b: 28, c: 16}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b + 23), Eq(c, b - 12), Eq(a + b + c, 95))" ], "shape": [ "solve: (Eq(a, N + b), Eq(c, N + b), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/15", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 15", "problem_latex": "In an election, in which 1073 ballots were cast, Mr.\nA receives 97 votes less than Mr. B, and Mr. C 120 votes\nmore than Mr. B. How many votes did each receive?", "markdown": "In an election, in which 1073 ballots were cast, Mr. A receives 97 votes less than Mr. B, and Mr. C 120 votes more than Mr. B. How many votes did each receive?", "answer_latex": [ "A, 253; B, 350; C, 470 votes." ], "answer_markdown": [ "A, 253; B, 350; C, 470 votes." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{A: 253, B: 350, C: 470}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b - 97), Eq(c, b + 120), Eq(a + b + c, 1073))" ], "shape": [ "solve: (Eq(a, N + b), Eq(c, N + b), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/16", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 16", "problem_latex": "A man owns three farms. In the first there are\n5 acres more than in the second and 7 acres less than in\nthe third. If there are 53 acres in all the farms together,\nhow many acres are there in each farm?", "markdown": "A man owns three farms. In the first there are 5 acres more than in the second and 7 acres less than in the third. If there are 53 acres in all the farms together, how many acres are there in each farm?", "answer_latex": [ "17; 12; 24 A." ], "answer_markdown": [ "17; 12; 24 A." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{f1: 17, f2: 12, f3: 24}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b + 5), Eq(a, c - 7), Eq(a + b + c, 53))" ], "shape": [ "solve: (Eq(a, N + b), Eq(a, N + c), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/17", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 17", "problem_latex": "Divide 111 into three parts so that the first part\nshall be 16 more than the second and 19 less than the\nthird.", "markdown": "Divide 111 into three parts so that the first part shall be 16 more than the second and 19 less than the third.", "answer_latex": [ "36; 20; 55." ], "answer_markdown": [ "36; 20; 55." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 36, b: 20, c: 55}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b + 16), Eq(a, c - 19), Eq(a + b + c, 111))" ], "shape": [ "solve: (Eq(a, N + b), Eq(a, N + c), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/18", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 18", "problem_latex": "Three firms lost \\$118,000 by fire. The second firm\nlost \\$6000 less than the first and \\$20,000 more than the\nthird. What was each firm's loss?", "markdown": "Three firms lost $118,000 by fire. The second firm lost $6000 less than the first and $20,000 more than the third. What was each firm’s loss?", "answer_latex": [ "\\$50,000; \\$44,000; \\$24,000." ], "answer_markdown": [ "$50,000; $44,000; $24,000." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 50000, b: 44000, c: 24000}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, a - 6000), Eq(b, c + 20000), Eq(a + b + c, 118000))" ], "shape": [ "solve: (Eq(b, N + a), Eq(b, N + c), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/2", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 2", "problem_latex": "The sum of the ages of two brothers is 43 years, and\none of them is 15 years older than the other. Find their\nages.", "markdown": "The sum of the ages of two brothers is 43 years, and one of them is 15 years older than the other. Find their ages.", "answer_latex": [ "14 yrs.; 29 yrs." ], "answer_markdown": [ "14 yrs.; 29 yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 29, b: 14}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b + 15), Eq(a + b, 43))" ], "shape": [ "solve: (Eq(a, N + b), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/3", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 3", "problem_latex": "At an election in which 1079 votes were cast the successful\ncandidate had a majority of 95. How many votes\ndid each of the two candidates receive?", "markdown": "At an election in which 1079 votes were cast the successful candidate had a majority of 95. How many votes did each of the two candidates receive?", "answer_latex": [ "492; 587 votes." ], "answer_markdown": [ "492; 587 votes." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 587, b: 492}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a - b, 95), Eq(a + b, 1079))" ], "shape": [ "solve: (Eq(a - b, N), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/4", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 4", "problem_latex": "Divide the number 70 into two parts, such that one\npart shall be 26 less than the other part.", "markdown": "Divide the number 70 into two parts, such that one part shall be 26 less than the other part.", "answer_latex": [ "22; 48." ], "answer_markdown": [ "22; 48." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 22, b: 48}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b - 26), Eq(a + b, 70))" ], "shape": [ "solve: (Eq(a, N + b), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/5", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 5", "problem_latex": "John and Henry together have 143 marbles. If I\nshould give Henry 15 more, he would have just as many\nas John. How many has each?", "markdown": "John and Henry together have 143 marbles. If I should give Henry 15 more, he would have just as many as John. How many has each?", "answer_latex": [ "J, 79; H, 64." ], "answer_markdown": [ "J, 79; H, 64." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{J: 79, H: 64}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, a + 15), Eq(a + b, 143))" ], "shape": [ "solve: (Eq(b, N + a), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/6", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 6", "problem_latex": "In a storehouse containing 57 barrels there are 3\nless barrels of flour than of meal. How many of each?", "markdown": "In a storehouse containing 57 barrels there are 3 less barrels of flour than of meal. How many of each?", "answer_latex": [ "Flour, 27 bbls.; meal, 30 bbls." ], "answer_markdown": [ "Flour, 27 bbls.; meal, 30 bbls." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{f: 27, m: 30}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b - 3), Eq(a + b, 57))" ], "shape": [ "solve: (Eq(a, N + b), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/7", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 7", "problem_latex": "A man whose herd of cows numbered 63 had\n17 more Jerseys than Holsteins. How many had he of\neach?", "markdown": "A man whose herd of cows numbered 63 had 17 more Jerseys than Holsteins. How many had he of each?", "answer_latex": [ "23 Hol.; 40 Jer." ], "answer_markdown": [ "23 Hol.; 40 Jer." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{h: 23, j: 40}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, a + 17), Eq(a + b, 63))" ], "shape": [ "solve: (Eq(b, N + a), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/8", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 8", "problem_latex": "Two men whose wages differ by 8 dollars receive\nboth together \\$44 per month. How much does each\nreceive?", "markdown": "Two men whose wages differ by 8 dollars receive both together $44 per month. How much does each receive?", "answer_latex": [ "\\$18; \\$26." ], "answer_markdown": [ "$18; $26." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 26, b: 18}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a - b, 8), Eq(a + b, 44))" ], "shape": [ "solve: (Eq(a - b, N), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-3/9", "set": "boyden-first-book-in-algebra-1895/ex-3", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 3, problem 9", "problem_latex": "Find two numbers whose sum is 99 and whose difference\nis 19.", "markdown": "Find two numbers whose sum is 99 and whose difference is 19.", "answer_latex": [ "40; 59." ], "answer_markdown": [ "40; 59." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 59, y: 40}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a - b, 19), Eq(a + b, 99))" ], "shape": [ "solve: (Eq(a - b, N), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/1", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 1", "problem_latex": "$\\sqrt{2025}$.", "markdown": "$\\sqrt{2025}$.", "answer_latex": [ "$45$." ], "answer_markdown": [ "$45$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 45.0, printed 45 (half-unit 0.5; correctly rounded at the printed digits: 45.0)", "problem_expr": "sqrt(2025)", "answer_expr": "45" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 45" ], "shape": [ "evaluate: N" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-81/3" ], "needs": [ "core.arith" ], "expectation": "X#45,5E-1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "2025 √x" ], "calculator_value": "+45E+0", "printed_value": "45", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/10", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 10", "problem_latex": "$\\sqrt[3]{389017}$.", "markdown": "$\\sqrt[3]{389017}$.", "answer_latex": [ "$73$." ], "answer_markdown": [ "$73$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 73.0, printed 73 (half-unit 0.5; correctly rounded at the printed digits: 73.0)", "problem_expr": "root(389017, 3)", "answer_expr": "73" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 73" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#73,5E-1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "389017 ENTER 3 GOLD ˣ√y" ], "calculator_value": "+730E-1", "printed_value": "73", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/11", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 11", "problem_latex": "$\\sqrt[3]{241804.367}$.", "markdown": "$\\sqrt[3]{241804.367}$.", "answer_latex": [ "$62.3$." ], "answer_markdown": [ "$62.3$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 62.3, printed 62.3 (half-unit 0.05; correctly rounded at the printed digits: 62.3)", "problem_expr": "root(241804.367, 3)", "answer_expr": "62.3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 623/10" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#62.3,5E-2", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "241804.367 ENTER 3 GOLD ˣ√y" ], "constants": [ { "value": "241804.367", "source": "the radicand in '\\sqrt[3]{241804.367}'" }, { "value": "3", "source": "the index of the root in '\\sqrt[3]{241804.367}'" } ], "calculator_value": "+6230E-2", "printed_value": "62.3", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/12", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 12", "problem_latex": "$\\sqrt{7039.21}$.", "markdown": "$\\sqrt{7039.21}$.", "answer_latex": [ "$83.9$." ], "answer_markdown": [ "$83.9$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 83.9, printed 83.9 (half-unit 0.05; correctly rounded at the printed digits: 83.9)", "problem_expr": "sqrt(7039.21)", "answer_expr": "83.9" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 839/10" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#83.9,5E-2", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "7039.21 √x" ], "calculator_value": "+839E-1", "printed_value": "83.9", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/13", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 13", "problem_latex": "$\\sqrt[3]{35.287552}$.", "markdown": "$\\sqrt[3]{35.287552}$.", "answer_latex": [ "$3.28$." ], "answer_markdown": [ "$3.28$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 3.28, printed 3.28 (half-unit 0.005; correctly rounded at the printed digits: 3.28)", "problem_expr": "root(35.287552, 3)", "answer_expr": "3.28" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 82/25" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#3.28,5E-3", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "35.287552 ENTER 3 GOLD ˣ√y" ], "constants": [ { "value": "3", "source": "the index 3 in the cube-root sign in 'Find the indicated roots: ∛35.287552' (root(35.287552, 3))" } ], "calculator_value": "+3280E-3", "printed_value": "3.28", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/14", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 14", "problem_latex": "$\\sqrt{2550.25}$.", "markdown": "$\\sqrt{2550.25}$.", "answer_latex": [ "$50.5$." ], "answer_markdown": [ "$50.5$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 50.5, printed 50.5 (half-unit 0.05; correctly rounded at the printed digits: 50.5)", "problem_expr": "sqrt(2550.25)", "answer_expr": "50.5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 101/2" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#50.5,5E-2", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/15", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 15", "problem_latex": "$\\sqrt{34.78312}$ to three decimal places.", "markdown": "$\\sqrt{34.78312}$ to three decimal places.", "answer_latex": [ "$5.898-$." ], "answer_markdown": [ "$5.898-$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 5.89772159397, printed 5.898 (half-unit 0.0005; correctly rounded at the printed digits: 5.898)", "problem_expr": "sqrt(34.78312)", "answer_expr": "5.898" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: sqrt(2173945)/250" ], "shape": [ "evaluate: N*N**N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#5.898,5E-4", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/16", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 16", "problem_latex": "$\\sqrt{7}$ to three decimal places.", "markdown": "$\\sqrt{7}$ to three decimal places.", "answer_latex": [ "$2.646-$." ], "answer_markdown": [ "$2.646-$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 2.64575131106, printed 2.646 (half-unit 0.0005; correctly rounded at the printed digits: 2.646)", "problem_expr": "sqrt(7)", "answer_expr": "2.646" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: sqrt(7)" ], "shape": [ "evaluate: N**N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#2.646-,5E-5", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/17", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 17", "problem_latex": "$\\sqrt[3]{.1255}$ to three decimal places.", "markdown": "$\\sqrt[3]{.1255}$ to three decimal places.", "answer_latex": [ "$.501-$." ], "answer_markdown": [ "$.501-$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 0.500665779748, printed 0.501 (half-unit 0.0005; correctly rounded at the printed digits: 0.501)", "problem_expr": "root(Rational(1255, 10000), 3)", "answer_expr": "Rational(501, 1000)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 2**(2/3)*251**(1/3)/20" ], "shape": [ "evaluate: N*N**(2*N)" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#0.501,5E-4", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/18", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 18", "problem_latex": "A merchant bought a bale of cloth containing just as many\npieces as there were yards in each piece. The whole number of\nyards was 1089. What was the number of pieces?", "markdown": "A merchant bought a bale of cloth containing just as many pieces as there were yards in each piece. The whole number of yards was 1089. What was the number of pieces?", "answer_latex": [ "$33$ pieces." ], "answer_markdown": [ "$33$ pieces." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 33}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x**2, 1089)" ], "shape": [ "solve: Eq(x**N, N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "1089 √x" ], "calculator_value": "+33E+0", "printed_value": "33", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/19", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 19", "problem_latex": "A regiment, consisting of 5476 men, is to be formed into a\nsolid square. How many men must be placed in each rank?", "markdown": "A regiment, consisting of 5476 men, is to be formed into a solid square. How many men must be placed in each rank?", "answer_latex": [ "$74$ men." ], "answer_markdown": [ "$74$ men." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 74}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x**2, 5476)" ], "shape": [ "solve: Eq(x**N, N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "5476 √x" ], "calculator_value": "+74E+0", "printed_value": "74", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/2", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 2", "problem_latex": "$\\sqrt{9409}$.", "markdown": "$\\sqrt{9409}$.", "answer_latex": [ "$97$." ], "answer_markdown": [ "$97$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 97.0, printed 97 (half-unit 0.5; correctly rounded at the printed digits: 97.0)", "problem_expr": "sqrt(9409)", "answer_expr": "97" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 97" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#97,5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/20", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 20", "problem_latex": "What is the depth of a cubical cistern which contains 5000\ngallons of water? (1 gallon = 231 cubic inches.)", "markdown": "What is the depth of a cubical cistern which contains 5000 gallons of water? (1 gallon = 231 cubic inches.)", "answer_latex": [ "$104.9+$ in." ], "answer_markdown": [ "$104.9+$ in." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 104.9}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x**3, 1155000)" ], "shape": [ "solve: Eq(x**N, N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/21", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 21", "problem_latex": "A farmer plants an orchard containing 8464 trees, and has as\nmany rows of trees as there are trees in each row. What is the\nnumber of trees in each row?", "markdown": "A farmer plants an orchard containing 8464 trees, and has as many rows of trees as there are trees in each row. What is the number of trees in each row?", "answer_latex": [ "$92$ trees." ], "answer_markdown": [ "$92$ trees." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 92}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x**2, 8464)" ], "shape": [ "solve: Eq(x**N, N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "8464 √x" ], "calculator_value": "+92E+0", "printed_value": "92", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/3", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 3", "problem_latex": "$\\sqrt{20449}$.", "markdown": "$\\sqrt{20449}$.", "answer_latex": [ "$143$." ], "answer_markdown": [ "$143$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 143.0, printed 143 (half-unit 0.5; correctly rounded at the printed digits: 143.0)", "problem_expr": "sqrt(20449)", "answer_expr": "143" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 143" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#143,5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/4", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 4", "problem_latex": "$\\sqrt{904401}$.", "markdown": "$\\sqrt{904401}$.", "answer_latex": [ "$951$." ], "answer_markdown": [ "$951$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 951.0, printed 951 (half-unit 0.5; correctly rounded at the printed digits: 951.0)", "problem_expr": "sqrt(904401)", "answer_expr": "951" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 951" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#951,5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/5", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 5", "problem_latex": "$\\sqrt{70.56}$.", "markdown": "$\\sqrt{70.56}$.", "answer_latex": [ "$8.4$." ], "answer_markdown": [ "$8.4$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 8.4, printed 8.4 (half-unit 0.05; correctly rounded at the printed digits: 8.4)", "problem_expr": "sqrt(70.56)", "answer_expr": "8.4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 42/5" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#8.4,5E-2", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "70.56 √x" ], "calculator_value": "+84E-1", "printed_value": "8.4", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/6", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 6", "problem_latex": "$\\sqrt{.9025}$.", "markdown": "$\\sqrt{.9025}$.", "answer_latex": [ "$.95$." ], "answer_markdown": [ "$.95$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 0.95, printed .95 (half-unit 0.005; correctly rounded at the printed digits: 0.95)", "problem_expr": "sqrt(0.9025)", "answer_expr": "0.95" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 19/20" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#.95,5E-3", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/7", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 7", "problem_latex": "$\\sqrt{94864}$.", "markdown": "$\\sqrt{94864}$.", "answer_latex": [ "$308$." ], "answer_markdown": [ "$308$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 308.0, printed 308 (half-unit 0.5; correctly rounded at the printed digits: 308.0)", "problem_expr": "sqrt(94864)", "answer_expr": "308" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 308" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#308,5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/8", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 8", "problem_latex": "$\\sqrt{.00000784}$", "markdown": "$\\sqrt{.00000784}$", "answer_latex": [ "$.0028$." ], "answer_markdown": [ "$.0028$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 0.0028, printed .0028 (half-unit 5.0e-5; correctly rounded at the printed digits: 0.0028)", "problem_expr": "sqrt(0.00000784)", "answer_expr": "0.0028" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 7/2500" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#.0028,5E-5", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-30/9", "set": "boyden-first-book-in-algebra-1895/ex-30", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 30, problem 9", "problem_latex": "$\\sqrt[3]{59.319}$.", "markdown": "$\\sqrt[3]{59.319}$.", "answer_latex": [ "$3.9$." ], "answer_markdown": [ "$3.9$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 3.9, printed 3.9 (half-unit 0.05; correctly rounded at the printed digits: 3.9)", "problem_expr": "root(59.319, 3)", "answer_expr": "3.9" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 39/10" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#3.9,5E-2", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "59.319 ENTER 3 1/x yˣ" ], "constants": [ { "value": "3", "source": "the index 3 in the cube root √[3]{59.319}" }, { "value": "59.319", "source": "the radicand in the problem text √[3]{59.319}" } ], "calculator_value": "+3899999999999999999999999999999999E-33", "printed_value": "3.9", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/1", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 1", "problem_latex": "$5a^2 - 25$.", "markdown": "$5a^2 - 25$.", "answer_latex": [ "$5(a^2-5)$" ], "answer_markdown": [ "$5(a^2-5)$" ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "5*a**2 - 25", "answer_expr": "5*(a**2 - 5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 5*a**2 - 25" ], "shape": [ "factor: N*a**N + N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/10", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 10", "problem_latex": "$7x - 7x^3 +14x^4$.", "markdown": "$7x - 7x^3 +14x^4$.", "answer_latex": [ "$7x(1-x^2+2x^3)$." ], "answer_markdown": [ "$7x(1-x^2+2x^3)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "7*x - 7*x**3 + 14*x**4", "answer_expr": "7*x*(1 - x**2 + 2*x**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 14*a**4 - 7*a**3 + 7*a" ], "shape": [ "factor: N*a + 2*N*a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/11", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 11", "problem_latex": "$3x^3 - x^2 + x$.", "markdown": "$3x^3 - x^2 + x$.", "answer_latex": [ "$x(3x^2-x+1)$." ], "answer_markdown": [ "$x(3x^2-x+1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "3*x**3 - x**2 + x", "answer_expr": "x*(3*x**2 - x + 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 3*a**3 - a**2 + a" ], "shape": [ "factor: N*a**N + a - a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/12", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 12", "problem_latex": "$a^3 - a^2 y + ay^2$.", "markdown": "$a^3 - a^2 y + ay^2$.", "answer_latex": [ "$a(a^2-ay+y^2)$." ], "answer_markdown": [ "$a(a^2-ay+y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**3 - a**2*y + a*y**2", "answer_expr": "a*(a**2 - a*y + y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**3 - a**2*b + a*b**2" ], "shape": [ "factor: a*b**N - a**N*b + a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/13", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 13", "problem_latex": "$3a(x + y) + 5mb(x + y) - 9d^2 x(x + y)$.", "markdown": "$3a(x + y) + 5mb(x + y) - 9d^2 x(x + y)$.", "answer_latex": [ "$(x+y)(3a+5mb-9d^2x)$." ], "answer_markdown": [ "$(x+y)(3a+5mb-9d^2x)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "3*a*(x + y) + 5*m*b*(x + y) - 9*d**2*x*(x + y)", "answer_expr": "(x + y)*(3*a + 5*m*b - 9*d**2*x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 3*a*(e + f) + 5*b*d*(e + f) - 9*c**2*e*(e + f)" ], "shape": [ "factor: N*a*(e + f) + N*b*d*(e + f) + N*c**N*e*(e + f)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/14", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 14", "problem_latex": "$4(a - b) - 15 x y (a - b) + (a - b) - 5 a^2 b(a - b)$.", "markdown": "$4(a - b) - 15 x y (a - b) + (a - b) - 5 a^2 b(a - b)$.", "answer_latex": [ "$5(a-b)(1-3xy-a^2b)$." ], "answer_markdown": [ "$5(a-b)(1-3xy-a^2b)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "4*(a - b) - 15*x*y*(a - b) + (a - b) - 5*a**2*b*(a - b)", "answer_expr": "5*(a - b)*(1 - 3*x*y - a**2*b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -5*a**2*b*(a - b) + 5*a - 5*b - 15*c*d*(a - b)" ], "shape": [ "factor: N*a + N*a**N*b*(a - b) + N*b + N*c*d*(a - b)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/15", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 15", "problem_latex": "$4x^3 y - 12a x^2 - 8 x y^3$.", "markdown": "$4x^3 y - 12a x^2 - 8 x y^3$.", "answer_latex": [ "$4xy(x^2-3xy-2y^2)$." ], "answer_markdown": [ "$4xy(x^2-3xy-2y^2)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "-299.19683810842275825", "-483.56795700815491324" ], "problem_expr": "4*x**3*y - 12*a*x**2 - 8*x*y**3", "answer_expr": "4*x*y*(x**2 - 3*x*y - 2*y**2)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: -12*a*b**2 + 4*b**3*c - 8*b*c**3" ], "shape": [ "factor: N*a*b**N + N*b*c**N + N*b**N*c" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/16", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 16", "problem_latex": "$6 a x^3 y^5 - 4 a x^2 y^6 + 2 a x y^7 - 2 a^2 x y^9$.", "markdown": "$6 a x^3 y^5 - 4 a x^2 y^6 + 2 a x y^7 - 2 a^2 x y^9$.", "answer_latex": [ "$2axy^5(3x^2-2xy+y^2-ay^4)$." ], "answer_markdown": [ "$2axy^5(3x^2-2xy+y^2-ay^4)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "6*a*x**3*y**5 - 4*a*x**2*y**6 + 2*a*x*y**7 - 2*a**2*x*y**9", "answer_expr": "2*a*x*y**5*(3*x**2 - 2*x*y + y**2 - a*y**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -2*a**2*b*c**9 + 6*a*b**3*c**5 - 4*a*b**2*c**6 + 2*a*b*c**7" ], "shape": [ "factor: N*a*b*c**N + 2*N*a*b**N*c**N + N*a**N*b*c**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/17", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 17", "problem_latex": "$51 x^5 y - 34 x^4 y^2 + 17 x^2 y^4$.", "markdown": "$51 x^5 y - 34 x^4 y^2 + 17 x^2 y^4$.", "answer_latex": [ "$17x^2y(3x^3-2x^2y+y^3)$." ], "answer_markdown": [ "$17x^2y(3x^3-2x^2y+y^3)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "51*x**5*y - 34*x**4*y**2 + 17*x**2*y**4", "answer_expr": "17*x**2*y*(3*x**3 - 2*x**2*y + y**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 51*a**5*b - 34*a**4*b**2 + 17*a**2*b**4" ], "shape": [ "factor: N*a**N*b + 2*N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/18", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 18", "problem_latex": "$6 a^2 b^2 - 3 a^3 b^3 c - 9 a b^3 c + 3 abc^2$.", "markdown": "$6 a^2 b^2 - 3 a^3 b^3 c - 9 a b^3 c + 3 abc^2$.", "answer_latex": [ "$3ab(2ab-a^2b^2c-3b^2c+c^2)$." ], "answer_markdown": [ "$3ab(2ab-a^2b^2c-3b^2c+c^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "6*a**2*b**2 - 3*a**3*b**3*c - 9*a*b**3*c + 3*a*b*c**2", "answer_expr": "3*a*b*(2*a*b - a**2*b**2*c - 3*b**2*c + c**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -3*a**3*b**3*c + 6*a**2*b**2 - 9*a*b**3*c + 3*a*b*c**2" ], "shape": [ "factor: N*a*b*c**N + N*a*b**N*c + N*a**N*b**N*c + N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/19", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 19", "problem_latex": "$3 a x^7 - 24 a x + 9 ax^5 - 3 ax^4 - 9 ax^6$.", "markdown": "$3 a x^7 - 24 a x + 9 ax^5 - 3 ax^4 - 9 ax^6$.", "answer_latex": [ "$3ax(x^6-8+3x^4-x^3-3x^5)$." ], "answer_markdown": [ "$3ax(x^6-8+3x^4-x^3-3x^5)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "3*a*x**7 - 24*a*x + 9*a*x**5 - 3*a*x**4 - 9*a*x**6", "answer_expr": "3*a*x*(x**6 - 8 + 3*x**4 - x**3 - 3*x**5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 3*a*b**7 - 9*a*b**6 + 9*a*b**5 - 3*a*b**4 - 24*a*b" ], "shape": [ "factor: N*a*b + 4*N*a*b**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/2", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 2", "problem_latex": "$16 + 64xy$.", "markdown": "$16 + 64xy$.", "answer_latex": [ "$16(1+4xy)$." ], "answer_markdown": [ "$16(1+4xy)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "16 + 64*x*y", "answer_expr": "16*(1 + 4*x*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 64*a*b + 16" ], "shape": [ "factor: N*a*b + N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/20", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 20", "problem_latex": "$27 a^8 b^2 c^3 - 81 a^7 b^3 c^3 + 81 a^6 b^4 c^3 - 27 a^5\nb^5 c^3 - 27 a^5 b^2 c^6$.", "markdown": "$27 a^8 b^2 c^3 - 81 a^7 b^3 c^3 + 81 a^6 b^4 c^3 - 27 a^5 b^5 c^3 - 27 a^5 b^2 c^6$.", "answer_latex": [ "$27a^5b^2c^3(a^3-3a^2b+3ab^2-b^3-c^3)$." ], "answer_markdown": [ "$27a^5b^2c^3(a^3-3a^2b+3ab^2-b^3-c^3)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "27*a**8*b**2*c**3 - 81*a**7*b**3*c**3 + 81*a**6*b**4*c**3 - 27*a**5*b**5*c**3 - 27*a**5*b**2*c**6", "answer_expr": "27*a**5*b**2*c**3*(a**3 - 3*a**2*b + 3*a*b**2 - b**3 - c**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 27*a**8*b**2*c**3 - 81*a**7*b**3*c**3 + 81*a**6*b**4*c**3 - 27*a**5*b**5*c**3 - 27*a**5*b**2*c**6" ], "shape": [ "factor: 5*N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/21", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 21", "problem_latex": "A lady bought a ribbon for $m$ cents, some tape for $d$\ncents, and some thread for $c$ cents, for which she paid $x$ cents\non account. How much remains due?", "markdown": "A lady bought a ribbon for $m$ cents, some tape for $d$ cents, and some thread for $c$ cents, for which she paid $x$ cents on account. How much remains due?", "answer_latex": [ "$m+d+c-x$ cts." ], "answer_markdown": [ "$m+d+c-x$ cts." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{R: m + d + c - x}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(d + x, a + b + c)" ], "shape": [ "solve: Eq(d + x, a + b + c)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/22", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 22", "problem_latex": "Julia has the same number of beads in each hand. If she\nshould change two from her left hand to her right hand, the right\nhand would contain twice as many as the left. How many beads has\nshe?", "markdown": "Julia has the same number of beads in each hand. If she should change two from her left hand to her right hand, the right hand would contain twice as many as the left. How many beads has she?", "answer_latex": [ "$12$ beads." ], "answer_markdown": [ "$12$ beads." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{n: 6, B: 12}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(x + 2, 2*x - 4))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N + x, N*x + N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/3", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 3", "problem_latex": "$2a - 2a^2$.", "markdown": "$2a - 2a^2$.", "answer_latex": [ "$2a(1-a)$." ], "answer_markdown": [ "$2a(1-a)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "2*a - 2*a**2", "answer_expr": "2*a*(1 - a)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -2*a**2 + 2*a" ], "shape": [ "factor: N*a + N*a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/4", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 4", "problem_latex": "$15a^2 - 225a^4$.", "markdown": "$15a^2 - 225a^4$.", "answer_latex": [ "$15a^2(1-15a^2)$." ], "answer_markdown": [ "$15a^2(1-15a^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "15*a**2 - 225*a**4", "answer_expr": "15*a**2*(1 - 15*a**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -225*a**4 + 15*a**2" ], "shape": [ "factor: 2*N*a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/5", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 5", "problem_latex": "$x^3 - x^2$.", "markdown": "$x^3 - x^2$.", "answer_latex": [ "$x^2(x-1)$." ], "answer_markdown": [ "$x^2(x-1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**3 - x**2", "answer_expr": "x**2*(x - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**3 - a**2" ], "shape": [ "factor: 0" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/6", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 6", "problem_latex": "$3a^2 + a^5$.", "markdown": "$3a^2 + a^5$.", "answer_latex": [ "$a^2(3+a^3)$." ], "answer_markdown": [ "$a^2(3+a^3)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "3*a**2 + a**5", "answer_expr": "a**2*(3 + a**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**5 + 3*a**2" ], "shape": [ "factor: N*a**N + a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/7", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 7", "problem_latex": "$a^2 - ab^2$.", "markdown": "$a^2 - ab^2$.", "answer_latex": [ "$a(a-b^2)$." ], "answer_markdown": [ "$a(a-b^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 - a*b**2", "answer_expr": "a*(a - b**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2 - a*b**2" ], "shape": [ "factor: -a*b**N + a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/8", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 8", "problem_latex": "$a^2 + ab$.", "markdown": "$a^2 + ab$.", "answer_latex": [ "$a(a+b)$." ], "answer_markdown": [ "$a(a+b)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 + a*b", "answer_expr": "a*(a + b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2 + a*b" ], "shape": [ "factor: a*b + a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-31/9", "set": "boyden-first-book-in-algebra-1895/ex-31", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 31, problem 9", "problem_latex": "$6a^3 + 2a^4 + 4a^5$.", "markdown": "$6a^3 + 2a^4 + 4a^5$.", "answer_latex": [ "$2a^3(3+a+2a^2)$." ], "answer_markdown": [ "$2a^3(3+a+2a^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "6*a**3 + 2*a**4 + 4*a**5", "answer_expr": "2*a**3*(3 + a + 2*a**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 4*a**5 + 2*a**4 + 6*a**3" ], "shape": [ "factor: 3*N*a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/1", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 1", "problem_latex": "$ax+ay+bx+by$.", "markdown": "$ax+ay+bx+by$.", "answer_latex": [ "$(a+b)(x+y)$." ], "answer_markdown": [ "$(a+b)(x+y)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a*x+a*y+b*x+b*y", "answer_expr": "(a+b)*(x+y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a*c + a*x + b*c + b*x" ], "shape": [ "factor: a*c + a*x + b*c + b*x" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/10", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 10", "problem_latex": "$y^3-y^2+y-1$.", "markdown": "$y^3-y^2+y-1$.", "answer_latex": [ "$(y^2 + 1)(y - 1)$." ], "answer_markdown": [ "$(y^2 + 1)(y - 1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "y**3-y**2+y-1", "answer_expr": "(y**2+1)*(y-1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**3 - x**2 + x - 1" ], "shape": [ "factor: x - 1" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-32/2", "wentworth-first-steps-in-algebra-1894/ex-39/22" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/11", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 11", "problem_latex": "$x^5+x^4-x^3-x^2+x+1$.", "markdown": "$x^5+x^4-x^3-x^2+x+1$.", "answer_latex": [ "$(x^4 - x^2 + 1)(x + 1)$." ], "answer_markdown": [ "$(x^4 - x^2 + 1)(x + 1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**5+x**4-x**3-x**2+x+1", "answer_expr": "(x**4-x**2+1)*(x+1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**5 + x**4 - x**3 - x**2 + x + 1" ], "shape": [ "factor: x + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/12", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 12", "problem_latex": "$a^2x+abx+ac+aby+b^2y+bc$.", "markdown": "$a^2x+abx+ac+aby+b^2y+bc$.", "answer_latex": [ "$(ax + by + c)(a + b)$." ], "answer_markdown": [ "$(ax + by + c)(a + b)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2*x+a*b*x+a*c+a*b*y+b**2*y+b*c", "answer_expr": "(a*x+b*y+c)*(a+b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2*x + a*b*d + a*b*x + a*c + b**2*d + b*c" ], "shape": [ "factor: a*b*d + a*b*x + a*c + a**N*x + b*c + b**N*d" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/13", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 13", "problem_latex": "$ax-bx+by+cy-cx-ay$.", "markdown": "$ax-bx+by+cy-cx-ay$.", "answer_latex": [ "$(a - b - c)(x - y)$." ], "answer_markdown": [ "$(a - b - c)(x - y)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a*x-b*x+b*y+c*y-c*x-a*y", "answer_expr": "(a-b-c)*(x-y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a*d + a*x + b*d - b*x + c*d - c*x" ], "shape": [ "factor: -a*d + a*x + b*d - b*x + c*d - c*x" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-32/11" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/14", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 14", "problem_latex": "$3ax+3ay-2bx-2by$.", "markdown": "$3ax+3ay-2bx-2by$.", "answer_latex": [ "$(3a - 2b)(x + y)$." ], "answer_markdown": [ "$(3a - 2b)(x + y)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "3*a*x+3*a*y-2*b*x-2*b*y", "answer_expr": "(3*a-2*b)*(x+y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 3*a*c + 3*a*x - 2*b*c - 2*b*x" ], "shape": [ "factor: N*a*c + N*a*x + N*b*c + N*b*x" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/15", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 15", "problem_latex": "$2ax-3by+cy-2ay+3bx-cx$.", "markdown": "$2ax-3by+cy-2ay+3bx-cx$.", "answer_latex": [ "$(2a + 3b - c)(x - y)$." ], "answer_markdown": [ "$(2a + 3b - c)(x - y)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "2*a*x-3*b*y+c*y-2*a*y+3*b*x-c*x", "answer_expr": "(2*a+3*b-c)*(x-y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -2*a*d + 2*a*x - 3*b*d + 3*b*x + c*d - c*x" ], "shape": [ "factor: N*a*d + N*a*x + N*b*d + N*b*x + c*d - c*x" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/16", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 16", "problem_latex": "$6amx+3amy-6anx-3any$.", "markdown": "$6amx+3amy-6anx-3any$.", "answer_latex": [ "$3a(2x + y)(m - n)$." ], "answer_markdown": [ "$3a(2x + y)(m - n)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "6*a*m*x+3*a*m*y-6*a*n*x-3*a*n*y", "answer_expr": "3*a*(2*x+y)*(m-n)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 3*a*b*d + 6*a*b*x - 3*a*c*d - 6*a*c*x" ], "shape": [ "factor: N*a*b*d + N*a*b*x + N*a*c*d + N*a*c*x" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/17", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 17", "problem_latex": "A man had 250 acres of land and 30 houses. After trading $x$\nof his houses for $y$ acres of land, how many has he of each?", "markdown": "A man had 250 acres of land and 30 houses. After trading $x$ of his houses for $y$ acres of land, how many has he of each?", "answer_latex": [ "$250 + yA.; $30 - x$ horses." ], "answer_markdown": [ "$250 + yA.; $30 - x$ horses." ], "checks": [ { "task": "other", "verdict": "FLAG-EXTRACTION", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/18", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 18", "problem_latex": "What is the number that will become four times as large by\nadding 36 to it?", "markdown": "What is the number that will become four times as large by adding 36 to it?", "answer_latex": [ "$12$." ], "answer_markdown": [ "$12$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 12}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x + 36, 4*x)" ], "shape": [ "solve: Eq(N + x, N*x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "36 ENTER 4 ENTER 1 −", "÷" ], "constants": [ { "value": "4", "source": "the 'four times' in the problem, the 4 in 4x of Eq(x + 36, 4*x)" }, { "value": "1", "source": "the implicit coefficient of x on the left side, x + 36 = 1·x + 36; the working 4x − x = 3x, so 36 = 3x and x = 36 ÷ (4 − 1)" } ], "calculator_value": "+12E+0", "printed_value": "12", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/19", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 19", "problem_latex": "The fifth and seventh of a number are together equal to 24.\nWhat is the number?", "markdown": "The fifth and seventh of a number are together equal to 24. What is the number?", "answer_latex": [ "$70$." ], "answer_markdown": [ "$70$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 70}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(12*x/35, 24)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "5 1/x 7 1/x +", "24 x↔y ÷" ], "constants": [ { "value": "5", "source": "the fifth in 'The fifth and seventh of a number'" }, { "value": "7", "source": "the seventh in 'The fifth and seventh of a number'" }, { "value": "24", "source": "the right-hand side in 'are together equal to 24'" } ], "calculator_value": "+6999999999999999999999999999999999E-32", "printed_value": "70", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/2", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 2", "problem_latex": "$x^2+ax+bx+ab$.", "markdown": "$x^2+ax+bx+ab$.", "answer_latex": [ "$(x+b)(x+a)$." ], "answer_markdown": [ "$(x+b)(x+a)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2+a*x+b*x+a*b", "answer_expr": "(x+b)*(x+a)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a*b + a*x + b*x + x**2" ], "shape": [ "factor: a*b + a*x + b*x + x**N" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-32/3" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/3", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 3", "problem_latex": "$ax^2+ay^2-bx^2-by^2$.", "markdown": "$ax^2+ay^2-bx^2-by^2$.", "answer_latex": [ "$(a-b)(x^2+y^2)$." ], "answer_markdown": [ "$(a-b)(x^2+y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a*x**2+a*y**2-b*x**2-b*y**2", "answer_expr": "(a-b)*(x**2+y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a*c**2 + a*x**2 - b*c**2 - b*x**2" ], "shape": [ "factor: a*c**N + a*x**N - b*c**N - b*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/4", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 4", "problem_latex": "$x^2-ax+5x-5a$.", "markdown": "$x^2-ax+5x-5a$.", "answer_latex": [ "$(x+5)(x-a)$." ], "answer_markdown": [ "$(x+5)(x-a)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2-a*x+5*x-5*a", "answer_expr": "(x+5)*(x-a)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a*x - 5*a + x**2 + 5*x" ], "shape": [ "factor: N*a + N*x - a*x + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/5", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 5", "problem_latex": "$ax-bx+ab-x^2$.", "markdown": "$ax-bx+ab-x^2$.", "answer_latex": [ "$(a-x)(x+b)$." ], "answer_markdown": [ "$(a-x)(x+b)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a*x-b*x+a*b-x**2", "answer_expr": "(a-x)*(x+b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a*b + a*x - b*x - x**2" ], "shape": [ "factor: a*b + a*x - b*x - x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/6", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 6", "problem_latex": "$x^2+mxy-4xy-4my^2$.", "markdown": "$x^2+mxy-4xy-4my^2$.", "answer_latex": [ "$(x-4y)(x+my)$." ], "answer_markdown": [ "$(x-4y)(x+my)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2+m*x*y-4*x*y-4*m*y**2", "answer_expr": "(x-4*y)*(x+m*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -4*a*b**2 + a*b*x - 4*b*x + x**2" ], "shape": [ "factor: N*a*b**N + N*b*x + a*b*x + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/7", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 7", "problem_latex": "$2x^4-x^3+4x-2$.", "markdown": "$2x^4-x^3+4x-2$.", "answer_latex": [ "$(x^3+2)(2x-1)$." ], "answer_markdown": [ "$(x^3+2)(2x-1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "2*x**4-x**3+4*x-2", "answer_expr": "(x**3+2)*(2*x-1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 2*x**4 - x**3 + 4*x - 2" ], "shape": [ "factor: N*x + N*x**N + N - x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/8", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 8", "problem_latex": "$mx-ma-nx+na$.", "markdown": "$mx-ma-nx+na$.", "answer_latex": [ "$(m-n)(x-a)$." ], "answer_markdown": [ "$(m-n)(x-a)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "m*x-m*a-n*x+n*a", "answer_expr": "(m-n)*(x-a)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a*b + a*c + b*x - c*x" ], "shape": [ "factor: -a*b + a*c + b*x - c*x" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-32/9", "set": "boyden-first-book-in-algebra-1895/ex-32", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 32, problem 9", "problem_latex": "$x^3+x^2+x+1$.", "markdown": "$x^3+x^2+x+1$.", "answer_latex": [ "$(x^2+1)(x+1)$." ], "answer_markdown": [ "$(x^2+1)(x+1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**3+x**2+x+1", "answer_expr": "(x**2+1)*(x+1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**3 + x**2 + x + 1" ], "shape": [ "factor: x + 2*x**N + 1" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-32/1" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/1", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 1", "problem_latex": "$x^2-y^2$.", "markdown": "$x^2-y^2$.", "answer_latex": [ "$(x+y)(x-y)$." ], "answer_markdown": [ "$(x+y)(x-y)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2 - y**2", "answer_expr": "(x + y)*(x - y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**2 + x**2" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-33/2" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/10", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 10", "problem_latex": "$16m^2-9n^2$.", "markdown": "$16m^2-9n^2$.", "answer_latex": [ "$(4m - 3n)(4m + 3n)$." ], "answer_markdown": [ "$(4m - 3n)(4m + 3n)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "16*m**2 - 9*n**2", "answer_expr": "(4*m - 3*n)*(4*m + 3*n)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -9*a**2 + 16*x**2" ], "shape": [ "factor: N*a**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/11", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 11", "problem_latex": "$81x^2y^4-25b^2d^2$.", "markdown": "$81x^2y^4-25b^2d^2$.", "answer_latex": [ "$(9xy^2 - 5bd)(9xy^2 - 5bd)$." ], "answer_markdown": [ "$(9xy^2 - 5bd)(9xy^2 - 5bd)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "15438.481136531468089", "14296.577035211102109" ], "problem_expr": "81*x**2*y**4 - 25*b**2*d**2", "answer_expr": "(9*x*y**2 - 5*b*d)*(9*x*y**2 - 5*b*d)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: -25*a**2*b**2 + 81*c**4*x**2" ], "shape": [ "factor: N*a**N*b**N + N*c**N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/12", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 12", "problem_latex": "$729m^4c^2x^{10}-10,000y^4$.", "markdown": "$729m^4c^2x^{10}-10,000y^4$.", "answer_latex": [ "$(27m^2cx^5 + 100y^2)(27m^2cx^5 - 100y^2)$." ], "answer_markdown": [ "$(27m^2cx^5 + 100y^2)(27m^2cx^5 - 100y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "729*m**4*c**2*x**10 - 10000*y**4", "answer_expr": "(27*m**2*c*x**5 + 100*y**2)*(27*m**2*c*x**5 - 100*y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 729*a**2*b**10*x**4 - 10000*c**4" ], "shape": [ "factor: N*a**N*b**N*x**N + N*c**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/13", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 13", "problem_latex": "$121m^2-64x^2$.", "markdown": "$121m^2-64x^2$.", "answer_latex": [ "$(11m + 8x)(11m - 8x)$." ], "answer_markdown": [ "$(11m + 8x)(11m - 8x)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "121*m**2 - 64*x**2", "answer_expr": "(11*m + 8*x)*(11*m - 8*x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -64*a**2 + 121*x**2" ], "shape": [ "factor: N*a**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/14", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 14", "problem_latex": "$x^4-y^4$.", "markdown": "$x^4-y^4$.", "answer_latex": [ "$(x^2 + y^2)(x + y)(x - y)$." ], "answer_markdown": [ "$(x^2 + y^2)(x + y)(x - y)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**4 - y**4", "answer_expr": "(x**2 + y**2)*(x + y)*(x - y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**4 + x**4" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/15", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 15", "problem_latex": "$m^8 - a^8$.", "markdown": "$m^8 - a^8$.", "answer_latex": [ "$(m^4 + a^4)(m^2 + a^2)(m + a)(m - a)$." ], "answer_markdown": [ "$(m^4 + a^4)(m^2 + a^2)(m + a)(m - a)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "m**8 - a**8", "answer_expr": "(m**4 + a**4)*(m**2 + a**2)*(m + a)*(m - a)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**8 + x**8" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/16", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 16", "problem_latex": "$a^4b^8 - l$.", "markdown": "$a^4b^8 - l$.", "answer_latex": [ "$(a^4b^4 + 1)(a^2b^2 + 1)(ab + 1)(ab - 1)$." ], "answer_markdown": [ "$(a^4b^4 + 1)(a^2b^2 + 1)(ab + 1)(ab - 1)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "18865.422092896495661", "188448.4331778790946" ], "problem_expr": "a**4*b**8 - l", "answer_expr": "(a**4*b**4 + 1)*(a**2*b**2 + 1)*(a*b + 1)*(a*b - 1)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: a**8*x**4 - b" ], "shape": [ "factor: a**N*x**N - b" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/17", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 17", "problem_latex": "$x^16 - b^16$.", "markdown": "$x^16 - b^16$.", "answer_latex": [ "$(x^8 + b^8)(x^4 + b^4)(x^2 + b^2)(x + b)(x - b)$." ], "answer_markdown": [ "$(x^8 + b^8)(x^4 + b^4)(x^2 + b^2)(x + b)(x - b)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**16 - b**16", "answer_expr": "(x**8 + b**8)*(x**4 + b**4)*(x**2 + b**2)*(x + b)*(x - b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**16 + x**16" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-54/76c" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/18", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 18", "problem_latex": "$16a^4 - 1$.", "markdown": "$16a^4 - 1$.", "answer_latex": [ "$(4a^2 + 1)(2a + 1)(2a - 1)$." ], "answer_markdown": [ "$(4a^2 + 1)(2a + 1)(2a - 1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "16*a**4 - 1", "answer_expr": "(4*a**2 + 1)*(2*a + 1)*(2*a - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 16*x**4 - 1" ], "shape": [ "factor: N*x**N - 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/19", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 19", "problem_latex": "$a^4 - ax^2$.", "markdown": "$a^4 - ax^2$.", "answer_latex": [ "$a(a + x)(a - x)$." ], "answer_markdown": [ "$a(a + x)(a - x)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "15.750865051903114187", "7.7508650519031141869" ], "problem_expr": "a**4 - a*x**2", "answer_expr": "a*(a + x)*(a - x)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: -a**2*x + x**4" ], "shape": [ "factor: -a**N*x + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/2", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 2", "problem_latex": "$m^2-n^2$.", "markdown": "$m^2-n^2$.", "answer_latex": [ "$(m + n)(m - n)$." ], "answer_markdown": [ "$(m + n)(m - n)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "m**2 - n**2", "answer_expr": "(m + n)*(m - n)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**2 + x**2" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-33/1" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/20", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 20", "problem_latex": "$5b^4 - 5a^2b^2$.", "markdown": "$5b^4 - 5a^2b^2$.", "answer_latex": [ "$5b^2(b + a)(b - a)$." ], "answer_markdown": [ "$5b^2(b + a)(b - a)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "5*b**4 - 5*a**2*b**2", "answer_expr": "5*b**2*(b + a)*(b - a)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -5*a**2*x**2 + 5*x**4" ], "shape": [ "factor: N*a**N*x**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/21", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 21", "problem_latex": "$ax^2 - ay^2 - bx^2 + by^2$.", "markdown": "$ax^2 - ay^2 - bx^2 + by^2$.", "answer_latex": [ "$(a - b)(x + y)(x - y)$." ], "answer_markdown": [ "$(a - b)(x + y)(x - y)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a*x**2 - a*y**2 - b*x**2 + b*y**2", "answer_expr": "(a - b)*(x + y)*(x - y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a*b**2 + a*c**2 + b**2*x - c**2*x" ], "shape": [ "factor: -a*b**N + a*c**N + b**N*x - c**N*x" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/22", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 22", "problem_latex": "$5ax - 5a^3x + 5ay - 5a^3y$.", "markdown": "$5ax - 5a^3x + 5ay - 5a^3y$.", "answer_latex": [ "$5a(a + y)(1 + a)(1 - a)$." ], "answer_markdown": [ "$5a(a + y)(1 + a)(1 - a)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "-231.70350196176642458", "-277.07025910663526491" ], "problem_expr": "5*a*x - 5*a**3*x + 5*a*y - 5*a**3*y", "answer_expr": "5*a*(a + y)*(1 + a)*(1 - a)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: -5*a*x**3 + 5*a*x - 5*b*x**3 + 5*b*x" ], "shape": [ "factor: N*a*x + N*a*x**N + N*b*x + N*b*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/23", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 23", "problem_latex": "$m^2 - y^2 - am + ay$.", "markdown": "$m^2 - y^2 - am + ay$.", "answer_latex": [ "$(m + y - a)(m - y)$." ], "answer_markdown": [ "$(m + y - a)(m - y)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "m**2 - y**2 - a*m + a*y", "answer_expr": "(m + y - a)*(m - y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a*b - a*x - b**2 + x**2" ], "shape": [ "factor: a*b - a*x - b**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/24", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 24", "problem_latex": "$a^2 - x^2 - a - x$.", "markdown": "$a^2 - x^2 - a - x$.", "answer_latex": [ "$(a - x + 1)(a + x)$." ], "answer_markdown": [ "$(a - x + 1)(a + x)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "-7.5834331717451523546", "-0.054485803324099722992" ], "problem_expr": "a**2 - x**2 - a - x", "answer_expr": "(a - x + 1)*(a + x)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: -a**2 - a + x**2 - x" ], "shape": [ "factor: -a - a**N - x + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/25", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 25", "problem_latex": "By how much does $x$ exceed $3y$?", "markdown": "By how much does $x$ exceed $3y$?", "answer_latex": [ "$x - 3y$." ], "answer_markdown": [ "$x - 3y$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x - 3*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/26", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 26", "problem_latex": "Eleven years ago C was three times as old as D whose age was\n$x$ years. What is C's present age ?", "markdown": "Eleven years ago C was three times as old as D whose age was $x$ years. What is C’s present age ?", "answer_latex": [ "$3x + 11$ yrs." ], "answer_markdown": [ "$3x + 11$ yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(c - 11, 3*x)", "answer_expr": "3*x + 11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x - 11, 3*a)" ], "shape": [ "solve: Eq(N + x, N*a)" ], "same_problem_in": [], "needs": [ "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/3", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 3", "problem_latex": "$a^2b^4-c^2d^2$.", "markdown": "$a^2b^4-c^2d^2$.", "answer_latex": [ "$(ab^2 + cd)(ab^2 - cd)$." ], "answer_markdown": [ "$(ab^2 + cd)(ab^2 - cd)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2*b**4 - c**2*d**2", "answer_expr": "(a*b**2 + c*d)*(a*b**2 - c*d)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**4*x**2 - b**2*c**2" ], "shape": [ "factor: a**N*x**N - b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/4", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 4", "problem_latex": "$m^2p^4-x^6y^4$.", "markdown": "$m^2p^4-x^6y^4$.", "answer_latex": [ "$(mp^2 - x^3y^2)(mp^2 + x^3y^2)$." ], "answer_markdown": [ "$(mp^2 - x^3y^2)(mp^2 + x^3y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "m**2*p**4 - x**6*y**4", "answer_expr": "(m*p**2 - x**3*y**2)*(m*p**2 + x**3*y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**4*x**2 - b**6*c**4" ], "shape": [ "factor: a**N*x**N - b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/5", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 5", "problem_latex": "$a^6b^2x^4-m^4c^8y^{10}$.", "markdown": "$a^6b^2x^4-m^4c^8y^{10}$.", "answer_latex": [ "$(a^3bx^2 + m^2c^4y^{10})(a^3bx^2 - m^2c^4y^{10})$." ], "answer_markdown": [ "$(a^3bx^2 + m^2c^4y^{10})(a^3bx^2 - m^2c^4y^{10})$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "152230.83976102356772", "-50937804.229230432483" ], "problem_expr": "a**6*b**2*x**4 - m**4*c**8*y**10", "answer_expr": "(a**3*b*x**2 + m**2*c**4*y**10)*(a**3*b*x**2 - m**2*c**4*y**10)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: a**2*d**4*x**6 - b**8*c**4*e**10" ], "shape": [ "factor: a**N*d**N*x**N - b**N*c**N*e**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/6", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 6", "problem_latex": "$x^2y^4z^4-c^2d^2m^4$.", "markdown": "$x^2y^4z^4-c^2d^2m^4$.", "answer_latex": [ "$(xy^2z^2 + cdm^2)(x^2y^2z^2 - cdm^2)$." ], "answer_markdown": [ "$(xy^2z^2 + cdm^2)(x^2y^2z^2 - cdm^2)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "-1754.346921273931883", "-1478.800977278042094" ], "problem_expr": "x**2*y**4*z**4 - c**2*d**2*m**4", "answer_expr": "(x*y**2*z**2 + c*d*m**2)*(x**2*y**2*z**2 - c*d*m**2)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: -a**2*b**2*c**4 + d**4*e**4*x**2" ], "shape": [ "factor: -a**N*b**N*c**N + d**N*e**N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/7", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 7", "problem_latex": "$x^4y^2-a^6y^4$.", "markdown": "$x^4y^2-a^6y^4$.", "answer_latex": [ "$(x^2y +a^3y^2)(x^2y - a^3y^2)$." ], "answer_markdown": [ "$(x^2y +a^3y^2)(x^2y - a^3y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**4*y**2 - a**6*y**4", "answer_expr": "(x**2*y + a**3*y**2)*(x**2*y - a**3*y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**6*b**4 + b**2*x**4" ], "shape": [ "factor: -a**N*b**N + b**N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/8", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 8", "problem_latex": "$g^6c^6-x^6z^8$.", "markdown": "$g^6c^6-x^6z^8$.", "answer_latex": [ "$(g^3c^3 - x^3z^4)(g^3c^3 + x^3z^4)$." ], "answer_markdown": [ "$(g^3c^3 - x^3z^4)(g^3c^3 + x^3z^4)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "g**6*c**6 - x**6*z**8", "answer_expr": "(g**3*c**3 - x**3*z**4)*(g**3*c**3 + x**3*z**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**6*x**6 - b**6*c**8" ], "shape": [ "factor: a**N*x**N - b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-33/9", "set": "boyden-first-book-in-algebra-1895/ex-33", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 33, problem 9", "problem_latex": "$4a^2-9x^2$.", "markdown": "$4a^2-9x^2$.", "answer_latex": [ "$(2a - 3x)(2a + 3x)$." ], "answer_markdown": [ "$(2a - 3x)(2a + 3x)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "4*a**2 - 9*x**2", "answer_expr": "(2*a - 3*x)*(2*a + 3*x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -9*a**2 + 4*x**2" ], "shape": [ "factor: N*a**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/1", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 1", "problem_latex": "$x^5 + y^5$", "markdown": "$x^5 + y^5$", "answer_latex": [ "$(x + y)(x^2 - xy + y^2)$." ], "answer_markdown": [ "$(x + y)(x^2 - xy + y^2)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "446.59606901998070302", "40.189040431429336721" ], "problem_expr": "x**5 + y**5", "answer_expr": "(x + y)*(x**2 - x*y + y**2)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: a**5 + x**5" ], "shape": [ "factor: a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/10", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 10", "problem_latex": "$27 + a^3b^6$", "markdown": "$27 + a^3b^6$", "answer_latex": [ "$(3 + ab^2)(9 -3ab^2 + a^2b^4)$." ], "answer_markdown": [ "$(3 + ab^2)(9 -3ab^2 + a^2b^4)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "27 + a**3*b**6", "answer_expr": "(3 + a*b**2)*(9 - 3*a*b**2 + a**2*b**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**6*x**3 + 27" ], "shape": [ "factor: N + a**N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/11", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 11", "problem_latex": "$y^3 + 1$", "markdown": "$y^3 + 1$", "answer_latex": [ "$(y + 1)(y^2 - y + 1)$." ], "answer_markdown": [ "$(y + 1)(y^2 - y + 1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "y**3 + 1", "answer_expr": "(y + 1)*(y**2 - y + 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**3 + 1" ], "shape": [ "factor: x**N + 1" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-36/1" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/12", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 12", "problem_latex": "$1 + b^3c^3$", "markdown": "$1 + b^3c^3$", "answer_latex": [ "$(1 + bc^3)(1 - bc^3 + b^2c^5)$." ], "answer_markdown": [ "$(1 + bc^3)(1 - bc^3 + b^2c^5)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "105.77259475218658892", "596.61761108492730278" ], "problem_expr": "1 + b**3*c**3", "answer_expr": "(1 + b*c**3)*(1 - b*c**3 + b**2*c**5)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: a**3*x**3 + 1" ], "shape": [ "factor: a**N*x**N + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/13", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 13", "problem_latex": "$\\frac{1}{8}a^6b^3+ c^0$", "markdown": "$\\frac{1}{8}a^6b^3+ c^0$", "answer_latex": [ "$(\\frac{1}{2}a^2b + c^3)(\\frac{1}{4}a^4b^2\n - \\frac{1}{2}a^2bc^3 + c^5)$." ], "answer_markdown": [ "$(\\frac{1}{2}a^2b + c^3)(\\frac{1}{4}a^4b^2 - \\frac{1}{2}a^2bc^3 + c^5)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "1.0002551382999641005", "15180.677632011173207" ], "problem_expr": "Rational(1,8)*a**6*b**3 + c**0", "answer_expr": "(Rational(1,2)*a**2*b + c**3)*(Rational(1,4)*a**4*b**2 - Rational(1,2)*a**2*b*c**3 + c**5)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: a**3*x**6/8 + 1" ], "shape": [ "factor: N*a**N*x**N + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/14", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 14", "problem_latex": "$\\frac{1}{27}x^3+ 1$", "markdown": "$\\frac{1}{27}x^3+ 1$", "answer_latex": [ "$(\\frac{1}{4}x + 1)(\\frac{1}{2}x^2 - \\frac{1}{4}x + 1)$." ], "answer_markdown": [ "$(\\frac{1}{4}x + 1)(\\frac{1}{2}x^2 - \\frac{1}{4}x + 1)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "1.1510109938002017339", "2.6262500725468289781" ], "problem_expr": "Rational(1,27)*x**3 + 1", "answer_expr": "(Rational(1,4)*x + 1)*(Rational(1,2)*x**2 - Rational(1,4)*x + 1)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: x**3/27 + 1" ], "shape": [ "factor: N*x**N + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/15", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 15", "problem_latex": "$(m + n)^3+ 8$", "markdown": "$(m + n)^3+ 8$", "answer_latex": [ "$(m + n + 2)\\{(m + n)^2 - 2(m + n) + 4\\}$." ], "answer_markdown": [ "$(m + n + 2)\\{(m + n)^2 - 2(m + n) + 4\\}$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "(m + n)**3 + 8", "answer_expr": "(m + n + 2)*((m + n)**2 - 2*(m + n) + 4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: (a + x)**3 + 8" ], "shape": [ "factor: N + (a + x)**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/16", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 16", "problem_latex": "$1 + (x - y)^3$", "markdown": "$1 + (x - y)^3$", "answer_latex": [ "$(1 - x - y)\\{1 - (x - y) + (x - y)^2\\}$." ], "answer_markdown": [ "$(1 - x - y)\\{1 - (x - y) + (x - y)^2\\}$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "1.1119414517961248285", "-3.3066450108239026063" ], "problem_expr": "1 + (x - y)**3", "answer_expr": "(1 - x - y)*(1 - (x - y) + (x - y)**2)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: (-a + x)**3 + 1" ], "shape": [ "factor: (-a + x)**N + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/17", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 17", "problem_latex": "$2a^2x^3y^6 + 2a^8b^9$", "markdown": "$2a^2x^3y^6 + 2a^8b^9$", "answer_latex": [ "$2a^2(xy^2 + a^2b^3) (x^2y^4 - a^2b^3xy^2 + a^4b^6)$." ], "answer_markdown": [ "$2a^2(xy^2 + a^2b^3) (x^2y^4 - a^2b^3xy^2 + a^4b^6)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "2*a**2*x**3*y**6 + 2*a**8*b**9", "answer_expr": "2*a**2*(x*y**2 + a**2*b**3)*(x**2*y**4 - a**2*b**3*x*y**2 + a**4*b**6)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 2*a**9*x**8 + 2*b**3*c**6*x**2" ], "shape": [ "factor: N*a**N*x**N + N*b**N*c**N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/18", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 18", "problem_latex": "$mx + my - nx - ny$", "markdown": "$mx + my - nx - ny$", "answer_latex": [ "$(m - n)(x + y)$" ], "answer_markdown": [ "$(m - n)(x + y)$" ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "m*x + m*y - n*x - n*y", "answer_expr": "(m - n)*(x + y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a*b - a*c + b*x + c*x" ], "shape": [ "factor: -a*b - a*c + b*x + c*x" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/19", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 19", "problem_latex": "$a^3x + b^3x - a^3y - b^3y$", "markdown": "$a^3x + b^3x - a^3y - b^3y$", "answer_latex": [ "$(x - y)(a + b)(a^2 - ab + b^2)$." ], "answer_markdown": [ "$(x - y)(a + b)(a^2 - ab + b^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**3*x + b**3*x - a**3*y - b**3*y", "answer_expr": "(x - y)*(a + b)*(a**2 - a*b + b**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**3*b - a**3*c + b*x**3 - c*x**3" ], "shape": [ "factor: a**N*b - a**N*c + b*x**N - c*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/2", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 2", "problem_latex": "$c^3 + d^3$", "markdown": "$c^3 + d^3$", "answer_latex": [ "$(c + d)(c^2 - cd + d^2)$." ], "answer_markdown": [ "$(c + d)(c^2 - cd + d^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "c**3 + d**3", "answer_expr": "(c + d)*(c**2 - c*d + d**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**3 + x**3" ], "shape": [ "factor: a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/20", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 20", "problem_latex": "$a^6 - b^6$", "markdown": "$a^6 - b^6$", "answer_latex": [ "$(a + b)(a^2 - ab + b^2)(a - b)(a^2 + ab + b^2)$." ], "answer_markdown": [ "$(a + b)(a^2 - ab + b^2)(a - b)(a^2 + ab + b^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**6 - b**6", "answer_expr": "(a + b)*(a**2 - a*b + b**2)*(a - b)*(a**2 + a*b + b**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**6 + x**6" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-35/21" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/21", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 21", "problem_latex": "$729x^6 - 64y^6$", "markdown": "$729x^6 - 64y^6$", "answer_latex": [ "$(27x^3 + 4y^3)(27x^3 - 4y^3)$." ], "answer_markdown": [ "$(27x^3 + 4y^3)(27x^3 - 4y^3)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "-85.8569089589490985", "19108.545831395835048" ], "problem_expr": "729*x**6 - 64*y**6", "answer_expr": "(27*x**3 + 4*y**3)*(27*x**3 - 4*y**3)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: -64*a**6 + 729*x**6" ], "shape": [ "factor: N*a**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/22", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 22", "problem_latex": "$1 - x^8$", "markdown": "$1 - x^8$", "answer_latex": [ "$(1 + x^4)(1 + x^2)(1 + x)(1 - x)$." ], "answer_markdown": [ "$(1 + x^4)(1 + x^2)(1 + x)(1 - x)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "1 - x**8", "answer_expr": "(1 + x**4)*(1 + x**2)*(1 + x)*(1 - x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -x**8 + 1" ], "shape": [ "factor: -x**N + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/23", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 23", "problem_latex": "A had $d$ dollars, but, after giving \\$26 to B, he had\none-third as many as B. How many has B? How many had B at first?", "markdown": "A had $d$ dollars, but, after giving $26 to B, he had one-third as many as B. How many has B? How many had B at first?", "answer_latex": [ "$3(d-26)$; $3d - 104$ dols." ], "answer_markdown": [ "$3(d-26)$; $3d - 104$ dols." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": { "b": "3*(d - 26)", "b0": "3*d - 104" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a, x - 26), Eq(b - 26, x/3))" ], "shape": [ "solve: (Eq(a, N + x), Eq(N + b, N*x))" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/24", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 24", "problem_latex": "How many units in $y$ tens?", "markdown": "How many units in $y$ tens?", "answer_latex": [ "$10y$." ], "answer_markdown": [ "$10y$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "10*y", "answer_expr": "10*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/25", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 25", "problem_latex": "If the sum of two numbers is $x$, and one of the numbers is\n8, what is the other number?", "markdown": "If the sum of two numbers is $x$, and one of the numbers is 8, what is the other number?", "answer_latex": [ "$x - 8$." ], "answer_markdown": [ "$x - 8$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(o + 8, x)", "answer_expr": "x - 8" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x + 8, a)" ], "shape": [ "solve: Eq(N + x, a)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/26", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 26", "problem_latex": "What does $a^3$ mean? What does $3a$ stand for? What is the\nproduct of $x^4$ and $0$?", "markdown": "What does $a^3$ mean? What does $3a$ stand for? What is the product of $x^4$ and $0$?", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/3", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 3", "problem_latex": "$a^3 + b^3c^3$", "markdown": "$a^3 + b^3c^3$", "answer_latex": [ "$(a + bc)(a^2 - abc + b^2c^2)$." ], "answer_markdown": [ "$(a + bc)(a^2 - abc + b^2c^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**3 + b**3*c**3", "answer_expr": "(a + b*c)*(a**2 - a*b*c + b**2*c**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**3*b**3 + x**3" ], "shape": [ "factor: a**N*b**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/4", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 4", "problem_latex": "$a^3x^3 + y^3$", "markdown": "$a^3x^3 + y^3$", "answer_latex": [ "$(ax + y)(a^2x^2 - axy + y^2)$." ], "answer_markdown": [ "$(ax + y)(a^2x^2 - axy + y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**3*x**3 + y**3", "answer_expr": "(a*x + y)*(a**2*x**2 - a*x*y + y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**3*x**3 + b**3" ], "shape": [ "factor: a**N*x**N + b**N" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-36/5" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/5", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 5", "problem_latex": "$8a^5b^3c^6 + m^6$", "markdown": "$8a^5b^3c^6 + m^6$", "answer_latex": [ "$(2abc^2 + m^2)(4a^2b^2c^4 - 2 abc^2m^2 + m^4)$." ], "answer_markdown": [ "$(2abc^2 + m^2)(4a^2b^2c^4 - 2 abc^2m^2 + m^4)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "929180.46051762897746", "250943.31152449416184" ], "problem_expr": "8*a**5*b**3*c**6 + m**6", "answer_expr": "(2*a*b*c**2 + m**2)*(4*a**2*b**2*c**4 - 2*a*b*c**2*m**2 + m**4)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: 8*a**3*b**6*x**5 + c**6" ], "shape": [ "factor: N*a**N*b**N*x**N + c**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/6", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 6", "problem_latex": "$x^6y^3 + 216a^3$", "markdown": "$x^6y^3 + 216a^3$", "answer_latex": [ "$(x^2y^3 + 6a)(x^4y^6 - 6ax^2y^3 + 36a^2)$." ], "answer_markdown": [ "$(x^2y^3 + 6a)(x^4y^6 - 6ax^2y^3 + 36a^2)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "347.61723903444439577", "345.32061216938551924" ], "problem_expr": "x**6*y**3 + 216*a**3", "answer_expr": "(x**2*y**3 + 6*a)*(x**4*y**6 - 6*a*x**2*y**3 + 36*a**2)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: 216*a**3 + b**3*x**6" ], "shape": [ "factor: N*a**N + b**N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/7", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 7", "problem_latex": "$a^6 + b^6$", "markdown": "$a^6 + b^6$", "answer_latex": [ "$(a^2 + b^2)(a^4 - a^2b^2 + b^4)$." ], "answer_markdown": [ "$(a^2 + b^2)(a^4 - a^2b^2 + b^4)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**6 + b**6", "answer_expr": "(a**2 + b**2)*(a**4 - a**2*b**2 + b**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**6 + x**6" ], "shape": [ "factor: a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/8", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 8", "problem_latex": "$64x^6 + y^6$", "markdown": "$64x^6 + y^6$", "answer_latex": [ "$(4x^2+y^2)(16x^4 - 4x^2y^2 + y^4)$." ], "answer_markdown": [ "$(4x^2+y^2)(16x^4 - 4x^2y^2 + y^4)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "64*x**6 + y**6", "answer_expr": "(4*x**2 + y**2)*(16*x**4 - 4*x**2*y**2 + y**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**6 + 64*x**6" ], "shape": [ "factor: N*x**N + a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-34/9", "set": "boyden-first-book-in-algebra-1895/ex-34", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 34, problem 9", "problem_latex": "$x^3 + 8$", "markdown": "$x^3 + 8$", "answer_latex": [ "$(x + 2)(x^2 - 2x + 4)$." ], "answer_markdown": [ "$(x + 2)(x^2 - 2x + 4)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**3 + 8", "answer_expr": "(x + 2)*(x**2 - 2*x + 4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**3 + 8" ], "shape": [ "factor: N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/1", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 1", "problem_latex": "$x^3 - a^3$", "markdown": "$x^3 - a^3$", "answer_latex": [ "$(x - a)(x^2 +ax + a^2)$." ], "answer_markdown": [ "$(x - a)(x^2 +ax + a^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**3 - a**3", "answer_expr": "(x - a)*(x**2 + a*x + a**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**3 + x**3" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-35/2" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/10", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 10", "problem_latex": "$27 - 64m^3x^6y^3.$", "markdown": "$27 - 64m^3x^6y^3.$", "answer_latex": [ "$(3 - 4mx^2y)(9+12mx^2y + 16m^2x^4y^2)$." ], "answer_markdown": [ "$(3 - 4mx^2y)(9+12mx^2y + 16m^2x^4y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "27 - 64*m**3*x**6*y**3", "answer_expr": "(3 - 4*m*x**2*y)*(9 + 12*m*x**2*y + 16*m**2*x**4*y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -64*a**6*b**3*x**3 + 27" ], "shape": [ "factor: N*a**N*b**N*x**N + N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/11", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 11", "problem_latex": "$a^3-b^6.$", "markdown": "$a^3-b^6.$", "answer_latex": [ "$(a-b^2)(a^2 + ab^2 + b^4)$." ], "answer_markdown": [ "$(a-b^2)(a^2 + ab^2 + b^4)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**3 - b**6", "answer_expr": "(a - b**2)*(a**2 + a*b**2 + b**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**6 + x**3" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/12", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 12", "problem_latex": "$m^6 - x^3.$", "markdown": "$m^6 - x^3.$", "answer_latex": [ "$(m^2 - x)(m^4 + m^2x + x^2)$." ], "answer_markdown": [ "$(m^2 - x)(m^4 + m^2x + x^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "m**6 - x**3", "answer_expr": "(m**2 - x)*(m**4 + m**2*x + x**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**3 + x**6" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/13", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 13", "problem_latex": "$x^3 - 1.$", "markdown": "$x^3 - 1.$", "answer_latex": [ "$(x-1)(x^2 + x + 1)$." ], "answer_markdown": [ "$(x-1)(x^2 + x + 1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**3 - 1", "answer_expr": "(x - 1)*(x**2 + x + 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**3 - 1" ], "shape": [ "factor: x**N - 1" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-35/2" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/14", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 14", "problem_latex": "$1 - y^3.$", "markdown": "$1 - y^3.$", "answer_latex": [ "$(1-y)(1 + y + y^2)$" ], "answer_markdown": [ "$(1-y)(1 + y + y^2)$" ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "1 - y**3", "answer_expr": "(1 - y)*(1 + y + y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -x**3 + 1" ], "shape": [ "factor: -x**N + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/15", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 15", "problem_latex": "$\\frac{1}{27}x^3y^6 - b^9.$", "markdown": "$\\frac{1}{27}x^3y^6 - b^9.$", "answer_latex": [ "$(\\frac{1}{3}xy^2 - b^3)(\\frac{1}{9}x^3y^4 + \\frac{1}{3}xy^2b^3 + b^6)$." ], "answer_markdown": [ "$(\\frac{1}{3}xy^2 - b^3)(\\frac{1}{9}x^3y^4 + \\frac{1}{3}xy^2b^3 + b^6)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "-71.361940288383199795", "-75.054430733370496051" ], "problem_expr": "Rational(1,27)*x**3*y**6 - b**9", "answer_expr": "(Rational(1,3)*x*y**2 - b**3)*(Rational(1,9)*x**3*y**4 + Rational(1,3)*x*y**2*b**3 + b**6)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: -a**9 + b**6*x**3/27" ], "shape": [ "factor: N*b**N*x**N - a**N" ], "same_problem_in": [], "needs": [ "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/16", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 16", "problem_latex": "$8 - \\frac{1}{64}m^6n^3.$", "markdown": "$8 - \\frac{1}{64}m^6n^3.$", "answer_latex": [ "$(2-\\frac{1}{4}m^2n)(4+\\frac{1}{2}m^2n + \\frac{1}{16}m^4n^2)$." ], "answer_markdown": [ "$(2-\\frac{1}{4}m^2n)(4+\\frac{1}{2}m^2n + \\frac{1}{16}m^4n^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "8 - Rational(1,64)*m**6*n**3", "answer_expr": "(2 - Rational(1,4)*m**2*n)*(4 + Rational(1,2)*m**2*n + Rational(1,16)*m**4*n**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**3*x**6/64 + 8" ], "shape": [ "factor: N*a**N*x**N + N" ], "same_problem_in": [], "needs": [ "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/17", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 17", "problem_latex": "$1 - (a + b)^3.$", "markdown": "$1 - (a + b)^3.$", "answer_latex": [ "$\\{1 - (a + b)\\} \\{1+ (a+b) + (a+b)^2\\}$." ], "answer_markdown": [ "$\\{1 - (a + b)\\} \\{1+ (a+b) + (a+b)^2\\}$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "1 - (a + b)**3", "answer_expr": "(1 - (a + b))*(1 + (a + b) + (a + b)**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -(a + x)**3 + 1" ], "shape": [ "factor: -(a + x)**N + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/18", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 18", "problem_latex": "$x^3y^3 - (x - y^2)^3.$", "markdown": "$x^3y^3 - (x - y^2)^3.$", "answer_latex": [ "$\\{xy - (x-y^2)\\} \\{x^2y^2 + xy(x - y^2) + (x - y^2)^2\\}$." ], "answer_markdown": [ "$\\{xy - (x-y^2)\\} \\{x^2y^2 + xy(x - y^2) + (x - y^2)^2\\}$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**3*y**3 - (x - y**2)**3", "answer_expr": "(x*y - (x - y**2))*(x**2*y**2 + x*y*(x - y**2) + (x - y**2)**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**3*x**3 - (-a**2 + x)**3" ], "shape": [ "factor: a**N*x**N - (-a**N + x)**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/19", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 19", "problem_latex": "$x^7 - xy^3.$", "markdown": "$x^7 - xy^3.$", "answer_latex": [ "$x(x^2 - y)(x^4 + x^2y + y^2)$." ], "answer_markdown": [ "$x(x^2 - y)(x^4 + x^2y + y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**7 - x*y**3", "answer_expr": "x*(x**2 - y)*(x**4 + x**2*y + y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**3*x + x**7" ], "shape": [ "factor: -a**N*x + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/2", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 2", "problem_latex": "$c^3 - b^3$", "markdown": "$c^3 - b^3$", "answer_latex": [ "$(c - b)(c^2 + cb + b^2)$." ], "answer_markdown": [ "$(c - b)(c^2 + cb + b^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "c**3 - b**3", "answer_expr": "(c - b)*(c**2 + c*b + b**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**3 + x**3" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-35/1" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/20", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 20", "problem_latex": "$ab^3 - ac^3 + mb^3 - mc^3.$", "markdown": "$ab^3 - ac^3 + mb^3 - mc^3.$", "answer_latex": [ "$(a + m)(b - c)(b^2 + bc + c^2)$." ], "answer_markdown": [ "$(a + m)(b - c)(b^2 + bc + c^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a*b**3 - a*c**3 + m*b**3 - m*c**3", "answer_expr": "(a + m)*(b - c)*(b**2 + b*c + c**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**3*c + a**3*x - b**3*c - b**3*x" ], "shape": [ "factor: a**N*c + a**N*x - b**N*c - b**N*x" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/21", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 21", "problem_latex": "$x^6 - y^6$ into four factors.", "markdown": "$x^6 - y^6$ into four factors.", "answer_latex": [ "$(x + y)(x^2 - xy + y^2)(x - y)(x^2 + xy + y^2)$." ], "answer_markdown": [ "$(x + y)(x^2 - xy + y^2)(x - y)(x^2 + xy + y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**6 - y**6", "answer_expr": "(x + y)*(x**2 - x*y + y**2)*(x - y)*(x**2 + x*y + y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**6 + x**6" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-34/20" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/22", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 22", "problem_latex": "$x^6 - x^5 + x^3 - x^2 - x + 1.$", "markdown": "$x^6 - x^5 + x^3 - x^2 - x + 1.$", "answer_latex": [ "$(x^5 + x^2 - 1)(x - 1)$." ], "answer_markdown": [ "$(x^5 + x^2 - 1)(x - 1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**6 - x**5 + x**3 - x**2 - x + 1", "answer_expr": "(x**5 + x**2 - 1)*(x - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**6 - x**5 + x**3 - x**2 - x + 1" ], "shape": [ "factor: -x + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/23", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 23", "problem_latex": "$a^2 - b^2 + a^3 -b^3.$", "markdown": "$a^2 - b^2 + a^3 -b^3.$", "answer_latex": [ "$(a - b)(a + b + a^2 + ab + b^2)$." ], "answer_markdown": [ "$(a - b)(a + b + a^2 + ab + b^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 - b**2 + a**3 - b**3", "answer_expr": "(a - b)*(a + b + a**2 + a*b + b**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**3 - a**2 + x**3 + x**2" ], "shape": [ "factor: -2*a**N + 2*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/24", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 24", "problem_latex": "$mx^3 + my^3 - x - y.$", "markdown": "$mx^3 + my^3 - x - y.$", "answer_latex": [ "$(x + y)(mx^2 - mxy + my^2 - 1)$." ], "answer_markdown": [ "$(x + y)(mx^2 - mxy + my^2 - 1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "m*x**3 + m*y**3 - x - y", "answer_expr": "(x + y)*(m*x**2 - m*x*y + m*y**2 - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a*b**3 + a*x**3 - b - x" ], "shape": [ "factor: a*b**N + a*x**N - b - x" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/25", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 25", "problem_latex": "How many hours will it take $x$ men to dig 75 bushels of\npotatoes if each man digs $y$ bushels an hour?", "markdown": "How many hours will it take $x$ men to dig 75 bushels of potatoes if each man digs $y$ bushels an hour?", "answer_latex": [ "$\\frac{75}{xy}$ hrs." ], "answer_markdown": [ "$\\frac{75}{xy}$ hrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{h: 75/(x*y)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a*b*x, 75)" ], "shape": [ "solve: Eq(a*b*x, N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/26", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 26", "problem_latex": "If there are $x$ tens, $y$ units, and $z$ hundreds in a\nnumber, what will represent the whole number of units?", "markdown": "If there are $x$ tens, $y$ units, and $z$ hundreds in a number, what will represent the whole number of units?", "answer_latex": [ "$100x + 10x + y$." ], "answer_markdown": [ "$100x + 10x + y$." ], "checks": [ { "task": "solve", "verdict": "FLAG-MISMATCH", "judge_why": "the equations leave [{x: z}]", "problem_expr": null, "answer_expr": "{N: 100*x + 10*x + y}" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "solve: Eq(x, 10*a + b + 100*c)" ], "shape": [ "solve: Eq(x, N*a + N*c + b)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/3", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 3", "problem_latex": "$a^3 - x^3y^3.$", "markdown": "$a^3 - x^3y^3.$", "answer_latex": [ "$(a - xy)(a^2 + axy + x^2y^2)$." ], "answer_markdown": [ "$(a - xy)(a^2 + axy + x^2y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**3 - x**3*y**3", "answer_expr": "(a - x*y)*(a**2 + a*x*y + x**2*y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**3*b**3 + x**3" ], "shape": [ "factor: -a**N*b**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/4", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 4", "problem_latex": "$m^3n^3 - c^3.$", "markdown": "$m^3n^3 - c^3.$", "answer_latex": [ "$(mn - c)(m^2n^2 + mnc + c^2)$." ], "answer_markdown": [ "$(mn - c)(m^2n^2 + mnc + c^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "m**3*n**3 - c**3", "answer_expr": "(m*n - c)*(m**2*n**2 + m*n*c + c**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**3 + b**3*x**3" ], "shape": [ "factor: -a**N + b**N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/5", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 5", "problem_latex": "$27m^3 - 8x^3.$", "markdown": "$27m^3 - 8x^3.$", "answer_latex": [ "$(3m - 2x)(9m^2 + 6mx + 4x^2)$." ], "answer_markdown": [ "$(3m - 2x)(9m^2 + 6mx + 4x^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "27*m**3 - 8*x**3", "answer_expr": "(3*m - 2*x)*(9*m**2 + 6*m*x + 4*x**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -8*a**3 + 27*x**3" ], "shape": [ "factor: N*a**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/6", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 6", "problem_latex": "$8x^3 -64y^3$", "markdown": "$8x^3 -64y^3$", "answer_latex": [ "$8(x - 2y)(x^2 + 2xy + 4y^2)$." ], "answer_markdown": [ "$8(x - 2y)(x^2 + 2xy + 4y^2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "8*x**3 - 64*y**3", "answer_expr": "8*(x - 2*y)*(x**2 + 2*x*y + 4*y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -64*a**3 + 8*x**3" ], "shape": [ "factor: N*a**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/7", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 7", "problem_latex": "$64a^3x^6b^3 - 125m^9c^3y^6.$", "markdown": "$64a^3x^6b^3 - 125m^9c^3y^6.$", "answer_latex": [ "$(4ax^2b - 5m^3cy^2)(16a^2x^4b^2 + 20abcm^3x^2y^2 + 25m^6c^2y^4)$." ], "answer_markdown": [ "$(4ax^2b - 5m^3cy^2)(16a^2x^4b^2 + 20abcm^3x^2y^2 + 25m^6c^2y^4)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "64*a**3*x**6*b**3 - 125*m**9*c**3*y**6", "answer_expr": "(4*a*x**2*b - 5*m**3*c*y**2)*(16*a**2*x**4*b**2 + 20*a*b*c*m**3*x**2*y**2 + 25*m**6*c**2*y**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 64*a**3*b**3*x**6 - 125*c**3*d**9*e**6" ], "shape": [ "factor: N*a**N*b**N*x**N + N*c**N*d**N*e**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/8", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 8", "problem_latex": "$27b^3c^6y^3 - 216a^9m^6x^6.$", "markdown": "$27b^3c^6y^3 - 216a^9m^6x^6.$", "answer_latex": [ "$27(bc^2y - 2a^3m^2x^2)(b^2c^4y^2 + 2a^3bc^2m^2x^2y + 4a^2m^4x^4)$." ], "answer_markdown": [ "$27(bc^2y - 2a^3m^2x^2)(b^2c^4y^2 + 2a^3bc^2m^2x^2y + 4a^2m^4x^4)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "-11339.067506498385843", "-5104.1705774566103613" ], "problem_expr": "27*b**3*c**6*y**3 - 216*a**9*m**6*x**6", "answer_expr": "27*(b*c**2*y - 2*a**3*m**2*x**2)*(b**2*c**4*y**2 + 2*a**3*b*c**2*m**2*x**2*y + 4*a**2*m**4*x**4)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: -216*a**9*c**6*d**6 + 27*b**6*e**3*x**3" ], "shape": [ "factor: N*a**N*c**N*d**N + N*b**N*e**N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-35/9", "set": "boyden-first-book-in-algebra-1895/ex-35", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 35, problem 9", "problem_latex": "$8x^9y^3 - 125.$", "markdown": "$8x^9y^3 - 125.$", "answer_latex": [ "$(2x^3y - 5)(4x^6y^2 + 10x^3y + 25)$." ], "answer_markdown": [ "$(2x^3y - 5)(4x^6y^2 + 10x^3y + 25)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "8*x**9*y**3 - 125", "answer_expr": "(2*x**3*y - 5)*(4*x**6*y**2 + 10*x**3*y + 25)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 8*a**3*x**9 - 125" ], "shape": [ "factor: N*a**N*x**N + N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/1", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 1", "problem_latex": "$a^2 + 2ax + x^2$.", "markdown": "$a^2 + 2ax + x^2$.", "answer_latex": [ "$(a + x)^2$." ], "answer_markdown": [ "$(a + x)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 + 2*a*x + x**2", "answer_expr": "(a + x)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2 + 2*a*x + x**2" ], "shape": [ "factor: N*a*x + a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/10", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 10", "problem_latex": "$4y^2 - 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4x^6y^4 + 4x^3y^8$.", "markdown": "$x^9 - 4x^6y^4 + 4x^3y^8$.", "answer_latex": [ "$x^3\\left(x^3-2y^4\\right)^2$." ], "answer_markdown": [ "$x^3\\left(x^3-2y^4\\right)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**9 - 4*x**6*y**4 + 4*x**3*y**8", "answer_expr": "x**3*(x**3 - 2*y**4)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 4*a**8*x**3 - 4*a**4*x**6 + x**9" ], "shape": [ "factor: 2*N*a**N*x**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/24", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 24", "problem_latex": "$18a^2y + 24ay^3 + 8y^5$.", "markdown": "$18a^2y + 24ay^3 + 8y^5$.", "answer_latex": [ "$2y\\left(3a+2y^2\\right)^2$." ], "answer_markdown": [ "$2y\\left(3a+2y^2\\right)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "18*a**2*y + 24*a*y**3 + 8*y**5", "answer_expr": "2*y*(3*a + 2*y**2)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 8*a**5 + 24*a**3*x + 18*a*x**2" ], "shape": [ "factor: N*a*x**N + N*a**N*x + N*a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/25", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 25", "problem_latex": "$3a^3x^5 - 30a^2bx^4 + 75ab^2x^3$.", "markdown": "$3a^3x^5 - 30a^2bx^4 + 75ab^2x^3$.", "answer_latex": [ "$3ax^3\\left(ax-5b\\right)^2$." ], "answer_markdown": [ "$3ax^3\\left(ax-5b\\right)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "3*a**3*x**5 - 30*a**2*b*x**4 + 75*a*b**2*x**3", "answer_expr": "3*a*x**3*(a*x - 5*b)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 75*a**2*b**3*x - 30*a*b**4*x**2 + 3*b**5*x**3" ], "shape": [ "factor: N*a*b**N*x**N + N*a**N*b**N*x + N*b**N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/26", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 26", "problem_latex": "$(x+y)^2 - 2a^2(x+y) + a^4$.", "markdown": "$(x+y)^2 - 2a^2(x+y) + a^4$.", "answer_latex": [ "$\\left(x+y-a^2\\right)^2$." ], "answer_markdown": [ "$\\left(x+y-a^2\\right)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "(x + y)**2 - 2*a**2*(x + y) + a**4", "answer_expr": "(x + y - a**2)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**4 - 2*a**2*(b + x) + (b + x)**2" ], "shape": [ "factor: N*a**N*(b + x) + a**N + (b + x)**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/27", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 27", "problem_latex": "$(m^2 - n^2)^2 - 2(m^4 - n^4) + (m^2 + n^2)^2$.", "markdown": "$(m^2 - n^2)^2 - 2(m^4 - n^4) + (m^2 + n^2)^2$.", "answer_latex": [ "$\\left\\{(m^2-n^2)-(m^2+n^2)\\right\\}^2$ or $\\left(-2n^2\\right)^2$." ], "answer_markdown": [ "$\\left\\{(m^2-n^2)-(m^2+n^2)\\right\\}^2$ or $\\left(-2n^2\\right)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "(m**2 - n**2)**2 - 2*(m**4 - n**4) + (m**2 + n**2)**2", "answer_expr": "(-2*n**2)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 2*a**4 - 2*x**4 + (-a**2 + x**2)**2 + (a**2 + x**2)**2" ], "shape": [ "factor: N*a**N + N*x**N + (-a**N + x**N)**N + (a**N + x**N)**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/28", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 28", "problem_latex": "$a^2 + 2ab + b^2 + 6a + 6b$.", "markdown": "$a^2 + 2ab + b^2 + 6a + 6b$.", "answer_latex": [ "$(a+b)(a+b+6)$." ], "answer_markdown": [ "$(a+b)(a+b+6)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 + 2*a*b + b**2 + 6*a + 6*b", "answer_expr": "(a + b)*(a + b + 6)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2 + 2*a*x + 6*a + x**2 + 6*x" ], "shape": [ "factor: N*a*x + N*a + N*x + a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/29", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 29", "problem_latex": "$x^2 + y^2 - 3x - 2xy + 3y$.", "markdown": "$x^2 + y^2 - 3x - 2xy + 3y$.", "answer_latex": [ "$(x-y)(x-y-3)$." ], "answer_markdown": [ "$(x-y)(x-y-3)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2 + y**2 - 3*x - 2*x*y + 3*y", "answer_expr": "(x - y)*(x - y - 3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2 - 2*a*x + 3*a + x**2 - 3*x" ], "shape": [ "factor: N*a*x + N*a + N*x + a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/3", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 3", "problem_latex": "$4a^2 + 4ay + y^2$.", "markdown": "$4a^2 + 4ay + y^2$.", "answer_latex": [ "$(2a + y)^2$." ], "answer_markdown": [ "$(2a + y)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "4*a**2 + 4*a*y + y**2", "answer_expr": "(2*a + y)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2 + 4*a*x + 4*x**2" ], "shape": [ "factor: N*a*x + N*x**N + a**N" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-37/1" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/30", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 30", "problem_latex": "$x^6 + y^6 - 2x^3y^3$.", "markdown": "$x^6 + y^6 - 2x^3y^3$.", "answer_latex": [ "$\\left(x-y\\right)^2\\left(x^2+xy+y^2\\right)^2$." ], "answer_markdown": [ "$\\left(x-y\\right)^2\\left(x^2+xy+y^2\\right)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**6 + y**6 - 2*x**3*y**3", "answer_expr": "(x - y)**2*(x**2 + x*y + y**2)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**6 - 2*a**3*x**3 + x**6" ], "shape": [ "factor: N*a**N*x**N + a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/31", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 31, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 31", "problem_latex": "$a^2 + 2xy$.", "markdown": "$a^2 + 2xy$.", "answer_latex": [ "$y^2$." ], "answer_markdown": [ "$y^2$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "a**2 + 2*x*y", "answer_expr": "y**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/32", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 32, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 32", "problem_latex": "$m^6 + 6m^3y$.", "markdown": "$m^6 + 6m^3y$.", "answer_latex": [ "$9y^2$." ], "answer_markdown": [ "$9y^2$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "m**6 + 6*m**3*y", "answer_expr": "9*y**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/33", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 33, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 33", "problem_latex": "$c^2 + d^2$.", "markdown": "$c^2 + d^2$.", "answer_latex": [ "$\\pm 2cd$." ], "answer_markdown": [ "$\\pm 2cd$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "c**2 + d**2", "answer_expr": "2*c*d" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/34", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 34, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 34", "problem_latex": "$(x - y)^4 + 2(x - y)^2$.", "markdown": "$(x - y)^4 + 2(x - y)^2$.", "answer_latex": [ "$1$." ], "answer_markdown": [ "$1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "(x - y)**4 + 2*(x - y)**2", "answer_expr": "1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/35", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 35, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 35", "problem_latex": "$(c - d)^2 - 6(c -d )$.", "markdown": "$(c - d)^2 - 6(c -d )$.", "answer_latex": [ "$9$." ], "answer_markdown": [ "$9$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "(c - d)**2 - 6*(c - d)", "answer_expr": "9" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/36", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 36, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 36", "problem_latex": "$9x^4y^2 - 12x^2y^3$.", "markdown": "$9x^4y^2 - 12x^2y^3$.", "answer_latex": [ "$4y^4$." ], "answer_markdown": [ "$4y^4$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "9*x**4*y**2 - 12*x**2*y**3", "answer_expr": "4*y**4" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/37", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 37, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 37", "problem_latex": "$30xy^4 + 9x^2y^6$.", "markdown": "$30xy^4 + 9x^2y^6$.", "answer_latex": [ "$25y^2$." ], "answer_markdown": [ "$25y^2$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "30*x*y**4 + 9*x**2*y**6", "answer_expr": "25*y**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/38", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 38, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 38", "problem_latex": "$25a^2b^2 + 36b^4c^2$.", "markdown": "$25a^2b^2 + 36b^4c^2$.", "answer_latex": [ "$\\pm 60ab^3c$." ], "answer_markdown": [ "$\\pm 60ab^3c$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "25*a**2*b**2 + 36*b**4*c**2", "answer_expr": "60*a*b**3*c" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/39", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 39, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 39", "problem_latex": "$49a^2b^2c^2 + 25a^2b^4d^2$.", "markdown": "$49a^2b^2c^2 + 25a^2b^4d^2$.", "answer_latex": [ "$\\pm 70a^2b^3cd$." ], "answer_markdown": [ "$\\pm 70a^2b^3cd$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "49*a**2*b**2*c**2 + 25*a**2*b**4*d**2", "answer_expr": "70*a**2*b**3*c*d" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/4", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 4", "problem_latex": "$a^2 + 4ab + 4b^2$.", "markdown": "$a^2 + 4ab + 4b^2$.", "answer_latex": [ "$(a + 2b)^2$." ], "answer_markdown": [ "$(a + 2b)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 + 4*a*b + 4*b**2", "answer_expr": "(a + 2*b)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 4*a**2 + 4*a*x + x**2" ], "shape": [ "factor: N*a*x + N*a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/40", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 40, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 40", "problem_latex": "$a^4 - 22a^2 + 9$ (two numbers).", "markdown": "$a^4 - 22a^2 + 9$ (two numbers).", "answer_latex": [ "$16a^2$ or $28a^2$." ], "answer_markdown": [ "$16a^2$ or $28a^2$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "a**4 - 22*a**2 + 9", "answer_expr": "16*a**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/41", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 41, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 41", "problem_latex": "$64a^2 - 177ay + 121y^2$.", "markdown": "$64a^2 - 177ay + 121y^2$.", "answer_latex": [ "$ay$ or $353ay$." ], "answer_markdown": [ "$ay$ or $353ay$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "64*a**2 - 177*a*y + 121*y**2", "answer_expr": "a*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/42", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 42, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 42", "problem_latex": "$a^4 - 10a^2b^2 + 9b^4$.", "markdown": "$a^4 - 10a^2b^2 + 9b^4$.", "answer_latex": [ "$4a^2b^2$ or $16a^2b^2$." ], "answer_markdown": [ "$4a^2b^2$ or $16a^2b^2$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "a**4 - 10*a**2*b**2 + 9*b**4", "answer_expr": "4*a**2*b**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/43", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 43, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 43", "problem_latex": "$x^4 + x^2 + 1$.", "markdown": "$x^4 + x^2 + 1$.", "answer_latex": [ "$x^2$ or $-3x^2$." ], "answer_markdown": [ "$x^2$ or $-3x^2$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "x**4 + x**2 + 1", "answer_expr": "x**2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/44", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 44, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 44", "problem_latex": "$a^2 + a + 1$.", "markdown": "$a^2 + a + 1$.", "answer_latex": [ "$a$ or $-3a$." ], "answer_markdown": [ "$a$ or $-3a$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "a**2 + a + 1", "answer_expr": "a" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "other:complete_the_square" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/45a", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 45, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 45a", "problem_latex": "A stream flows at the rate of $a$ miles an hour, and a man\ncan row in still water $b$ miles an hour. How far can the man row\nup the stream in an hour? In 6 hours? How far down the stream in\nan hour? In 3 hours?", "markdown": "A stream flows at the rate of $a$ miles an hour, and a man can row in still water $b$ miles an hour. How far can the man row up the stream in an hour? In 6 hours? How far down the stream in an hour? In 3 hours?", "answer_latex": [ "$b-a$" ], "answer_markdown": [ "$b-a$" ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "b - a" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/45b", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 45, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 45b", "problem_latex": "A stream flows at the rate of $a$ miles an hour, and a man\ncan row in still water $b$ miles an hour. How far can the man row\nup the stream in an hour? In 6 hours? How far down the stream in\nan hour? In 3 hours?", "markdown": "A stream flows at the rate of $a$ miles an hour, and a man can row in still water $b$ miles an hour. How far can the man row up the stream in an hour? In 6 hours? How far down the stream in an hour? In 3 hours?", "answer_latex": [ "$6(b-a)$" ], "answer_markdown": [ "$6(b-a)$" ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "6*(b - a)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/45c", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 45, "part": "c", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 45c", "problem_latex": "A stream flows at the rate of $a$ miles an hour, and a man\ncan row in still water $b$ miles an hour. How far can the man row\nup the stream in an hour? In 6 hours? How far down the stream in\nan hour? In 3 hours?", "markdown": "A stream flows at the rate of $a$ miles an hour, and a man can row in still water $b$ miles an hour. How far can the man row up the stream in an hour? In 6 hours? How far down the stream in an hour? In 3 hours?", "answer_latex": [ "$b+a$" ], "answer_markdown": [ "$b+a$" ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "b + a" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/45d", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 45, "part": "d", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 45d", "problem_latex": "A stream flows at the rate of $a$ miles an hour, and a man\ncan row in still water $b$ miles an hour. How far can the man row\nup the stream in an hour? In 6 hours? How far down the stream in\nan hour? In 3 hours?", "markdown": "A stream flows at the rate of $a$ miles an hour, and a man can row in still water $b$ miles an hour. How far can the man row up the stream in an hour? In 6 hours? How far down the stream in an hour? In 3 hours?", "answer_latex": [ "$3(b+a)$ miles." ], "answer_markdown": [ "$3(b+a)$ miles." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "3*(b + a)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/46", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 46, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 46", "problem_latex": "A cistern can he filled by two pipes in 3 hours and 5 hours\nrespectively. What part of the cistern will be filled by both\npipes running together for one hour?", "markdown": "A cistern can he filled by two pipes in 3 hours and 5 hours respectively. What part of the cistern will be filled by both pipes running together for one hour?", "answer_latex": [ "$\\frac{8}{15}$ of the cistern." ], "answer_markdown": [ "$\\frac{8}{15}$ of the cistern." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 0.533333333333, printed 8/15 (half-unit 1.0e-40; correctly rounded at the printed digits: 0.533333333333)", "problem_expr": "Rational(1, 3) + Rational(1, 5)", "answer_expr": "Rational(8, 15)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 8/15" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": "X#\\frac{8}{15},5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/47a", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 47, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 47a", "problem_latex": "Nine years ago Henry was three times as old as Julius. If\nHenry is $b$ years old, how old was Julius then? How old is Julius\nnow?", "markdown": "Nine years ago Henry was three times as old as Julius. If Henry is $b$ years old, how old was Julius then? How old is Julius now?", "answer_latex": [ "$\\frac{b-9}{3}$;" ], "answer_markdown": [ "$\\frac{b-9}{3}$;" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(3*x, b - 9)", "answer_expr": "(b - 9)/3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*x, a - 9)" ], "shape": [ "solve: Eq(N*x, N + a)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/47b", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 47, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 47b", "problem_latex": "Nine years ago Henry was three times as old as Julius. If\nHenry is $b$ years old, how old was Julius then? How old is Julius\nnow?", "markdown": "Nine years ago Henry was three times as old as Julius. If Henry is $b$ years old, how old was Julius then? How old is Julius now?", "answer_latex": [ "$\\frac{b-9}{3}+9$ years." ], "answer_markdown": [ "$\\frac{b-9}{3}+9$ years." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(3*(J - 9), b - 9)", "answer_expr": "(b - 9)/3 + 9" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*x - 27, a - 9)" ], "shape": [ "solve: Eq(N*x + N, N + a)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/5", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 5", "problem_latex": "$x^2 - 6cx + 9c^2$.", "markdown": "$x^2 - 6cx + 9c^2$.", "answer_latex": [ "$(x - 3c)^2$." ], "answer_markdown": [ "$(x - 3c)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2 - 6*c*x + 9*c**2", "answer_expr": "(x - 3*c)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 9*a**2 - 6*a*x + x**2" ], "shape": [ "factor: N*a*x + N*a**N + x**N" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-37/7", "wentworth-first-steps-in-algebra-1894/ex-39/8" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/6", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 6", "problem_latex": "$16x^2 - 8xy + y^2$.", "markdown": "$16x^2 - 8xy + y^2$.", "answer_latex": [ "$(4x - y)^2$." ], "answer_markdown": [ "$(4x - y)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "16*x**2 - 8*x*y + y**2", "answer_expr": "(4*x - y)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2 - 8*a*x + 16*x**2" ], "shape": [ "factor: N*a*x + N*x**N + a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/7", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 7", "problem_latex": "$a^2 + 2a + 1$.", "markdown": "$a^2 + 2a + 1$.", "answer_latex": [ "$(a + 1)^2$." ], "answer_markdown": [ "$(a + 1)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 + 2*a + 1", "answer_expr": "(a + 1)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 + 2*x + 1" ], "shape": [ "factor: N*x + x**N + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/8", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 8", "problem_latex": "$9 - 6x + x^2$.", "markdown": "$9 - 6x + x^2$.", "answer_latex": [ "$(3 - x)^2$." ], "answer_markdown": [ "$(3 - x)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "9 - 6*x + x**2", "answer_expr": "(3 - x)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 - 6*x + 9" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-36/9", "set": "boyden-first-book-in-algebra-1895/ex-36", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 36, problem 9", "problem_latex": "$x^2 - 10x + 25$.", "markdown": "$x^2 - 10x + 25$.", "answer_latex": [ "$(x - 5)^2$." ], "answer_markdown": [ "$(x - 5)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2 - 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4*a - 77", "answer_expr": "(a-11)*(a+7)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 - 4*x - 77" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/11", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 11", "problem_latex": "$x^2-2x-63$.", "markdown": "$x^2-2x-63$.", "answer_latex": [ "$(x-9)(x+7)$." ], "answer_markdown": [ "$(x-9)(x+7)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2 - 2*x - 63", "answer_expr": "(x-9)*(x+7)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 - 2*x - 63" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/12", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 12", "problem_latex": "$a^2+10a-75$.", "markdown": "$a^2+10a-75$.", "answer_latex": [ "$(a+15)(a-5)$." ], "answer_markdown": [ "$(a+15)(a-5)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 + 10*a - 75", "answer_expr": "(a+15)*(a-5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 + 10*x - 75" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/13", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 13", "problem_latex": "$a^2-24a+143$.", "markdown": "$a^2-24a+143$.", "answer_latex": [ "$(a-11)(a-13)$." ], "answer_markdown": [ "$(a-11)(a-13)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 - 24*a + 143", "answer_expr": "(a-11)*(a-13)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 - 24*x + 143" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/14", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 14", "problem_latex": "$x^6-4x^3-117$.", "markdown": "$x^6-4x^3-117$.", "answer_latex": [ "$(a^3-13)(a^3+9)$." ], "answer_markdown": [ "$(a^3-13)(a^3+9)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**6 - 4*x**3 - 117", "answer_expr": "(x**3-13)*(x**3+9)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**6 - 4*x**3 - 117" ], "shape": [ "factor: N*x**N + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/15", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 15", "problem_latex": "$x^6+4x^3-77$.", "markdown": "$x^6+4x^3-77$.", "answer_latex": [ "$(x^3+11)(x^3-7)$." ], "answer_markdown": [ "$(x^3+11)(x^3-7)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**6 + 4*x**3 - 77", "answer_expr": "(x**3+11)*(x**3-7)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**6 + 4*x**3 - 77" ], "shape": [ "factor: N*x**N + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/16", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 16", "problem_latex": "$30+11x+x^2$.", "markdown": "$30+11x+x^2$.", "answer_latex": [ "$(6+x)(5+x)$." ], "answer_markdown": [ "$(6+x)(5+x)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "30 + 11*x + x**2", "answer_expr": "(6+x)*(5+x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 + 11*x + 30" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/17", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 17", "problem_latex": "$21+10a+a^2$.", "markdown": "$21+10a+a^2$.", "answer_latex": [ "$(7+a)(3+a)$." ], "answer_markdown": [ "$(7+a)(3+a)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "21 + 10*a + a**2", "answer_expr": "(7+a)*(3+a)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 + 10*x + 21" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/18", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 18", "problem_latex": "$35-12x+x^2$.", "markdown": "$35-12x+x^2$.", "answer_latex": [ "$(7-x)(5-x)$, or $(x-7)(x-5)$." ], "answer_markdown": [ "$(7-x)(5-x)$, or $(x-7)(x-5)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "35 - 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14*x**2*y**2 + 45*y**4", "answer_expr": "(x**2-5*y**2)*(x+3*y)*(x-3*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 45*a**4 - 14*a**2*x**2 + x**4" ], "shape": [ "factor: N*a**N*x**N + N*a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/25", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 25", "problem_latex": "$x^5-23x^4+132x^3$.", "markdown": "$x^5-23x^4+132x^3$.", "answer_latex": [ "$x^3(x-12)(x-11)$." ], "answer_markdown": [ "$x^3(x-12)(x-11)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**5 - 23*x**4 + 132*x**3", "answer_expr": "x**3*(x-12)*(x-11)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**5 - 23*x**4 + 132*x**3" ], "shape": [ "factor: 2*N*x**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/26", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 26", "problem_latex": "$a^6-12a^5+35a^4$.", "markdown": "$a^6-12a^5+35a^4$.", "answer_latex": [ "$a^4(a-7)(a-5)$." ], "answer_markdown": [ "$a^4(a-7)(a-5)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**6 - 12*a**5 + 35*a**4", "answer_expr": "a**4*(a-7)*(a-5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**6 - 12*x**5 + 35*x**4" ], "shape": [ "factor: 2*N*x**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/27", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 27", "problem_latex": "$3ax^4-39ax^2+108a$.", "markdown": "$3ax^4-39ax^2+108a$.", "answer_latex": [ "$3a(x+3)(x-3)(x+2)(x-2)$." ], "answer_markdown": [ "$3a(x+3)(x-3)(x+2)(x-2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "3*a*x**4 - 39*a*x**2 + 108*a", "answer_expr": "3*a*(x+3)*(x-3)*(x+2)*(x-2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 3*a*x**4 - 39*a*x**2 + 108*a" ], "shape": [ "factor: 2*N*a*x**N + N*a" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/28", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 28", "problem_latex": "$3a^3-12a^2b+12ab^2$.", "markdown": "$3a^3-12a^2b+12ab^2$.", "answer_latex": [ "$3a\\left(a-2b\\right)^2$." ], "answer_markdown": [ "$3a\\left(a-2b\\right)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "3*a**3 - 12*a**2*b + 12*a*b**2", "answer_expr": "3*a*(a-2*b)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 12*a**2*x - 12*a*x**2 + 3*x**3" ], "shape": [ "factor: N*a*x**N + N*a**N*x + N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/29", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 29", "problem_latex": "$c^5d^3-c^2-a^2c^3d^3+a^2$.", "markdown": "$c^5d^3-c^2-a^2c^3d^3+a^2$.", "answer_latex": [ "$(c-a)(c+a)(cd-1)(c^2d^2+cd+1)$." ], "answer_markdown": [ "$(c-a)(c+a)(cd-1)(c^2d^2+cd+1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "c**5*d**3 - c**2 - a**2*c**3*d**3 + a**2", "answer_expr": "(c-a)*(c+a)*(c*d-1)*(c**2*d**2+c*d+1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**2*b**3*x**3 + a**2 + b**3*x**5 - x**2" ], "shape": [ "factor: -a**N*b**N*x**N + a**N + b**N*x**N - x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/3", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 3", "problem_latex": "$x^2-5x+6$.", "markdown": "$x^2-5x+6$.", "answer_latex": [ "$(x-3)(x-2)$." ], "answer_markdown": [ "$(x-3)(x-2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2 - 5*x + 6", "answer_expr": "(x-3)*(x-2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 - 5*x + 6" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-38/2" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/30", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 30", "problem_latex": "$ax^2+bx^2-5bx-5ax+6b+6a$.", "markdown": "$ax^2+bx^2-5bx-5ax+6b+6a$.", "answer_latex": [ "$(a+b)(x-3)(x-2)$." ], "answer_markdown": [ "$(a+b)(x-3)(x-2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a*x**2 + b*x**2 - 5*b*x - 5*a*x + 6*b + 6*a", "answer_expr": "(a+b)*(x-3)*(x-2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a*x**2 - 5*a*x + 6*a + b*x**2 - 5*b*x + 6*b" ], "shape": [ "factor: N*a*x + N*a + N*b*x + N*b + a*x**N + b*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/31", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 31, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 31", "problem_latex": "A field can be mowed by two men in $a$ hours and $b$ hours\nrespectively. What part of the field can be mowed by both men\nworking together for one hour?", "markdown": "A field can be mowed by two men in $a$ hours and $b$ hours respectively. What part of the field can be mowed by both men working together for one hour?", "answer_latex": [ "$\\frac{1}{a}+\\frac{1}{b}$." ], "answer_markdown": [ "$\\frac{1}{a}+\\frac{1}{b}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(r, 1/a + 1/b)", "answer_expr": "1/a + 1/b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x, 1/b + 1/a)" ], "shape": [ "solve: Eq(x, 1/b + 1/a)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/32", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 32, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 32", "problem_latex": "In how many days can two men do as much as $x$ men in 7\ndays?", "markdown": "In how many days can two men do as much as $x$ men in 7 days?", "answer_latex": [ "$\\frac{7x}{2}$ days." ], "answer_markdown": [ "$\\frac{7x}{2}$ days." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(2*d, 7*x)", "answer_expr": "7*x/2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(2*x, 7*a)" ], "shape": [ "solve: Eq(N*x, N*a)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/4", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 4", "problem_latex": "$a^2-7a+10$.", "markdown": "$a^2-7a+10$.", "answer_latex": [ "$(a-5)(a-2)$." ], "answer_markdown": [ "$(a-5)(a-2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 - 7*a + 10", "answer_expr": "(a-5)*(a-2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 - 7*x + 10" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/5", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 5", "problem_latex": "$y^2-10y+16$.", "markdown": "$y^2-10y+16$.", "answer_latex": [ "$(y-8)(y-2)$." ], "answer_markdown": [ "$(y-8)(y-2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "y**2 - 10*y + 16", "answer_expr": "(y-8)*(y-2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 - 10*x + 16" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/6", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 6", "problem_latex": "$c^2-c-6$.", "markdown": "$c^2-c-6$.", "answer_latex": [ "$(c-3)(c+2)$." ], "answer_markdown": [ "$(c-3)(c+2)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "c**2 - c - 6", "answer_expr": "(c-3)*(c+2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 - x - 6" ], "shape": [ "factor: N - x + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/7", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 7", "problem_latex": "$x^2+4x-5$.", "markdown": "$x^2+4x-5$.", "answer_latex": [ "$(x+5)(x-1)$." ], "answer_markdown": [ "$(x+5)(x-1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2 + 4*x - 5", "answer_expr": "(x+5)*(x-1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 + 4*x - 5" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-38/5" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/8", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 8", "problem_latex": "$x^2+5x-6$.", "markdown": "$x^2+5x-6$.", "answer_latex": [ "$(x+6)(x-1)$." ], "answer_markdown": [ "$(x+6)(x-1)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2 + 5*x - 6", "answer_expr": "(x+6)*(x-1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 + 5*x - 6" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-37/9", "set": "boyden-first-book-in-algebra-1895/ex-37", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 37, problem 9", "problem_latex": "$y^2+8y-65$.", "markdown": "$y^2+8y-65$.", "answer_latex": [ "$(y+13)(y-5)$." ], "answer_markdown": [ "$(y+13)(y-5)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "y**2 + 8*y - 65", "answer_expr": "(y+13)*(y-5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 + 8*x - 65" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/1", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 1", "problem_latex": "Divide $50a+9a^4+24-67a^2$ by $a+a^2-6$.", "markdown": "Divide $50a+9a^4+24-67a^2$ by $a+a^2-6$.", "answer_latex": [ "$9a^2 - 9a - 4$." ], "answer_markdown": [ "$9a^2 - 9a - 4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(50*a+9*a**4+24-67*a**2)/(a+a**2-6)", "answer_expr": "9*a**2 - 9*a - 4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (9*x**4 - 67*x**2 + 50*x + 24)/(x**2 + x - 6)" ], "shape": [ "identity: (N*x + 2*N*x**N + N)/(N + x + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/10", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 10", "problem_latex": "$8c^6-d^9$.", "markdown": "$8c^6-d^9$.", "answer_latex": [ "$\\left(2c^2 - d^3\\right)\\left(4c^4 + 2c^2d^3 + d^6\\right)$." ], "answer_markdown": [ "$\\left(2c^2 - d^3\\right)\\left(4c^4 + 2c^2d^3 + d^6\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "8*c**6-d**9", "answer_expr": "(2*c**2-d**3)*(4*c**4+2*c**2*d**3+d**6)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**9 + 8*x**6" ], "shape": [ "factor: N*x**N - a**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/11", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 11", "problem_latex": "$1+64x^3$.", "markdown": "$1+64x^3$.", "answer_latex": [ "$\\left(1 + 4x\\right)\\left(1 - 4x + 16x^2\\right)$." ], "answer_markdown": [ "$\\left(1 + 4x\\right)\\left(1 - 4x + 16x^2\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "1+64*x**3", "answer_expr": "(1+4*x)*(1-4*x+16*x**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 64*x**3 + 1" ], "shape": [ "factor: N*x**N + 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/12", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 12", "problem_latex": "$a^6-1$.", "markdown": "$a^6-1$.", "answer_latex": [ "$\\left(a+1\\right)\\left(a^2 - a + 1\\right)\n\\left(a - 1\\right)\\left(a^2 + a + 1\\right)$." ], "answer_markdown": [ "$\\left(a+1\\right)\\left(a^2 - a + 1\\right) \\left(a - 1\\right)\\left(a^2 + a + 1\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**6-1", "answer_expr": "(a+1)*(a**2-a+1)*(a-1)*(a**2+a+1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**6 - 1" ], "shape": [ "factor: x**N - 1" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/13", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 13", "problem_latex": "$x^3+2x^2-x-2$.", "markdown": "$x^3+2x^2-x-2$.", "answer_latex": [ "$\\left(x+2\\right)\\left(x+1\\right)\\left(x-1\\right)$." ], "answer_markdown": [ "$\\left(x+2\\right)\\left(x+1\\right)\\left(x-1\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**3+2*x**2-x-2", "answer_expr": "(x+2)*(x+1)*(x-1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**3 + 2*x**2 - x - 2" ], "shape": [ "factor: N*x**N + N - x + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/14", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 14", "problem_latex": "$x^5-y^5$.", "markdown": "$x^5-y^5$.", "answer_latex": [ "$\\left(x-y\\right)\\left(x^4 + x^3y + x^2y^2 + xy^3 + y^4\\right)$." ], "answer_markdown": [ "$\\left(x-y\\right)\\left(x^4 + x^3y + x^2y^2 + xy^3 + y^4\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**5-y**5", "answer_expr": "(x-y)*(x**4+x**3*y+x**2*y**2+x*y**3+y**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**5 + x**5" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/15", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 15", "problem_latex": "$27+12x+x^2$.", "markdown": "$27+12x+x^2$.", "answer_latex": [ "$\\left(9+x\\right)\\left(3+x\\right)$." ], "answer_markdown": [ "$\\left(9+x\\right)\\left(3+x\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "27+12*x+x**2", "answer_expr": "(9+x)*(3+x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 + 12*x + 27" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/16", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 16", "problem_latex": "Find the cube root of $96m-64-40m^3+m^6+6m^5$.", "markdown": "Find the cube root of $96m-64-40m^3+m^6+6m^5$.", "answer_latex": [ "$m^2 + 2m - 4$." ], "answer_markdown": [ "$m^2 + 2m - 4$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "96*m-64-40*m**3+m**6+6*m**5", "answer_expr": "m**2 + 2*m - 4" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/17", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 17", "problem_latex": "Simplify $\\left(m+2n\\right)^2-\\left(2m-n\\right)^2$.", "markdown": "Simplify $\\left(m+2n\\right)^2-\\left(2m-n\\right)^2$.", "answer_latex": [ "$-3m^2 + 8mn + 3n^2$." ], "answer_markdown": [ "$-3m^2 + 8mn + 3n^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(m+2*n)**2-(2*m-n)**2", "answer_expr": "-3*m**2 + 8*m*n + 3*n**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -(-a + 2*x)**2 + (2*a + x)**2" ], "shape": [ "identity: (N*a + x)**N - (N*x - a)**N" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/18", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 18", "problem_latex": "Simplify $(5+7x)(5-7x)-\\left(3+2x\\right)^2+(x-9)(x-4)$.", "markdown": "Simplify $(5+7x)(5-7x)-\\left(3+2x\\right)^2+(x-9)(x-4)$.", "answer_latex": [ "$52 - 25x - 52x^2$." ], "answer_markdown": [ "$52 - 25x - 52x^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(5+7*x)*(5-7*x)-(3+2*x)**2+(x-9)*(x-4)", "answer_expr": "52 - 25*x - 52*x**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-7*x + 5)*(7*x + 5) + (x - 9)*(x - 4) - (2*x + 3)**2" ], "shape": [ "identity: (N + x)**2 + (N*x + N)**2 - (N*x + N)**N" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/19", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 19", "problem_latex": "Simplify $(y+x)(y^2-xy+x^2)-(y-x)(y^2+yx+x^2)$.", "markdown": "Simplify $(y+x)(y^2-xy+x^2)-(y-x)(y^2+yx+x^2)$.", "answer_latex": [ "$2x^3$." ], "answer_markdown": [ "$2x^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(y+x)*(y**2-x*y+x**2)-(y-x)*(y**2+y*x+x**2)", "answer_expr": "2*x**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -(a - x)*(a**2 + a*x + x**2) + (a + x)*(a**2 - a*x + x**2)" ], "shape": [ "identity: -(a - x)*(a*x + a**N + x**N) + (a + x)*(-a*x + a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/2", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 2", "problem_latex": "Find the square root of\n\\[\n12y^5-14y^3+1-8y^4+4y+9y^6.\n\\]", "markdown": "Find the square root of 12y^5-14y^3+1-8y^4+4y+9y^6.", "answer_latex": [ "$3y^3 + 2y^2 - 2y - 1$." ], "answer_markdown": [ "$3y^3 + 2y^2 - 2y - 1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "12*y**5-14*y**3+1-8*y**4+4*y+9*y**6", "answer_expr": "3*y**3 + 2*y**2 - 2*y - 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/20", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 20", "problem_latex": "Find three consecutive numbers whose sum is 57.", "markdown": "Find three consecutive numbers whose sum is 57.", "answer_latex": [ "18; 19; 20." ], "answer_markdown": [ "18; 19; 20." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 18, b: 19, c: 20}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 1), Eq(b, a + 1), Eq(a + b + x, 57))" ], "shape": [ "solve: (Eq(a, x + 1), Eq(b, a + 1), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/21", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 21", "problem_latex": "What number, being increased by three-fifths of itself, will\nequal twice itself diminished by 24?", "markdown": "What number, being increased by three-fifths of itself, will equal twice itself diminished by 24?", "answer_latex": [ "60." ], "answer_markdown": [ "60." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 60}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(8*x/5, 2*x - 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y^4$." ], "answer_markdown": [ "$x^4 - y^4$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x+y)*(x-y)*(x**2+y**2)", "answer_expr": "x**4 - y**4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a + x)*(a + x)*(a**2 + x**2)" ], "shape": [ "identity: (-a + x)*(a + x)*(a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/4", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 4", "problem_latex": "What must be subtracted from $a^3-5a^2+27a-1$ to produce\n$a+1$?", "markdown": "What must be subtracted from $a^3-5a^2+27a-1$ to produce $a+1$?", "answer_latex": [ "$a^3 - 5a^2 + 26a - 2$." ], "answer_markdown": [ "$a^3 - 5a^2 + 26a - 2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "a**3-5*a**2+27*a-1-(a+1)", "answer_expr": "a**3 - 5*a**2 + 26*a - 2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: x**3 - 5*x**2 + 26*x - 2" ], "shape": [ "identity: N*x + N*x**N + N + x**N" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/5", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 5", "problem_latex": "Expand $\\left(x^2y-4z^3a^4\\right)^3$.", "markdown": "Expand $\\left(x^2y-4z^3a^4\\right)^3$.", "answer_latex": [ "$x^6y^3 - 12x^4y^2z^3a^4 + 48x^2yz^8a^8 - 64z^9a^{12}$." ], "answer_markdown": [ "$x^6y^3 - 12x^4y^2z^3a^4 + 48x^2yz^8a^8 - 64z^9a^{12}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-2039474385.4733165029", "-2022575795.3772983019" ], "problem_expr": "(x**2*y-4*z**3*a**4)**3", "answer_expr": "x**6*y**3 - 12*x**4*y**2*z**3*a**4 + 48*x**2*y*z**8*a**8 - 64*z**9*a**12" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (-4*a**4*c**3 + b*x**2)**3" ], "shape": [ "identity: (N*a**N*c**N + b*x**N)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/6", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 6", "problem_latex": "$x^2-11x+10$.", "markdown": "$x^2-11x+10$.", "answer_latex": [ "$\\left(x-10\\right)\\left(x-1\\right)$." ], "answer_markdown": [ "$\\left(x-10\\right)\\left(x-1\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2-11*x+10", "answer_expr": "(x-10)*(x-1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 - 11*x + 10" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/7", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 7", "problem_latex": "$\\left(a+b\\right)^2-\\left(c+d\\right)^2$.", "markdown": "$\\left(a+b\\right)^2-\\left(c+d\\right)^2$.", "answer_latex": [ "$\\left(a + b + c + d\\right)\\left(a + b - c - d\\right)$." ], "answer_markdown": [ "$\\left(a + b + c + d\\right)\\left(a + b - c - d\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "(a+b)**2-(c+d)**2", "answer_expr": "(a+b+c+d)*(a+b-c-d)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: (a + x)**2 - (b + c)**2" ], "shape": [ "factor: (a + x)**N - (b + c)**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/8", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 8", "problem_latex": "$6x^3+4x^2-9x-6$.", "markdown": "$6x^3+4x^2-9x-6$.", "answer_latex": [ "$\\left(2x^2 - 3\\right)\\left(3x + 2\\right)$." ], "answer_markdown": [ "$\\left(2x^2 - 3\\right)\\left(3x + 2\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "6*x**3+4*x**2-9*x-6", "answer_expr": "(2*x**2-3)*(3*x+2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 6*x**3 + 4*x**2 - 9*x - 6" ], "shape": [ "factor: N*x + 2*N*x**N + N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-38/9", "set": "boyden-first-book-in-algebra-1895/ex-38", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 38, problem 9", "problem_latex": "$9x^8-66x^6+121x^4$.", "markdown": "$9x^8-66x^6+121x^4$.", "answer_latex": [ "$x^4\\left(3x^2 - 11\\right)^2$." ], "answer_markdown": [ "$x^4\\left(3x^2 - 11\\right)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "9*x**8-66*x**6+121*x**4", "answer_expr": "x**4*(3*x**2-11)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 9*x**8 - 66*x**6 + 121*x**4" ], "shape": [ "factor: 3*N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/1", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 1", "problem_latex": "$3a^4 b^3 + 6a^2 b^5$ and $9a^3 b^2 + 18 a b^3$.", "markdown": "$3a^4 b^3 + 6a^2 b^5$ and $9a^3 b^2 + 18 a b^3$.", "answer_latex": [ "$3ab^2$." ], "answer_markdown": [ "$3ab^2$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "3*a*b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (18*a**3*x + 9*a**2*x**3, 6*a**5*x**2 + 3*a**3*x**4)" ], "shape": [ "hcf: (N*a**N*x + N*a**N*x**N, 2*N*a**N*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/10", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 10", "problem_latex": "$y^3 - y$, $y^3 + 9y^2 - 10y$, and $y^4-y$.", "markdown": "$y^3 - y$, $y^3 + 9y^2 - 10y$, and $y^4-y$.", "answer_latex": [ "$y\\left(y-1\\right)$." ], "answer_markdown": [ "$y\\left(y-1\\right)$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "y*(y - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (x**3 - x, x**4 - x, x**3 + 9*x**2 - 10*x)" ], "shape": [ "hcf: (-x + x**N, -x + x**N, N*x + N*x**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/11", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 11", "problem_latex": "$x^2 - y^2$, $xy - y^2 + xz - yz$, and $x^3 - x^2 y + xy^2 -\ny^3$.", "markdown": "$x^2 - y^2$, $xy - y^2 + xz - yz$, and $x^3 - x^2 y + xy^2 - y^3$.", "answer_latex": [ "$x-y$." ], "answer_markdown": [ "$x-y$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "x - y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (-a**2 + x**2, -a**3 + a**2*x - a*x**2 + x**3, -a**2 - a*b + a*x + b*x)" ], "shape": [ "hcf: (-a**N + x**N, -a*x**N + a**N*x - a**N + x**N, -a*b + a*x - a**N + b*x)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/12", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 12", "problem_latex": "$3a c^5 d^3 - 3a c^2 - 3a^3 c^3 d^3 + 3a3$ and $9a^2 c^4 -\n9a^6$.", "markdown": "$3a c^5 d^3 - 3a c^2 - 3a^3 c^3 d^3 + 3a3$ and $9a^2 c^4 - 9a^6$.", "answer_latex": [ "$3a\\left(c^2-a^2\\right)$." ], "answer_markdown": [ "$3a\\left(c^2-a^2\\right)$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "3*a*(c**2 - a**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (9*a**4*x**2 - 9*x**6, 3*a**5*b**3*x - 3*a**3*b**3*x**3 - 3*a**2*x + 3*x**3)" ], "shape": [ "hcf: (N*a**N*x**N + N*x**N, N*a**N*b**N*x + N*a**N*b**N*x**N + N*a**N*x + N*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/13", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 13", "problem_latex": "$64x^{11} - 8x^2 y^6$ and $12x^8 + 3x^2 y^4 - 12x^5 y^2$.", "markdown": "$64x^{11} - 8x^2 y^6$ and $12x^8 + 3x^2 y^4 - 12x^5 y^2$.", "answer_latex": [ "$x^2\\left(2x^3-y^2\\right)$." ], "answer_markdown": [ "$x^2\\left(2x^3-y^2\\right)$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "x**2*(2*x**3 - y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (-8*a**6*x**2 + 64*x**11, 3*a**4*x**2 - 12*a**2*x**5 + 12*x**8)" ], "shape": [ "hcf: (N*a**N*x**N + N*x**N, 2*N*a**N*x**N + N*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/14", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 14", "problem_latex": "A merchant mixes $a$ pounds of tea worth $x$ cents a pound\nwith $b$ pounds worth $y$ cents a pound. How much is the mixture\nworth per pound?", "markdown": "A merchant mixes $a$ pounds of tea worth $x$ cents a pound with $b$ pounds worth $y$ cents a pound. How much is the mixture worth per pound?", "answer_latex": [ "$\\displaystyle \\frac{ax+by}{a+b}$ cts." ], "answer_markdown": [ "$\\displaystyle \\frac{ax+by}{a+b}$ cts." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "(a*x + b*y)/(a + b)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/15", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 15", "problem_latex": "If a man bought a horse for $x$ dollars and sold him so as\nto gain $5 \\%$, what will represent the number of dollars he\ngained?", "markdown": "If a man bought a horse for $x$ dollars and sold him so as to gain $5 \\%$, what will represent the number of dollars he gained?", "answer_latex": [ "$\\displaystyle \\frac{5}{100}x$ dols." ], "answer_markdown": [ "$\\displaystyle \\frac{5}{100}x$ dols." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "Rational(5,100)*x" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/16", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 16", "problem_latex": "The difference between two numbers is 6, and if 4 be added\nto the greater, the result will be three times the smaller. What\nare the numbers?", "markdown": "The difference between two numbers is 6, and if 4 be added to the greater, the result will be three times the smaller. What are the numbers?", "answer_latex": [ "5; 11." ], "answer_markdown": [ "5; 11." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 11, y: 5}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(x + 4, 3*a), Eq(-a + x, 6))" ], "shape": [ "solve: (Eq(N + x, N*a), Eq(-a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/2", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 2", "problem_latex": "$5 x^5 y - 15 x^2 y^2$ and $15x^3 y^3 - 45 x y^5$.", "markdown": "$5 x^5 y - 15 x^2 y^2$ and $15x^3 y^3 - 45 x y^5$.", "answer_latex": [ "$5xy$." ], "answer_markdown": [ "$5xy$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "5*x*y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (-45*a**5*x + 15*a**3*x**3, -15*a**2*x**2 + 5*a*x**5)" ], "shape": [ "hcf: (N*a**N*x + N*a**N*x**N, N*a*x**N + N*a**N*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/3", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 3", "problem_latex": "$2x^5 y^4 + 2x^2 y^7$ and $6 x^3 y^3 - 6x y^5$.", "markdown": "$2x^5 y^4 + 2x^2 y^7$ and $6 x^3 y^3 - 6x y^5$.", "answer_latex": [ "$2xy^3\\left(x+y\\right)$." ], "answer_markdown": [ "$2xy^3\\left(x+y\\right)$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "2*x*y**3*(x + y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (-6*a**5*x + 6*a**3*x**3, 2*a**7*x**2 + 2*a**4*x**5)" ], "shape": [ "hcf: (N*a**N*x + N*a**N*x**N, 2*N*a**N*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/4", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 4", "problem_latex": "$3a^6 b - 3a^3 b^4$ and $12a^4 b^4 - 12a^2 b^6$.", "markdown": "$3a^6 b - 3a^3 b^4$ and $12a^4 b^4 - 12a^2 b^6$.", "answer_latex": [ "$3a^2b\\left(a-b\\right)$." ], "answer_markdown": [ "$3a^2b\\left(a-b\\right)$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "3*a**2*b*(a - b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (-12*a**6*x**2 + 12*a**4*x**4, -3*a**4*x**3 + 3*a*x**6)" ], "shape": [ "hcf: (2*N*a**N*x**N, N*a*x**N + N*a**N*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/5", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 5", "problem_latex": "$mx - ma - nx + na$ and $m^3 - n^3$.", "markdown": "$mx - ma - nx + na$ and $m^3 - n^3$.", "answer_latex": [ "$m-n$." ], "answer_markdown": [ "$m-n$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "m - n" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (-b**3 + x**3, a*b - a*x - b*c + c*x)" ], "shape": [ "hcf: (-b**N + x**N, a*b - a*x - b*c + c*x)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/6", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 6", "problem_latex": "$81 x^8 - 16$ and $81x^8-72x^4 + 16$.", "markdown": "$81 x^8 - 16$ and $81x^8-72x^4 + 16$.", "answer_latex": [ "$9x^4-4$." ], "answer_markdown": [ "$9x^4-4$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "9*x**4 - 4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (81*x**8 - 16, 81*x**8 - 72*x**4 + 16)" ], "shape": [ "hcf: (N*x**N + N, 2*N*x**N + N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/7", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 7", "problem_latex": "$x^2 - 20 - x$, $3x^2 - 24 x + 45$, and $x^2 - 5x$.", "markdown": "$x^2 - 20 - x$, $3x^2 - 24 x + 45$, and $x^2 - 5x$.", "answer_latex": [ "$x-5$." ], "answer_markdown": [ "$x-5$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "x - 5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (x**2 - 5*x, x**2 - x - 20, 3*x**2 - 24*x + 45)" ], "shape": [ "hcf: (N*x + x**N, N - x + x**N, N*x + N*x**N + N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/8", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 8", "problem_latex": "$x^2 +x -6$, $x^2-15 - 2x$, and $3x^2-27$.", "markdown": "$x^2 +x -6$, $x^2-15 - 2x$, and $3x^2-27$.", "answer_latex": [ "$x+3$." ], "answer_markdown": [ "$x+3$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "x + 3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (3*x**2 - 27, x**2 - 2*x - 15, x**2 + x - 6)" ], "shape": [ "hcf: (N*x**N + N, N*x + N + x**N, N + x + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-39/9", "set": "boyden-first-book-in-algebra-1895/ex-39", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 39, problem 9", "problem_latex": "$a^4 - 16$, $a2 -a -6$, and $(a^2 -4)^2$.", "markdown": "$a^4 - 16$, $a2 -a -6$, and $(a^2 -4)^2$.", "answer_latex": [ "$a+2$." ], "answer_markdown": [ "$a+2$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "a + 2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: ((x**2 - 4)**2, x**4 - 16, x**2 - x - 6)" ], "shape": [ "hcf: ((N + x**N)**N, N + x**N, N - x + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/1", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 1", "problem_latex": "Charles and Henry together have 49 marbles, and\nCharles has twice as many as Henry and 4 more. How\nmany marbles has each?", "markdown": "Charles and Henry together have 49 marbles, and Charles has twice as many as Henry and 4 more. How many marbles has each?", "answer_latex": [ "C, 34; H, 15." ], "answer_markdown": [ "C, 34; H, 15." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{c: 34, h: 15}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 2*a + 4), Eq(a + x, 49))" ], "shape": [ "solve: (Eq(x, N*a + N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/10", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 10", "problem_latex": "Divide the number 23 into three parts, such that the second\nis 1 more than the first, and the third is twice the second.", "markdown": "Divide the number 23 into three parts, such that the second is 1 more than the first, and the third is twice the second.", "answer_latex": [ "5; 6; 12." ], "answer_markdown": [ "5; 6; 12." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{p1: 5, p2: 6, p3: 12}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 1), Eq(b, 2*a), Eq(a + b + x, 23))" ], "shape": [ "solve: (Eq(a, x + 1), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/11", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 11", "problem_latex": "Divide the number 137 into three parts, such that\nthe second shall be 3 more than the first, and the third\nfive times the second.", "markdown": "Divide the number 137 into three parts, such that the second shall be 3 more than the first, and the third five times the second.", "answer_latex": [ "17; 20; 100." ], "answer_markdown": [ "17; 20; 100." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 17, b: 20, c: 100}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 3), Eq(b, 5*a), Eq(a + b + x, 137))" ], "shape": [ "solve: (Eq(a, N + x), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/12", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 12", "problem_latex": "Mr. Ames builds three houses. The first cost \\$2000\nmore than the second, and the third twice as much as the\nfirst. If they all together cost \\$18,000, what was the cost\nof each house?", "markdown": "Mr. Ames builds three houses. The first cost $2000 more than the second, and the third twice as much as the first. If they all together cost $18,000, what was the cost of each house?", "answer_latex": [ "\\$5000; \\$3000; \\$10,000." ], "answer_markdown": [ "$5000; $3000; $10,000." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{f: 5000, s: 3000, t: 10000}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, a + 2000), Eq(b, 2*x), Eq(a + b + x, 18000))" ], "shape": [ "solve: (Eq(x, N + a), Eq(b, N*x), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/13", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 13", "problem_latex": "An artist, who had painted three pictures, charged\n\\$18 more for the second than the first, and three times as\nmuch for the third as the second. If he received \\$322 for\nthe three, what was the price of each picture?", "markdown": "An artist, who had painted three pictures, charged $18 more for the second than the first, and three times as much for the third as the second. If he received $322 for the three, what was the price of each picture?", "answer_latex": [ "\\$50; \\$68; \\$204." ], "answer_markdown": [ "$50; $68; $204." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{f: 50, s: 68, t: 204}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 18), Eq(b, 3*a), Eq(a + b + x, 322))" ], "shape": [ "solve: (Eq(a, N + x), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/14", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 14", "problem_latex": "Three men, A, B, and C, invest \\$47,000 in business.\nB puts in \\$500 more than twice as much as A, and C puts\nin three times as much as B. How many dollars does each\nput into the business?", "markdown": "Three men, A, B, and C, invest $47,000 in business. B puts in $500 more than twice as much as A, and C puts in three times as much as B. How many dollars does each put into the business?", "answer_latex": [ "A, \\$5000; B, \\$10,500; C, \\$31,500." ], "answer_markdown": [ "A, $5000; B, $10,500; C, $31,500." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{A: 5000, B: 10500, C: 31500}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x + 500), Eq(b, 3*a), Eq(a + b + x, 47000))" ], "shape": [ "solve: (Eq(a, N*x + N), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/15", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 15", "problem_latex": "In three lots of land there are 80,750 feet. The\nsecond lot contains 250 feet more than three times as\nmuch as the first lot, and the third lot contains twice as\nmuch as the second. What is the size of each lot?", "markdown": "In three lots of land there are 80,750 feet. The second lot contains 250 feet more than three times as much as the first lot, and the third lot contains twice as much as the second. What is the size of each lot?", "answer_latex": [ "8000; 24,250; 48,500ft." ], "answer_markdown": [ "8000; 24,250; 48,500ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{f: 8000, s: 24250, t: 48500}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 3*x + 250), Eq(b, 2*a), Eq(a + b + x, 80750))" ], "shape": [ "solve: (Eq(a, N*x + N), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/16", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 16", "problem_latex": "A man leaves by his will \\$225,000 to be divided\nas follows: his son to receive \\$10,000 less than twice as\nmuch as the daughter, and the widow four times as much\nas the son. What was the share of each?", "markdown": "A man leaves by his will $225,000 to be divided as follows: his son to receive $10,000 less than twice as much as the daughter, and the widow four times as much as the son. What was the share of each?", "answer_latex": [ "Daughter, \\$25,000; son, \\$40,000; widow, \\$160,000." ], "answer_markdown": [ "Daughter, $25,000; son, $40,000; widow, $160,000." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{d: 25000, s: 40000, w: 160000}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x - 10000), Eq(b, 4*a), Eq(a + b + x, 225000))" ], "shape": [ "solve: (Eq(a, N*x + N), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/17", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 17", "problem_latex": "A man and his two sons picked 25 quarts of berries.\nThe older son picked 5 quarts less than three times as\nmany as the younger son, and the father picked twice as\nmany as the older son. How many quarts did each pick?", "markdown": "A man and his two sons picked 25 quarts of berries. The older son picked 5 quarts less than three times as many as the younger son, and the father picked twice as many as the older son. How many quarts did each pick?", "answer_latex": [ "Father, 14 qts.; older son, 7 qts.; younger son, 4 qts." ], "answer_markdown": [ "Father, 14 qts.; older son, 7 qts.; younger son, 4 qts." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{F: 14, O: 7, Y: 4}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 2*a), Eq(a, 3*b - 5), Eq(a + b + x, 25))" ], "shape": [ "solve: (Eq(x, N*a), Eq(a, N*b + N), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/18", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 18", "problem_latex": "Three brothers have 574 stamps. John has 15 less than Henry,\nand Thomas has 4 more than John. How many has each?", "markdown": "Three brothers have 574 stamps. John has 15 less than Henry, and Thomas has 4 more than John. How many has each?", "answer_latex": [ "H, 200 stamps; J, 185 stamps; T, 189 stamps." ], "answer_markdown": [ "H, 200 stamps; J, 185 stamps; T, 189 stamps." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{H: 200, J: 185, T: 189}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x - 15), Eq(b, a + 4), Eq(a + b + x, 574))" ], "shape": [ "solve: (Eq(a, N + x), Eq(b, N + a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/2", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 2", "problem_latex": "In an orchard containing 33 trees the number of\npear trees is 5 more than three times the number of apple\ntrees. How many are there of each kind?", "markdown": "In an orchard containing 33 trees the number of pear trees is 5 more than three times the number of apple trees. How many are there of each kind?", "answer_latex": [ "26 pear; 7 apple." ], "answer_markdown": [ "26 pear; 7 apple." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{p: 26, a: 7}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 3*a + 5), Eq(a + x, 33))" ], "shape": [ "solve: (Eq(x, N*a + N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/3", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 3", "problem_latex": "John and Mary gathered 23 quarts of nuts. John\ngathered 2 quarts more than twice as many as Mary. How\nmany quarts did each gather?", "markdown": "John and Mary gathered 23 quarts of nuts. John gathered 2 quarts more than twice as many as Mary. How many quarts did each gather?", "answer_latex": [ "J, 16 qts.; M, 7 qts." ], "answer_markdown": [ "J, 16 qts.; M, 7 qts." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{j: 16, m: 7}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 2*a + 2), Eq(a + x, 23))" ], "shape": [ "solve: (Eq(x, N*a + N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/4", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 4", "problem_latex": "To the double of a number I add 17 and obtain as\na result 147. What is the number?", "markdown": "To the double of a number I add 17 and obtain as a result 147. What is the number?", "answer_latex": [ "65." ], "answer_markdown": [ "65." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(2*x + 17, 147)", "answer_expr": "65" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(2*x + 17, 147)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": "X=65", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "147 ENTER 17 −", "2 ÷" ], "calculator_value": "+65E+0", "printed_value": "65", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/5", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 5", "problem_latex": "To four times a number I add 23 and obtain 95.\nWhat is the number?", "markdown": "To four times a number I add 23 and obtain 95. What is the number?", "answer_latex": [ "18." ], "answer_markdown": [ "18." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(4*x + 23, 95)", "answer_expr": "18" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(4*x + 23, 95)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": "X=18", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "95 ENTER 23 −", "4 ÷" ], "calculator_value": "+18E+0", "printed_value": "18", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/6", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 6", "problem_latex": "From three times a number I take 25 and obtain 47.\nWhat is the number?", "markdown": "From three times a number I take 25 and obtain 47. What is the number?", "answer_latex": [ "24." ], "answer_markdown": [ "24." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(3*x - 25, 47)", "answer_expr": "24" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*x - 25, 47)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": "X=24", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "47 ENTER 25 +", "3 ÷" ], "calculator_value": "+24E+0", "printed_value": "24", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/7", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 7", "problem_latex": "Find a number which being multiplied by 5 and having 14\nadded to the product will equal 69.", "markdown": "Find a number which being multiplied by 5 and having 14 added to the product will equal 69.", "answer_latex": [ "11." ], "answer_markdown": [ "11." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(5*x + 14, 69)", "answer_expr": "11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(5*x + 14, 69)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": "X=11", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "69 ENTER 14 −", "5 ÷" ], "calculator_value": "+11E+0", "printed_value": "11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/8", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 8", "problem_latex": "I bought some tea and coffee for \\$10.39. If I paid for the\ntea 61 cents more than five times as much as for the coffee, how\nmuch did I pay for each?", "markdown": "I bought some tea and coffee for $10.39. If I paid for the tea 61 cents more than five times as much as for the coffee, how much did I pay for each?", "answer_latex": [ "Tea, \\$8.76; coffee, \\$1.63." ], "answer_markdown": [ "Tea, $8.76; coffee, $1.63." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{t: Rational(876, 100), c: Rational(163, 100)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 5*a + 61/100), Eq(a + x, 1039/100))" ], "shape": [ "solve: (Eq(x, N*a + N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-4/9", "set": "boyden-first-book-in-algebra-1895/ex-4", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 4, problem 9", "problem_latex": "Two houses together contain 48 rooms. If the second house\nhas 3 more than twice as many rooms as the first, how many rooms\nhas each house?", "markdown": "Two houses together contain 48 rooms. If the second house has 3 more than twice as many rooms as the first, how many rooms has each house?", "answer_latex": [ "15; 33 rooms." ], "answer_markdown": [ "15; 33 rooms." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{f: 15, s: 33}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x + 3), Eq(a + x, 48))" ], "shape": [ "solve: (Eq(a, N*x + N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/1", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 1", "problem_latex": "$a^{2} - 4$ and $a^{2} + 3 a - 10$.", "markdown": "$a^{2} - 4$ and $a^{2} + 3 a - 10$.", "answer_latex": [ "$\\left(a^2-4\\right)\\left(a+5\\right)$." ], "answer_markdown": [ "$\\left(a^2-4\\right)\\left(a+5\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(a**2 - 4)*(a + 5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**2 - 4, x**2 + 3*x - 10)" ], "shape": [ "lcm: (N + x**N, N*x + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/10", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 10", "problem_latex": "$x^6 + x^3$, $2x^4 - 2x^2$, and $x^2 + x$.", "markdown": "$x^6 + x^3$, $2x^4 - 2x^2$, and $x^2 + x$.", "answer_latex": [ "$2x^3\\left(x^3+1\\right)\\left(x-1\\right)$." ], "answer_markdown": [ "$2x^3\\left(x^3+1\\right)\\left(x-1\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "2*x**3*(x**3 + 1)*(x - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**2 + x, 2*x**4 - 2*x**2, x**6 + x**3)" ], "shape": [ "lcm: (x + x**N, 2*N*x**N, 2*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/11", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 11", "problem_latex": "$a^4 + 2a^2 + 1$, $1 - 2a^2 + a^4$, and $1 - a^4$.", "markdown": "$a^4 + 2a^2 + 1$, $1 - 2a^2 + a^4$, and $1 - a^4$.", "answer_latex": [ "$\\left(1-a^4\\right)^2$." ], "answer_markdown": [ "$\\left(1-a^4\\right)^2$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(1 - a**4)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (-x**4 + 1, x**4 - 2*x**2 + 1, x**4 + 2*x**2 + 1)" ], "shape": [ "lcm: (-x**N + 1, N*x**N + x**N + 1, N*x**N + x**N + 1)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/12", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 12", "problem_latex": "$a^2z - x^2z$, $3ax - 3x^2$, and $2ax + 2a^2$.", "markdown": "$a^2z - x^2z$, $3ax - 3x^2$, and $2ax + 2a^2$.", "answer_latex": [ "$6axz\\left(a^2 - x^2\\right)$." ], "answer_markdown": [ "$6axz\\left(a^2 - x^2\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "6*a*x*z*(a**2 - x**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (2*a*x + 2*x**2, -3*a**2 + 3*a*x, -a**2*b + b*x**2)" ], "shape": [ "lcm: (N*a*x + N*x**N, N*a*x + N*a**N, -a**N*b + b*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/13", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 13", "problem_latex": "$am + an - 3m - 3n$, $m^2 - n^2$, and $a^2 - 10a + 21$.", "markdown": "$am + an - 3m - 3n$, $m^2 - n^2$, and $a^2 - 10a + 21$.", "answer_latex": [ "$\\left(m^2-n^2\\right)\\left(a^2-10a+21\\right)$." ], "answer_markdown": [ "$\\left(m^2-n^2\\right)\\left(a^2-10a+21\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(m**2 - n**2)*(a**2 - 10*a + 21)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (a**2 - b**2, x**2 - 10*x + 21, a*x - 3*a + b*x - 3*b)" ], "shape": [ "lcm: (a**N - b**N, N*x + N + x**N, N*a + N*b + a*x + b*x)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/14", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 14", "problem_latex": "$3b - 3b^2$, $1 - b^3$, and $2x - 2b^2x$.", "markdown": "$3b - 3b^2$, $1 - b^3$, and $2x - 2b^2x$.", "answer_latex": [ "$6bx\\left(1-b^3\\right)\\left(1+b\\right)$." ], "answer_markdown": [ "$6bx\\left(1-b^3\\right)\\left(1+b\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "6*b*x*(1 - b**3)*(1 + b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (-x**3 + 1, -3*x**2 + 3*x, -2*a*x**2 + 2*a)" ], "shape": [ "lcm: (-x**N + 1, N*x + N*x**N, N*a*x**N + N*a)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/15", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 15", "problem_latex": "$a^2 - x^2 - a - x$, $5a^2b - 10abx + 5bx^2$, and $a^2b -\nabx - ab$.", "markdown": "$a^2 - x^2 - a - x$, $5a^2b - 10abx + 5bx^2$, and $a^2b - abx - ab$.", "answer_latex": [ "$5ab\\left(a+x\\right)\\left(a-x\\right)^2\\left(a-x-1\\right)$." ], "answer_markdown": [ "$5ab\\left(a+x\\right)\\left(a-x\\right)^2\\left(a-x-1\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "5*a*b*(a + x)*(a - x)**2*(a - x - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (-a*b*x + a*x**2 - a*x, 5*a*b**2 - 10*a*b*x + 5*a*x**2, -b**2 - b + x**2 - x)" ], "shape": [ "lcm: (-a*b*x - a*x + a*x**N, N*a*b*x + N*a*b**N + N*a*x**N, -b - b**N - x + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/16", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 16", "problem_latex": "The thermometer now indicates $c$ degrees above zero, but\nyesterday it indicated $y$ degrees below zero. How much warmer is\nit to-day than yesterday?", "markdown": "The thermometer now indicates $c$ degrees above zero, but yesterday it indicated $y$ degrees below zero. How much warmer is it to-day than yesterday?", "answer_latex": [ "$c + y$ degrees." ], "answer_markdown": [ "$c + y$ degrees." ], "checks": [ { "task": "identity", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "c - (-y)", "answer_expr": "c + y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "identity: a + x" ], "shape": [ "identity: a + x" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/17", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 17", "problem_latex": "A certain county extends from $b$ degrees north latitude to\n$y$ degrees north latitude. What is the extent of the county from\nnorth to south?", "markdown": "A certain county extends from $b$ degrees north latitude to $y$ degrees north latitude. What is the extent of the county from north to south?", "answer_latex": [ "$b - y$, or $y - b$ degrees." ], "answer_markdown": [ "$b - y$, or $y - b$ degrees." ], "checks": [ { "task": "identity", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "b - y", "answer_expr": "b - y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "identity: -a + x" ], "shape": [ "identity: -a + x" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/18", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 18", "problem_latex": "If A can build a wall in $x$ days, what part of the wall\nwill he build in two days?", "markdown": "If A can build a wall in $x$ days, what part of the wall will he build in two days?", "answer_latex": [ "$\\frac{2}{x}$." ], "answer_markdown": [ "$\\frac{2}{x}$." ], "checks": [ { "task": "identity", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "2*(1/x)", "answer_expr": "2/x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "identity: 2/x" ], "shape": [ "identity: N/x" ], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/19", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 19", "problem_latex": "How many times can $x^3 + 12$ be subtracted from $x^6 + 24\nx^3 + 144$?", "markdown": "How many times can $x^3 + 12$ be subtracted from $x^6 + 24 x^3 + 144$?", "answer_latex": [ "$x^3 + 12$." ], "answer_markdown": [ "$x^3 + 12$." ], "checks": [ { "task": "identity", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "(x**6 + 24*x**3 + 144)/(x**3 + 12)", "answer_expr": "x**3 + 12" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "identity: (x**6 + 24*x**3 + 144)/(x**3 + 12)" ], "shape": [ "identity: (N*x**N + N + x**N)/(N + x**N)" ], "same_problem_in": [], "needs": [ "cas.cancel" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/2", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 2", "problem_latex": "$x^{3} + 1$ and $x^{2} + 2 x + 1$.", "markdown": "$x^{3} + 1$ and $x^{2} + 2 x + 1$.", "answer_latex": [ "$\\left(x^3+1\\right)\\left(x+1\\right)$." ], "answer_markdown": [ "$\\left(x^3+1\\right)\\left(x+1\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(x**3 + 1)*(x + 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**3 + 1, x**2 + 2*x + 1)" ], "shape": [ "lcm: (x**N + 1, N*x + x**N + 1)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/20", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 20", "problem_latex": "Divide \\$2142 between two men so that one shall receive six\ntimes as much as the other.", "markdown": "Divide $2142 between two men so that one shall receive six times as much as the other.", "answer_latex": [ "\\$\\,306; \\$\\,1836." ], "answer_markdown": [ "$ 306; $ 1836." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{s: 306, L: 1836}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 6*x), Eq(a + x, 2142))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/3", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 3", "problem_latex": "$x^{2} - 2 x - 15$ and $x^{2} - 9$.", "markdown": "$x^{2} - 2 x - 15$ and $x^{2} - 9$.", "answer_latex": [ "$\\left(x^2-9\\right)\\left(x-5\\right)$." ], "answer_markdown": [ "$\\left(x^2-9\\right)\\left(x-5\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(x**2 - 9)*(x - 5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**2 - 9, x**2 - 2*x - 15)" ], "shape": [ "lcm: (N + x**N, N*x + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/4", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 4", "problem_latex": "$x^{4} - 4 x^{2} + 3$ and $x^{6} - 1$.", "markdown": "$x^{4} - 4 x^{2} + 3$ and $x^{6} - 1$.", "answer_latex": [ "$\\left(x^6-1\\right)\\left(x^2-3\\right)$." ], "answer_markdown": [ "$\\left(x^6-1\\right)\\left(x^2-3\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(x**6 - 1)*(x**2 - 3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**6 - 1, x**4 - 4*x**2 + 3)" ], "shape": [ "lcm: (x**N - 1, N*x**N + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/5", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 5", "problem_latex": "$x^2 - 1$, $x^2 - 4x + 3$, and $2x^2 - 2x - 12$.", "markdown": "$x^2 - 1$, $x^2 - 4x + 3$, and $2x^2 - 2x - 12$.", "answer_latex": [ "$2\\left(x^2-1\\right)\\left(x-3\\right)\\left(x+2\\right)$." ], "answer_markdown": [ "$2\\left(x^2-1\\right)\\left(x-3\\right)\\left(x+2\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "2*(x**2 - 1)*(x - 3)*(x + 2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**2 - 1, x**2 - 4*x + 3, 2*x**2 - 2*x - 12)" ], "shape": [ "lcm: (x**N - 1, N*x + N + x**N, N*x + N*x**N + N)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/6", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 6", "problem_latex": "$a^3 + 1 + 3a + 3a^2$ and $am - 2 - 2a + m$.", "markdown": "$a^3 + 1 + 3a + 3a^2$ and $am - 2 - 2a + m$.", "answer_latex": [ "$\\left(a+1\\right)^3\\left(m-2\\right)$." ], "answer_markdown": [ "$\\left(a+1\\right)^3\\left(m-2\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(a + 1)**3*(m - 2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**3 + 3*x**2 + 3*x + 1, a*x + a - 2*x - 2)" ], "shape": [ "lcm: (N*x + N*x**N + x**N + 1, N*x + N + a*x + a)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/7", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 7", "problem_latex": "$a^2 - 4$, $a^2 + 3a - 10$, $a^2 - 25$, $a^2 - 9$, $a^2 - 8a\n+ 15$, and $a^2 + 5a + 6$.", "markdown": "$a^2 - 4$, $a^2 + 3a - 10$, $a^2 - 25$, $a^2 - 9$, $a^2 - 8a + 15$, and $a^2 + 5a + 6$.", "answer_latex": [ "$\\left(a^2-4\\right)\\left(a^2-25\\right)\\left(a^2-9\\right)$." ], "answer_markdown": [ "$\\left(a^2-4\\right)\\left(a^2-25\\right)\\left(a^2-9\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(a**2 - 4)*(a**2 - 25)*(a**2 - 9)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**2 - 25, x**2 - 9, x**2 - 4, x**2 - 8*x + 15, x**2 + 3*x - 10, x**2 + 5*x + 6)" ], "shape": [ "lcm: (N + x**N, N + x**N, N + x**N, N*x + N + x**N, N*x + N + x**N, N*x + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/8", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 8", "problem_latex": "$x^3 - 1 - 3x^2 + 3x$ and $xy - 3 - y +3x$.", "markdown": "$x^3 - 1 - 3x^2 + 3x$ and $xy - 3 - y +3x$.", "answer_latex": [ "$\\left(x-1\\right)^3\\left(y+3\\right)$." ], "answer_markdown": [ "$\\left(x-1\\right)^3\\left(y+3\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(x - 1)**3*(y + 3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**3 - 3*x**2 + 3*x - 1, a*x - a + 3*x - 3)" ], "shape": [ "lcm: (N*x + N*x**N + x**N - 1, N*x + N + a*x - a)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-40/9", "set": "boyden-first-book-in-algebra-1895/ex-40", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 40, problem 9", "problem_latex": "$x^2 - 1$, $x^2 - 9$, $x^2 - 2x - 3$, $x^2 - 16$, $x^2 - x -\n12$, $x^2 + 5x + 4$.", "markdown": "$x^2 - 1$, $x^2 - 9$, $x^2 - 2x - 3$, $x^2 - 16$, $x^2 - x - 12$, $x^2 + 5x + 4$.", "answer_latex": [ "$\\left(x^2-1\\right)\\left(x^2-9\\right)\\left(x^2-16\\right)$." ], "answer_markdown": [ "$\\left(x^2-1\\right)\\left(x^2-9\\right)\\left(x^2-16\\right)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(x**2 - 1)*(x**2 - 9)*(x**2 - 16)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**2 - 16, x**2 - 9, x**2 - 1, x**2 - 2*x - 3, x**2 - x - 12, x**2 + 5*x + 4)" ], "shape": [ "lcm: (N + x**N, N + x**N, x**N - 1, N*x + N + x**N, N - x + x**N, N*x + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/1", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 1", "problem_latex": "$\\frac{\\displaystyle 15x^3y^2z}{\\displaystyle 40x^2y^2z^2}$.", "markdown": "$\\frac{\\displaystyle 15x^3y^2z}{\\displaystyle 40x^2y^2z^2}$.", "answer_latex": [ "$\\displaystyle \\frac{3x}{8z}$." ], "answer_markdown": [ "$\\displaystyle \\frac{3x}{8z}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(15*x**3*y**2*z)/(40*x**2*y**2*z**2)", "answer_expr": "3*x/(8*z)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*x/(8*a)" ], "shape": [ "identity: N*x/a" ], "same_problem_in": [], "needs": [ "cas.cancel" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/10", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 10", "problem_latex": "$\\displaystyle \\frac{a^2xy-x^3y^3}{ax^2-x^3y}$", "markdown": "$\\displaystyle \\frac{a^2xy-x^3y^3}{ax^2-x^3y}$", "answer_latex": [ "$\\displaystyle \\frac{y(a+xy)}{x}$." ], "answer_markdown": [ "$\\displaystyle \\frac{y(a+xy)}{x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**2*x*y-x**3*y**3)/(a*x**2-x**3*y)", "answer_expr": "y*(a+x*y)/x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2*b*x - b**3*x**3)/(a*x**2 - b*x**3)" ], "shape": [ "identity: (a**N*b*x - b**N*x**N)/(a*x**N - b*x**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/11", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 11", "problem_latex": "$\\displaystyle \\frac{a^4-b^4}{(a^2+2ab+b^2)(a^2+b^2)}$", "markdown": "$\\displaystyle \\frac{a^4-b^4}{(a^2+2ab+b^2)(a^2+b^2)}$", "answer_latex": [ "$\\displaystyle \\frac{a-b}{a+b}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a-b}{a+b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**4-b**4)/((a**2+2*a*b+b**2)*(a**2+b**2))", "answer_expr": "(a-b)/(a+b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a**4 + x**4)/((a**2 + x**2)*(a**2 + 2*a*x + x**2))" ], "shape": [ "identity: (-a**N + x**N)/((a**N + x**N)*(N*a*x + a**N + x**N))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/12", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 12", "problem_latex": "$\\displaystyle \\frac{x^8 -y^8}{(x^4+y^4)(x^4-2x^2y^2+y^4)}$", "markdown": "$\\displaystyle \\frac{x^8 -y^8}{(x^4+y^4)(x^4-2x^2y^2+y^4)}$", "answer_latex": [ "$\\displaystyle \\frac{x^2+y^2}{x^2-y^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2+y^2}{x^2-y^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**8-y**8)/((x**4+y**4)*(x**4-2*x**2*y**2+y**4))", "answer_expr": "(x**2+y**2)/(x**2-y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a**8 + x**8)/((a**4 + x**4)*(a**4 - 2*a**2*x**2 + x**4))" ], "shape": [ "identity: (-a**N + x**N)/((a**N + x**N)*(N*a**N*x**N + a**N + x**N))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/13", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 13", "problem_latex": "$\\displaystyle \\frac{a^2x^2-16a^2}{ax^2+9ax+20a}$", "markdown": "$\\displaystyle \\frac{a^2x^2-16a^2}{ax^2+9ax+20a}$", "answer_latex": [ "$\\displaystyle \\frac{a(x - 4)}{x + 5}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a(x - 4)}{x + 5}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**2*x**2-16*a**2)/(a*x**2+9*a*x+20*a)", "answer_expr": "a*(x-4)/(x+5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2*x**2 - 16*a**2)/(a*x**2 + 9*a*x + 20*a)" ], "shape": [ "identity: (N*a**N + a**N*x**N)/(N*a*x + N*a + a*x**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/14", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 14", "problem_latex": "$\\displaystyle \\frac{a^4-14a^2-51}{a^4-2a^2-15}$", "markdown": "$\\displaystyle \\frac{a^4-14a^2-51}{a^4-2a^2-15}$", "answer_latex": [ "$\\displaystyle \\frac{a^2 - 17}{a^2 - 5}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a^2 - 17}{a^2 - 5}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**4-14*a**2-51)/(a**4-2*a**2-15)", "answer_expr": "(a**2-17)/(a**2-5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**4 - 14*x**2 - 51)/(x**4 - 2*x**2 - 15)" ], "shape": [ "identity: 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/15", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 15", "problem_latex": "$\\displaystyle \\frac{3+4x+x^2}{6+5x+x^2}$", "markdown": "$\\displaystyle \\frac{3+4x+x^2}{6+5x+x^2}$", "answer_latex": [ "$\\displaystyle \\frac{1 + x}{2 + x}$." ], "answer_markdown": [ "$\\displaystyle \\frac{1 + x}{2 + x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3+4*x+x**2)/(6+5*x+x**2)", "answer_expr": "(1+x)/(2+x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**2 + 4*x + 3)/(x**2 + 5*x + 6)" ], "shape": [ "identity: 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/16", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 16", "problem_latex": "$\\displaystyle \\frac{a^2-a^2b^2}{(a-ab)^2}$", "markdown": "$\\displaystyle \\frac{a^2-a^2b^2}{(a-ab)^2}$", "answer_latex": [ "$\\displaystyle \\frac{1 + b}{1 - b}$." ], "answer_markdown": [ "$\\displaystyle \\frac{1 + b}{1 - b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**2-a**2*b**2)/((a-a*b)**2)", "answer_expr": "(1+b)/(1-b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a**2*x**2 + x**2)/(-a*x + x)**2" ], "shape": [ "identity: (-a*x + x)**N*(-a**N*x**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/17", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 17", "problem_latex": "At two-thirds of a cent apiece, what $b$ apples cost?", "markdown": "At two-thirds of a cent apiece, what $b$ apples cost?", "answer_latex": [ "$\\displaystyle \\frac{2}{3}b$, or $\\displaystyle \\frac{2b}{3}$ cts." ], "answer_markdown": [ "$\\displaystyle \\frac{2}{3}b$, or $\\displaystyle \\frac{2b}{3}$ cts." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "2*b/3" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/18", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 18", "problem_latex": "James is $x$ times as old as George. If James is $a$ years\nold, how old is George?", "markdown": "James is $x$ times as old as George. If James is $a$ years old, how old is George?", "answer_latex": [ "$\\displaystyle \\frac{a}{x}$ years." ], "answer_markdown": [ "$\\displaystyle \\frac{a}{x}$ years." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{G: a/x}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(b*x, a)" ], "shape": [ "solve: Eq(b*x, a)" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-6/2" ], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/2", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 2", "problem_latex": "$\\frac{\\displaystyle 12x^5y^2z^3}{\\displaystyle 30xy^3z^3}$.", "markdown": "$\\frac{\\displaystyle 12x^5y^2z^3}{\\displaystyle 30xy^3z^3}$.", "answer_latex": [ "$\\displaystyle \\frac{2x^4}{5y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2x^4}{5y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(12*x**5*y**2*z**3)/(30*x*y**3*z**3)", "answer_expr": "2*x**4/(5*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*x**4/(5*a)" ], "shape": [ "identity: N*x**N/a" ], "same_problem_in": [], "needs": [ "cas.cancel" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/3", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 3", "problem_latex": "$\\displaystyle \\frac{x^2-7x+12}{x^3+x-20}$.", "markdown": "$\\displaystyle \\frac{x^2-7x+12}{x^3+x-20}$.", "answer_latex": [ "$\\displaystyle \\frac{x-3}{x+5}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x-3}{x+5}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-0.43645277968452160583", "-0.43958868894601542416" ], "problem_expr": "(x**2-7*x+12)/(x**3+x-20)", "answer_expr": "(x-3)/(x+5)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (x**2 - 7*x + 12)/(x**3 + x - 20)" ], "shape": [ "identity: (N*x + N + x**N)/(N + x + x**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/4", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 4", "problem_latex": "$\\displaystyle \\frac{x^2+9x+18}{x^2-2x-15}$.", "markdown": "$\\displaystyle \\frac{x^2+9x+18}{x^2-2x-15}$.", "answer_latex": [ "$\\displaystyle \\frac{x+6}{x-5}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x+6}{x-5}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2+9*x+18)/(x**2-2*x-15)", "answer_expr": "(x+6)/(x-5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**2 + 9*x + 18)/(x**2 - 2*x - 15)" ], "shape": [ "identity: 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/5", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 5", "problem_latex": "$\\displaystyle \\frac{a^6+a^4}{a^4-1}$", "markdown": "$\\displaystyle \\frac{a^6+a^4}{a^4-1}$", "answer_latex": [ "$\\displaystyle \\frac{a^4}{a^2-1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a^4}{a^2-1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**6+a**4)/(a**4-1)", "answer_expr": "a**4/(a**2-1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**6 + x**4)/(x**4 - 1)" ], "shape": [ "identity: 2*x**N/(x**N - 1)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/6", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 6", "problem_latex": "$\\displaystyle \\frac{x^5-x^2}{x^6-1}$", "markdown": "$\\displaystyle \\frac{x^5-x^2}{x^6-1}$", "answer_latex": [ "$\\displaystyle \\frac{x^2}{x^3+1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2}{x^3+1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**5-x**2)/(x**6-1)", "answer_expr": "x**2/(x**3+1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**5 - x**2)/(x**6 - 1)" ], "shape": [ "identity: 0" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/7", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 7", "problem_latex": "$\\displaystyle \\frac{mx - ny + nx - my}{ax-2by+2bx-ay}$", "markdown": "$\\displaystyle \\frac{mx - ny + nx - my}{ax-2by+2bx-ay}$", "answer_latex": [ "$\\displaystyle \\frac{m+n}{a+2b}$." ], "answer_markdown": [ "$\\displaystyle \\frac{m+n}{a+2b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(m*x-n*y+n*x-m*y)/(a*x-2*b*y+2*b*x-a*y)", "answer_expr": "(m+n)/(a+2*b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-c*e + c*x - d*e + d*x)/(-a*e + a*x - 2*b*e + 2*b*x)" ], "shape": [ "identity: (-c*e + c*x - d*e + d*x)/(N*b*e + N*b*x - a*e + a*x)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/8", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 8", "problem_latex": "$\\displaystyle \\frac{ac-bd+ad-bc}{ax-2by+2ay-bx}$", "markdown": "$\\displaystyle \\frac{ac-bd+ad-bc}{ax-2by+2ay-bx}$", "answer_latex": [ "$\\displaystyle \\frac{c+d}{x+2y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{c+d}{x+2y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a*c-b*d+a*d-b*c)/(a*x-2*b*y+2*a*y-b*x)", "answer_expr": "(c+d)/(x+2*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a*c + a*d - b*c - b*d)/(2*a*e + a*x - 2*b*e - b*x)" ], "shape": [ "identity: (a*c + a*d - b*c - b*d)/(N*a*e + N*b*e + a*x - b*x)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-42/9", "set": "boyden-first-book-in-algebra-1895/ex-42", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 42, problem 9", "problem_latex": "$\\displaystyle \\frac{ac^2d-a^3d^3}{a^3c+a^4d}$", "markdown": "$\\displaystyle \\frac{ac^2d-a^3d^3}{a^3c+a^4d}$", "answer_latex": [ "$\\displaystyle \\frac{d(c-ad)}{a^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{d(c-ad)}{a^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a*c**2*d-a**3*d**3)/(a**3*c+a**4*d)", "answer_expr": "d*(c-a*d)/a**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2*b*x - b**3*x**3)/(a*x**3 + b*x**4)" ], "shape": [ "identity: (a**N*b*x - b**N*x**N)/(a*x**N + b*x**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/1", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 1", "problem_latex": "$ \\displaystyle \\frac{bx - cx + m}{x}$", "markdown": "$ \\displaystyle \\frac{bx - cx + m}{x}$", "answer_latex": [ "$\\displaystyle b-c+\\frac{m}{x}$." ], "answer_markdown": [ "$\\displaystyle b-c+\\frac{m}{x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(b*x - c*x + m)/x", "answer_expr": "b - c + m/x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a*d - b*d + c)/d" ], "shape": [ "identity: (a*d - b*d + c)/d" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/10", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 10", "problem_latex": "$\\displaystyle \\frac{a^3 - b^3}{a + b}$", "markdown": "$\\displaystyle \\frac{a^3 - b^3}{a + b}$", "answer_latex": [ "$\\displaystyle a^2-ab+b^2-\\frac{2b^3}{a+b}$." ], "answer_markdown": [ "$\\displaystyle a^2-ab+b^2-\\frac{2b^3}{a+b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**3 - b**3)/(a + b)", "answer_expr": "a**2 - a*b + b**2 - 2*b**3/(a + b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3 - b**3)/(a + b)" ], "shape": [ "identity: (a**N - b**N)/(a + b)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/11", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 11", "problem_latex": "$\\displaystyle \\frac{8a^3}{2a - 1}$", "markdown": "$\\displaystyle \\frac{8a^3}{2a - 1}$", "answer_latex": [ "$\\displaystyle 4a^2+2a+1+\\frac{1}{2a-1}$." ], "answer_markdown": [ "$\\displaystyle 4a^2+2a+1+\\frac{1}{2a-1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "8*a**3/(2*a - 1)", "answer_expr": "4*a**2 + 2*a + 1 + 1/(2*a - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 8*a**3/(2*a - 1)" ], "shape": [ "identity: N*a**N/(N*a - 1)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/12", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 12", "problem_latex": "$\\displaystyle \\frac{27 x^3}{3x + 1}$", "markdown": "$\\displaystyle \\frac{27 x^3}{3x + 1}$", "answer_latex": [ "$\\displaystyle 9x^2-3x+1-\\frac{1}{3x+1}$." ], "answer_markdown": [ "$\\displaystyle 9x^2-3x+1-\\frac{1}{3x+1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "27*x**3/(3*x + 1)", "answer_expr": "9*x**2 - 3*x + 1 - 1/(3*x + 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 27*a**3/(3*a + 1)" ], "shape": [ "identity: N*a**N/(N*a + 1)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/13", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 13", "problem_latex": "$\\displaystyle \\frac{3x^3 + 8x^2 + 2}{x^2 + 2x - 1}$", "markdown": "$\\displaystyle \\frac{3x^3 + 8x^2 + 2}{x^2 + 2x - 1}$", "answer_latex": [ "$\\displaystyle 3x+2-\\frac{x-4}{x^2+2x-1}$." ], "answer_markdown": [ "$\\displaystyle 3x+2-\\frac{x-4}{x^2+2x-1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3*x**3 + 8*x**2 + 2)/(x**2 + 2*x - 1)", "answer_expr": "3*x + 2 - (x - 4)/(x**2 + 2*x - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (3*a**3 + 8*a**2 + 2)/(a**2 + 2*a - 1)" ], "shape": [ "identity: (2*N*a**N + N)/(N*a + a**N - 1)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/14", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 14", "problem_latex": "$\\displaystyle \\frac{2a^3 + 3a^2 + 10a - 4}{a^2 + 3a + 2}$", "markdown": "$\\displaystyle \\frac{2a^3 + 3a^2 + 10a - 4}{a^2 + 3a + 2}$", "answer_latex": [ "$\\displaystyle 2a-3+\\frac{15a+2}{a^2+3a+2}$." ], "answer_markdown": [ "$\\displaystyle 2a-3+\\frac{15a+2}{a^2+3a+2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*a**3 + 3*a**2 + 10*a - 4)/(a**2 + 3*a + 2)", "answer_expr": "2*a - 3 + (15*a + 2)/(a**2 + 3*a + 2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a**3 + 3*a**2 + 10*a - 4)/(a**2 + 3*a + 2)" ], "shape": [ "identity: (N*a + 2*N*a**N + N)/(N*a + N + a**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/15", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 15", "problem_latex": "$\\displaystyle \\frac{2a^4 + 6a^3 - 6a + 2}{a^2 +a - 1}$", "markdown": "$\\displaystyle \\frac{2a^4 + 6a^3 - 6a + 2}{a^2 +a - 1}$", "answer_latex": [ "$ 2a^2+4a-2$." ], "answer_markdown": [ "$ 2a^2+4a-2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*a**4 + 6*a**3 - 6*a + 2)/(a**2 + a - 1)", "answer_expr": "2*a**2 + 4*a - 2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a**4 + 6*a**3 - 6*a + 2)/(a**2 + a - 1)" ], "shape": [ "identity: (N*a + 2*N*a**N + N)/(a + a**N - 1)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/16", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 16", "problem_latex": "$\\displaystyle \\frac{3x^4 - 5x^3 + x - 1}{x^2 - x - 1}$", "markdown": "$\\displaystyle \\frac{3x^4 - 5x^3 + x - 1}{x^2 - x - 1}$", "answer_latex": [ "$3x^2-2x+1$." ], "answer_markdown": [ "$3x^2-2x+1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3*x**4 - 5*x**3 + x - 1)/(x**2 - x - 1)", "answer_expr": "3*x**2 - 2*x + 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (3*a**4 - 5*a**3 + a - 1)/(a**2 - a - 1)" ], "shape": [ "identity: (2*N*a**N + a - 1)/(-a + a**N - 1)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/17", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 17", "problem_latex": "$ \\displaystyle x + y - \\frac{xy}{x - y}$", "markdown": "$ \\displaystyle x + y - \\frac{xy}{x - y}$", "answer_latex": [ "$\\displaystyle \\frac{x^2-y^2-xy}{x-y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2-y^2-xy}{x-y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x + y - x*y/(x - y)", "answer_expr": "(x**2 - y**2 - x*y)/(x - y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a*b/(a - b) + a + b" ], "shape": [ "identity: -a*b/(a - b) + a + b" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/18", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 18", "problem_latex": "$\\displaystyle a - b - \\frac{2 ab}{a + b}$", "markdown": "$\\displaystyle a - b - \\frac{2 ab}{a + b}$", "answer_latex": [ "$\\displaystyle \\frac{a^2-2ab-b^2}{a+b}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a^2-2ab-b^2}{a+b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "a - b - 2*a*b/(a + b)", "answer_expr": "(a**2 - 2*a*b - b**2)/(a + b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -2*a*b/(a + b) + a - b" ], "shape": [ "identity: N*a*b/(a + b) + a - b" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/19", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 19", "problem_latex": "$\\displaystyle -c + d + \\frac{c^3 + d^3}{c^2 + cd + d^2}$", "markdown": "$\\displaystyle -c + d + \\frac{c^3 + d^3}{c^2 + cd + d^2}$", "answer_latex": [ "$\\displaystyle \\frac{2d^3}{c^2+cd+d^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2d^3}{c^2+cd+d^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "-c + d + (c**3 + d**3)/(c**2 + c*d + d**2)", "answer_expr": "2*d**3/(c**2 + c*d + d**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a + b + (a**3 + b**3)/(a**2 + a*b + b**2)" ], "shape": [ "identity: -a + b + (a**N + b**N)/(a*b + a**N + b**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/2", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 2", "problem_latex": "$ \\displaystyle \\frac{mn + an + x}{n}$", "markdown": "$ \\displaystyle \\frac{mn + an + x}{n}$", "answer_latex": [ "$\\displaystyle m+a+\\frac{x}{n}$." ], "answer_markdown": [ "$\\displaystyle m+a+\\frac{x}{n}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(m*n + a*n + x)/n", "answer_expr": "m + a + x/n" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a*c + b*c + d)/c" ], "shape": [ "identity: (a*c + b*c + d)/c" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/20", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 20", "problem_latex": "$\\displaystyle \\frac{x^2y + xy^2}{x - y} + x^2 - y^2$", "markdown": "$\\displaystyle \\frac{x^2y + xy^2}{x - y} + x^2 - y^2$", "answer_latex": [ "$\\displaystyle \\frac{x^3+y^3}{x-y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^3+y^3}{x-y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2*y + x*y**2)/(x - y) + x**2 - y**2", "answer_expr": "(x**3 + y**3)/(x - y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**2 - b**2 + (a**2*b + a*b**2)/(a - b)" ], "shape": [ "identity: a**N - b**N + (a*b**N + a**N*b)/(a - b)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/21", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 21", "problem_latex": "$\\displaystyle \\frac{x+2}{3x - 1} - x - 2$", "markdown": "$\\displaystyle \\frac{x+2}{3x - 1} - x - 2$", "answer_latex": [ "$\\displaystyle \\frac{4-4x-3x^2}{3x-1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{4-4x-3x^2}{3x-1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x + 2)/(3*x - 1) - x - 2", "answer_expr": "(4 - 4*x - 3*x**2)/(3*x - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a + (a + 2)/(3*a - 1) - 2" ], "shape": [ "identity: N - a + (N + a)/(N*a - 1)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/22", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 22", "problem_latex": "$\\displaystyle 2a - 1 - \\frac{a-2}{a+3}$", "markdown": "$\\displaystyle 2a - 1 - \\frac{a-2}{a+3}$", "answer_latex": [ "$\\displaystyle \\frac{2a^2+4a-1}{a+3}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2a^2+4a-1}{a+3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "2*a - 1 - (a - 2)/(a + 3)", "answer_expr": "(2*a**2 + 4*a - 1)/(a + 3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a - (a - 2)/(a + 3) - 1" ], "shape": [ "identity: N*a - 2" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/23", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 23", "problem_latex": "$\\displaystyle a^2 - 3a + 2 - \\frac{a + 3}{2a^2 - 1}$", "markdown": "$\\displaystyle a^2 - 3a + 2 - \\frac{a + 3}{2a^2 - 1}$", "answer_latex": [ "$\\displaystyle \\frac{2a^4-6a^3+3a^2+2a-5}{2a^2-1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2a^4-6a^3+3a^2+2a-5}{2a^2-1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2 - 3*a + 2 - (a + 3)/(2*a**2 - 1)", "answer_expr": "(2*a**4 - 6*a**3 + 3*a**2 + 2*a - 5)/(2*a**2 - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**2 - 3*a - (a + 3)/(2*a**2 - 1) + 2" ], "shape": [ "identity: N*a + N + a**N - (N + a)/(N*a**N - 1)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/24", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 24", "problem_latex": "$\\displaystyle 2 x^2 + x - 3 - \\frac{x - 2}{3 x^2 + 1}$", "markdown": "$\\displaystyle 2 x^2 + x - 3 - \\frac{x - 2}{3 x^2 + 1}$", "answer_latex": [ "$\\displaystyle \\frac{6x^4+3x^3-7x^2-1}{3x^2+1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{6x^4+3x^3-7x^2-1}{3x^2+1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "2*x**2 + x - 3 - (x - 2)/(3*x**2 + 1)", "answer_expr": "(6*x**4 + 3*x**3 - 7*x**2 - 1)/(3*x**2 + 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a**2 + a - (a - 2)/(3*a**2 + 1) - 3" ], "shape": [ "identity: N*a**N + N + a - (N + a)/(N*a**N + 1)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/25", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 25", "problem_latex": "$\\displaystyle \\frac{3x + 2}{x^2 + x + 2} - 1$.", "markdown": "$\\displaystyle \\frac{3x + 2}{x^2 + x + 2} - 1$.", "answer_latex": [ "$\\displaystyle \\frac{4x-x^2}{x^2-x+2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{4x-x^2}{x^2-x+2}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "0.2797190720165793564", "1.0847791428303479321" ], "problem_expr": "(3*x + 2)/(x**2 + x + 2) - 1", "answer_expr": "(4*x - x**2)/(x**2 - x + 2)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (3*a + 2)/(a**2 + a + 2) - 1" ], "shape": [ "identity: (N*a + N)/(N + a + a**N) - 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/26", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 26", "problem_latex": "$\\displaystyle 1 - \\frac{2a^2 + 3}{a^2 - 2a + 3}$.", "markdown": "$\\displaystyle 1 - \\frac{2a^2 + 3}{a^2 - 2a + 3}$.", "answer_latex": [ "$\\displaystyle -\\frac{a^2+2a}{a^2-2a+3}$." ], "answer_markdown": [ "$\\displaystyle -\\frac{a^2+2a}{a^2-2a+3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "1 - (2*a**2 + 3)/(a**2 - 2*a + 3)", "answer_expr": "-(a**2 + 2*a)/(a**2 - 2*a + 3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -(2*a**2 + 3)/(a**2 - 2*a + 3) + 1" ], "shape": [ "identity: -(N*a**N + N)/(N*a + N + a**N) + 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/27", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 27", "problem_latex": "$\\displaystyle \\frac{a^2}{a^2 - a + 3} - a^2 - a - 1$.", "markdown": "$\\displaystyle \\frac{a^2}{a^2 - a + 3} - a^2 - a - 1$.", "answer_latex": [ "$\\displaystyle -\\frac{a^4+2a^2+2a+3}{a^2-a+3}$." ], "answer_markdown": [ "$\\displaystyle -\\frac{a^4+2a^2+2a+3}{a^2-a+3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2/(a**2 - a + 3) - a**2 - a - 1", "answer_expr": "-(a**4 + 2*a**2 + 2*a + 3)/(a**2 - a + 3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**2 + a**2/(a**2 - a + 3) - a - 1" ], "shape": [ "identity: -a - a**N + a**N/(N - a + a**N) - 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/28", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 28", "problem_latex": "$\\displaystyle \\frac{x^4}{x^2 + x - 1} - x^2 + x - 1$.", "markdown": "$\\displaystyle \\frac{x^4}{x^2 + x - 1} - x^2 + x - 1$.", "answer_latex": [ "$\\displaystyle \\frac{x^2-2x+1}{x^2+x-1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2-2x+1}{x^2+x-1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x**4/(x**2 + x - 1) - x**2 + x - 1", "answer_expr": "(x**2 - 2*x + 1)/(x**2 + x - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**4/(a**2 + a - 1) - a**2 + a - 1" ], "shape": [ "identity: a - a**N + a**N/(a + a**N - 1) - 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/29", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 29", "problem_latex": "$\\displaystyle \\frac{a^2}{2}, \\frac{xy}{3},\n\\frac{5ab^2}{4}.$", "markdown": "$\\displaystyle \\frac{a^2}{2}, \\frac{xy}{3}, \\frac{5ab^2}{4}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/3", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 3", "problem_latex": "$\\displaystyle \\frac{x^2 + y^2 + 3}{x - y}$", "markdown": "$\\displaystyle \\frac{x^2 + y^2 + 3}{x - y}$", "answer_latex": [ "$\\displaystyle x+y+\\frac{3}{x-y}$." ], "answer_markdown": [ "$\\displaystyle x+y+\\frac{3}{x-y}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "5.0938189615688887038", "4.8856330932256318441" ], "problem_expr": "(x**2 + y**2 + 3)/(x - y)", "answer_expr": "x + y + 3/(x - y)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (a**2 + b**2 + 3)/(a - b)" ], "shape": [ "identity: (N + a**N + b**N)/(a - b)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/30", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 30", "problem_latex": "$\\displaystyle \\frac{x^3}{3}, \\frac{am}{2},\n\\frac{3x^2y}{5}.$", "markdown": "$\\displaystyle \\frac{x^3}{3}, \\frac{am}{2}, \\frac{3x^2y}{5}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/31", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 31, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 31", "problem_latex": "$\\displaystyle \\frac{7x^2}{3y}, \\frac{5xy}{2a},\n\\frac{x^3}{ay}.$", "markdown": "$\\displaystyle \\frac{7x^2}{3y}, \\frac{5xy}{2a}, \\frac{x^3}{ay}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/32", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 32, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 32", "problem_latex": "$\\displaystyle \\frac{2a^2}{7m}, \\frac{5ab}{3n},\n\\frac{b^4}{mn}.$", "markdown": "$\\displaystyle \\frac{2a^2}{7m}, \\frac{5ab}{3n}, \\frac{b^4}{mn}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/33", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 33, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 33", "problem_latex": "$\\displaystyle \\frac{5}{y+x}, \\frac{3x}{x-y},\n\\frac{2ab}{x^2-y^2}.$", "markdown": "$\\displaystyle \\frac{5}{y+x}, \\frac{3x}{x-y}, \\frac{2ab}{x^2-y^2}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/34", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 34, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 34", "problem_latex": "$\\displaystyle \\frac{2}{3+a}, \\frac{5a}{a-3},\n\\frac{2ax}{a^2-9}.$", "markdown": "$\\displaystyle \\frac{2}{3+a}, \\frac{5a}{a-3}, \\frac{2ax}{a^2-9}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/35", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 35, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 35", "problem_latex": "$\\displaystyle \\frac{b^2}{a^2-ab}, \\frac{a^2b}{a^2-b^2}.$", "markdown": "$\\displaystyle \\frac{b^2}{a^2-ab}, \\frac{a^2b}{a^2-b^2}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/36", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 36, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 36", "problem_latex": "$\\displaystyle \\frac{m^3}{nm+n^2},\n\\frac{m^2n}{m^2-n^2}.$", "markdown": "$\\displaystyle \\frac{m^3}{nm+n^2}, \\frac{m^2n}{m^2-n^2}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "FLAG-EXTRACTION", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/37", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 37, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 37", "problem_latex": "$\\displaystyle \\frac{2}{x^4-y^4}, \\frac{3}{x^2 + xy -\n2y^2}.$", "markdown": "$\\displaystyle \\frac{2}{x^4-y^4}, \\frac{3}{x^2 + xy - 2y^2}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/38", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 38, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 38", "problem_latex": "$\\displaystyle \\frac{5}{a^8-b^8}, \\frac{2}{a^4 - 4a^2b^2 +\n3b^4}.$", "markdown": "$\\displaystyle \\frac{5}{a^8-b^8}, \\frac{2}{a^4 - 4a^2b^2 + 3b^4}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/39", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 39, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 39", "problem_latex": "$\\displaystyle \\frac{a-1}{a^2-2a-15}, \\frac{a+2}{a^2+a-6},\n\\frac{a+3}{a^2-7a+10}.$", "markdown": "$\\displaystyle \\frac{a-1}{a^2-2a-15}, \\frac{a+2}{a^2+a-6}, \\frac{a+3}{a^2-7a+10}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/4", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 4", "problem_latex": "$\\displaystyle \\frac{a^3 + b^3 + 3}{x - y}$", "markdown": "$\\displaystyle \\frac{a^3 + b^3 + 3}{x - y}$", "answer_latex": [ "$\\displaystyle a^2-ab+b^2-\\frac{2}{a+b}$." ], "answer_markdown": [ "$\\displaystyle a^2-ab+b^2-\\frac{2}{a+b}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "58.588867188160292756", "8.3429251481164890419" ], "problem_expr": "(a**3 + b**3 + 3)/(x - y)", "answer_expr": "a**2 - a*b + b**2 - 2/(a + b)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (a**3 + b**3 + 3)/(c - d)" ], "shape": [ "identity: (N + a**N + b**N)/(c - d)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/40", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 40, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 40", "problem_latex": "$\\displaystyle \\frac{x+1}{x^2-x-6}, \\frac{x-2}{x^2+6x+8},\n\\frac{x+2}{x^2+x-12}.$", "markdown": "$\\displaystyle \\frac{x+1}{x^2-x-6}, \\frac{x-2}{x^2+6x+8}, \\frac{x+2}{x^2+x-12}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/41", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 41, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 41", "problem_latex": "$\\displaystyle \\frac{x^2+3x+2}{x^2-x-6},\n\\frac{x^2-x}{x^2+5x+4}, \\frac{x^2-6x+9}{x^2+x-12}.$", "markdown": "$\\displaystyle \\frac{x^2+3x+2}{x^2-x-6}, \\frac{x^2-x}{x^2+5x+4}, \\frac{x^2-6x+9}{x^2+x-12}.$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/42", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 42, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 42", "problem_latex": "If $x$ quarts of milk cost $m$ cents, what will one pint\ncost?", "markdown": "If $x$ quarts of milk cost $m$ cents, what will one pint cost?", "answer_latex": [ "$\\displaystyle \\frac{m}{2x}$ ct." ], "answer_markdown": [ "$\\displaystyle \\frac{m}{2x}$ ct." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(2*x*p, m)", "answer_expr": "{p: m/(2*x)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(2*b*x, a)" ], "shape": [ "solve: Eq(N*b*x, a)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/43", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 43, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 43", "problem_latex": "Express four consecutive numbers of which $a$ is the\nlargest.", "markdown": "Express four consecutive numbers of which $a$ is the largest.", "answer_latex": [ "$a-3$, $a-2$, $a-1$, $a$." ], "answer_markdown": [ "$a-3$, $a-2$, $a-1$, $a$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{n1: a - 3, n2: a - 2, n3: a - 1, n4: a}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, c - 1), Eq(c, d - 1), Eq(d, e - 1), Eq(e, a))" ], "shape": [ "solve: (Eq(b, c - 1), Eq(c, d - 1), Eq(d, e - 1), Eq(e, a))" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/44", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 44, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 44", "problem_latex": "What is the next even number above $2m$?", "markdown": "What is the next even number above $2m$?", "answer_latex": [ "$2m+2$." ], "answer_markdown": [ "$2m+2$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "2*m + 2" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/45", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 45, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 45", "problem_latex": "What is the next odd number below $4a+1$?", "markdown": "What is the next odd number below $4a+1$?", "answer_latex": [ "$4a-1$." ], "answer_markdown": [ "$4a-1$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "4*a - 1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/5", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 5", "problem_latex": "$\\displaystyle \\frac{6 a^3 b^2 c - 9 a^2 b^2 + 3 c}{3 a^2\nb}$", "markdown": "$\\displaystyle \\frac{6 a^3 b^2 c - 9 a^2 b^2 + 3 c}{3 a^2 b}$", "answer_latex": [ "$\\displaystyle 2abc-3b+\\frac{c}{a^2b}$." ], "answer_markdown": [ "$\\displaystyle 2abc-3b+\\frac{c}{a^2b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(6*a**3*b**2*c - 9*a**2*b**2 + 3*c)/(3*a**2*b)", "answer_expr": "2*a*b*c - 3*b + c/(a**2*b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (6*a**3*b**2*c - 9*a**2*b**2 + 3*c)/(3*a**2*b)" ], "shape": [ "identity: N*a**N*(N*a**N*b**N*c + N*a**N*b**N + N*c)/b" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/6", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 6", "problem_latex": "$\\displaystyle \\frac{6 x^3 y^2 + 10 x^2 y^2 z - 2 m}{2 x\ny^2}$", "markdown": "$\\displaystyle \\frac{6 x^3 y^2 + 10 x^2 y^2 z - 2 m}{2 x y^2}$", "answer_latex": [ "$\\displaystyle 3x^2+5xz-\\frac{m}{xy^2}$." ], "answer_markdown": [ "$\\displaystyle 3x^2+5xz-\\frac{m}{xy^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(6*x**3*y**2 + 10*x**2*y**2*z - 2*m)/(2*x*y**2)", "answer_expr": "3*x**2 + 5*x*z - m/(x*y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-2*a + 6*b**3*c**2 + 10*b**2*c**2*d)/(2*b*c**2)" ], "shape": [ "identity: N*c**N*(N*a + N*b**N*c**N*d + N*b**N*c**N)/b" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/7", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 7", "problem_latex": "$\\displaystyle \\frac{x^3 + 2 x^2 - 2 x + 1}{x^2 - x - 1}$", "markdown": "$\\displaystyle \\frac{x^3 + 2 x^2 - 2 x + 1}{x^2 - x - 1}$", "answer_latex": [ "$\\displaystyle x+3+\\frac{2x+4}{x^2-x-1}$." ], "answer_markdown": [ "$\\displaystyle x+3+\\frac{2x+4}{x^2-x-1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**3 + 2*x**2 - 2*x + 1)/(x**2 - x - 1)", "answer_expr": "x + 3 + (2*x + 4)/(x**2 - x - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3 + 2*a**2 - 2*a + 1)/(a**2 - a - 1)" ], "shape": [ "identity: (N*a + N*a**N + a**N + 1)/(-a + a**N - 1)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/8", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 8", "problem_latex": "$\\displaystyle \\frac{2 a^3 + a^2 - 2a + 1}{a^2 + a - 2}$", "markdown": "$\\displaystyle \\frac{2 a^3 + a^2 - 2a + 1}{a^2 + a - 2}$", "answer_latex": [ "$\\displaystyle 2a-1+\\frac{3a-1}{a^2+a-2}$." ], "answer_markdown": [ "$\\displaystyle 2a-1+\\frac{3a-1}{a^2+a-2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*a**3 + a**2 - 2*a + 1)/(a**2 + a - 2)", "answer_expr": "2*a - 1 + (3*a - 1)/(a**2 + a - 2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a**3 + a**2 - 2*a + 1)/(a**2 + a - 2)" ], "shape": [ "identity: (N*a + N*a**N + a**N + 1)/(N + a + a**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-43/9", "set": "boyden-first-book-in-algebra-1895/ex-43", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 43, problem 9", "problem_latex": "$\\displaystyle \\frac{x^3 + y^3}{x - y}$", "markdown": "$\\displaystyle \\frac{x^3 + y^3}{x - y}$", "answer_latex": [ "$\\displaystyle x^2+xy+y^2+\\frac{2y^3}{x-y}$." ], "answer_markdown": [ "$\\displaystyle x^2+xy+y^2+\\frac{2y^3}{x-y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**3 + y**3)/(x - y)", "answer_expr": "x**2 + x*y + y**2 + 2*y**3/(x - y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3 + b**3)/(a - b)" ], "shape": [ "identity: (a**N + b**N)/(a - b)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/1", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 1", "problem_latex": "$\\displaystyle \\frac{2a}{3}+\\frac{a}{4}-\\frac{5a}{6}$.", "markdown": "$\\displaystyle \\frac{2a}{3}+\\frac{a}{4}-\\frac{5a}{6}$.", "answer_latex": [ "$\\displaystyle \\frac{a}{12}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a}{12}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "2*a/3 + a/4 - 5*a/6", "answer_expr": "a/12" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: x/12" ], "shape": [ "identity: N*x" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/10", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 10", "problem_latex": "$\\displaystyle \\frac{2a^2}{a^2-b^2}-\\frac{2a}{a+b}$.", "markdown": "$\\displaystyle \\frac{2a^2}{a^2-b^2}-\\frac{2a}{a+b}$.", "answer_latex": [ "$\\displaystyle \\frac{2 a b}{a^{2} - b^{2}}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2 a b}{a^{2} - b^{2}}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "2*a**2/(a**2 - b**2) - 2*a/(a + b)", "answer_expr": "2*a*b/(a**2 - b**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*x**2/(-a**2 + x**2) - 2*x/(a + x)" ], "shape": [ "identity: N*x/(a + x) + N*x**N/(-a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/11", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 11", "problem_latex": "$\\displaystyle \\frac{2a-3b}{a-2b}-\\frac{2a-b}{a-b}$.", "markdown": "$\\displaystyle \\frac{2a-3b}{a-2b}-\\frac{2a-b}{a-b}$.", "answer_latex": [ "$\\displaystyle \\frac{b^{2}}{(a - 2 b)(a - b)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{b^{2}}{(a - 2 b)(a - b)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*a - 3*b)/(a - 2*b) - (2*a - b)/(a - b)", "answer_expr": "b**2/((a - 2*b)*(a - b))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-3*a + 2*x)/(-2*a + x) - (-a + 2*x)/(-a + x)" ], "shape": [ "identity: (N*a + N*x)/(N*a + x) - (N*x - a)/(-a + x)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/12", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 12", "problem_latex": "$\\displaystyle \\frac{x+4}{x+5}-\\frac{x+2}{x+3}$.", "markdown": "$\\displaystyle \\frac{x+4}{x+5}-\\frac{x+2}{x+3}$.", "answer_latex": [ "$\\displaystyle \\frac{2}{(x + 5)(x + 3)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2}{(x + 5)(x + 3)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x + 4)/(x + 5) - (x + 2)/(x + 3)", "answer_expr": "2/((x + 5)*(x + 3))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -(x + 2)/(x + 3) + (x + 4)/(x + 5)" ], "shape": [ "identity: 0" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/13", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 13", "problem_latex": "$\\displaystyle \\frac{x-4y}{x-2y}-\\frac{x^2-4y^2}{x^2+2xy}$.", "markdown": "$\\displaystyle \\frac{x-4y}{x-2y}-\\frac{x^2-4y^2}{x^2+2xy}$.", "answer_latex": [ "$\\displaystyle - \\frac{4 y^{2}}{x (x - 2 y)}$." ], "answer_markdown": [ "$\\displaystyle - \\frac{4 y^{2}}{x (x - 2 y)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - 4*y)/(x - 2*y) - (x**2 - 4*y**2)/(x**2 + 2*x*y)", "answer_expr": "-4*y**2/(x*(x - 2*y))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-4*a + x)/(-2*a + x) - (-4*a**2 + x**2)/(2*a*x + x**2)" ], "shape": [ "identity: -(N*a**N + x**N)/(N*a*x + x**N) + 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/14", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 14", "problem_latex": "$\\displaystyle \\frac{x-7}{x+2}+\\frac{x+4}{x-3}$.", "markdown": "$\\displaystyle \\frac{x-7}{x+2}+\\frac{x+4}{x-3}$.", "answer_latex": [ "$\\displaystyle \\frac{2 x^{2} - 4 x + 29}{(x + 2)(x - 3)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2 x^{2} - 4 x + 29}{(x + 2)(x - 3)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - 7)/(x + 2) + (x + 4)/(x - 3)", "answer_expr": "(2*x**2 - 4*x + 29)/((x + 2)*(x - 3))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 7)/(x + 2) + (x + 4)/(x - 3)" ], "shape": [ "identity: N" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/15", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 15", "problem_latex": "$\\displaystyle\n\\frac{\\left(x+2a\\right)^2}{x^3-8a^3}-\\frac{1}{x-2a}$.", "markdown": "$\\displaystyle \\frac{\\left(x+2a\\right)^2}{x^3-8a^3}-\\frac{1}{x-2a}$.", "answer_latex": [ "$\\displaystyle \\frac{2 a x}{x^{3} - 8 a^{3}}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2 a x}{x^{3} - 8 a^{3}}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x + 2*a)**2/(x**3 - 8*a**3) - 1/(x - 2*a)", "answer_expr": "2*a*x/(x**3 - 8*a**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a + x)**2/(-8*a**3 + x**3) - 1/(-2*a + x)" ], "shape": [ "identity: (N*a + x)**N/(N*a**N + x**N) - 1/(N*a + x)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/16", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 16", "problem_latex": "$\\displaystyle\n\\frac{x^6+x^3y^3+y^6}{x^3+y^3}+\\frac{x^6-x^3y^3+y^6}{x^3-y^3}$.", "markdown": "$\\displaystyle \\frac{x^6+x^3y^3+y^6}{x^3+y^3}+\\frac{x^6-x^3y^3+y^6}{x^3-y^3}$.", "answer_latex": [ "$\\displaystyle \\frac{2 x^{9}}{x^{6} - y^{6}}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2 x^{9}}{x^{6} - y^{6}}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**6 + x**3*y**3 + y**6)/(x**3 + y**3) + (x**6 - x**3*y**3 + y**6)/(x**3 - y**3)", "answer_expr": "2*x**9/(x**6 - y**6)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**6 + a**3*x**3 + x**6)/(a**3 + x**3) + (a**6 - a**3*x**3 + x**6)/(-a**3 + x**3)" ], "shape": [ "identity: (a**N*x**N + a**N + x**N)/(a**N + x**N) + (-a**N*x**N + a**N + x**N)/(-a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/17", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 17", "problem_latex": "$\\displaystyle \\frac{m - 3}{m + 2} - \\frac{m - 2}{m+3} +\n\\frac{1}{m - 1}$", "markdown": "$\\displaystyle \\frac{m - 3}{m + 2} - \\frac{m - 2}{m+3} + \\frac{1}{m - 1}$", "answer_latex": [ "$\\displaystyle \\frac{m^{2} + 11}{(m - 1)(m + 2)(m + 3)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{m^{2} + 11}{(m - 1)(m + 2)(m + 3)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(m - 3)/(m + 2) - (m - 2)/(m + 3) + 1/(m - 1)", "answer_expr": "(m**2 + 11)/((m - 1)*(m + 2)*(m + 3))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 3)/(x + 2) - (x - 2)/(x + 3) + 1/(x - 1)" ], "shape": [ "identity: 1/(x - 1)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/18", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 18", "problem_latex": "$\\displaystyle \\frac{2 (4a + b)}{15 a^2 - 15 b^2} -\n\\frac{1}{5 (a+b)} - \\frac{1}{3a - 3b}$", "markdown": "$\\displaystyle \\frac{2 (4a + b)}{15 a^2 - 15 b^2} - \\frac{1}{5 (a+b)} - \\frac{1}{3a - 3b}$", "answer_latex": [ "0." ], "answer_markdown": [ "0." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "2*(4*a + b)/(15*a**2 - 15*b**2) - 1/(5*(a + b)) - 1/(3*a - 3*b)", "answer_expr": "0" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a + 8*x)/(-15*a**2 + 15*x**2) - 1/(5*a + 5*x) - 1/(-3*a + 3*x)" ], "shape": [ "identity: (N*a + N*x)/(N*a**N + N*x**N) - 2/(N*a + N*x)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/19", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 19", "problem_latex": "$\\displaystyle \\frac{3x^3 - 3x^2 + x - 1}{3x^3 - 3x^2 - x +\n1} - \\frac{3x^3 + 3x^2 - x - 1}{3x^3 + 3x^2 + x + 1}$", "markdown": "$\\displaystyle \\frac{3x^3 - 3x^2 + x - 1}{3x^3 - 3x^2 - x + 1} - \\frac{3x^3 + 3x^2 - x - 1}{3x^3 + 3x^2 + x + 1}$", "answer_latex": [ "$\\displaystyle \\frac{2(9 x^{4} + 1)}{9 x^{4} - 1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2(9 x^{4} + 1)}{9 x^{4} - 1}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "1.2045447504569534372", "2.3347222652498528455" ], "problem_expr": "(3*x**3 - 3*x**2 + x - 1)/(3*x**3 - 3*x**2 - x + 1) - (3*x**3 + 3*x**2 - x - 1)/(3*x**3 + 3*x**2 + x + 1)", "answer_expr": "2*(9*x**4 + 1)/(9*x**4 - 1)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: -(3*x**3 + 3*x**2 - x - 1)/(3*x**3 + 3*x**2 + x + 1) + (3*x**3 - 3*x**2 + x - 1)/(3*x**3 - 3*x**2 - x + 1)" ], "shape": [ "identity: -(2*N*x**N - x - 1)/(2*N*x**N + x + 1) + (2*N*x**N + x - 1)/(2*N*x**N - x + 1)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/2", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 2", "problem_latex": "$\\displaystyle \\frac{2x}{5}+\\frac{1}{3} x-\\frac{2x}{3}$.", "markdown": "$\\displaystyle \\frac{2x}{5}+\\frac{1}{3} x-\\frac{2x}{3}$.", "answer_latex": [ "$\\displaystyle \\frac{x}{15}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x}{15}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "2*x/5 + x/3 - 2*x/3", "answer_expr": "x/15" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: x/15" ], "shape": [ "identity: N*x" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/20", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 20", "problem_latex": "$\\displaystyle \\frac{1}{a^2 - 7a + 12} - \\frac{1}{a^2 - 5a +\n6}$", "markdown": "$\\displaystyle \\frac{1}{a^2 - 7a + 12} - \\frac{1}{a^2 - 5a + 6}$", "answer_latex": [ "$\\displaystyle \\frac{2}{(a - 2)(a - 3)(a - 4)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2}{(a - 2)(a - 3)(a - 4)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "1/(a**2 - 7*a + 12) - 1/(a**2 - 5*a + 6)", "answer_expr": "2/((a - 2)*(a - 3)*(a - 4))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -1/(x**2 - 5*x + 6) + 1/(x**2 - 7*x + 12)" ], "shape": [ "identity: 0" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/21", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 21", "problem_latex": "$\\displaystyle \\frac{a-1}{a-2} + \\frac{5 - 2a}{a^2 - 5a + 6}\n+ \\frac{a-2}{a-3}$", "markdown": "$\\displaystyle \\frac{a-1}{a-2} + \\frac{5 - 2a}{a^2 - 5a + 6} + \\frac{a-2}{a-3}$", "answer_latex": [ "2." ], "answer_markdown": [ "2." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a - 1)/(a - 2) + (5 - 2*a)/(a**2 - 5*a + 6) + (a - 2)/(a - 3)", "answer_expr": "2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-2*x + 5)/(x**2 - 5*x + 6) + (x - 1)/(x - 2) + (x - 2)/(x - 3)" ], "shape": [ "identity: (N*x + N)/(N*x + N + x**N) + 1 + (x - 1)/(N + x)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/22", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 22", "problem_latex": "$\\displaystyle \\frac{1}{a^2 + 3a + 2} + \\frac{2a}{a^2 + 4a +\n3} + \\frac{1}{a^2 + 5a + 6}$", "markdown": "$\\displaystyle \\frac{1}{a^2 + 3a + 2} + \\frac{2a}{a^2 + 4a + 3} + \\frac{1}{a^2 + 5a + 6}$", "answer_latex": [ "$\\displaystyle \\frac{2}{a + 3}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2}{a + 3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "1/(a**2 + 3*a + 2) + 2*a/(a**2 + 4*a + 3) + 1/(a**2 + 5*a + 6)", "answer_expr": "2/(a + 3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*x/(x**2 + 4*x + 3) + 1/(x**2 + 5*x + 6) + 1/(x**2 + 3*x + 2)" ], "shape": [ "identity: N*x/(N*x + N + x**N) + 2/(N*x + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/23", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 23", "problem_latex": "$\\displaystyle \\frac{x+2}{x-5} + \\frac{x-3}{x+4} -\n\\frac{2x^2 - 3x - 2}{x^2 - x - 20}$", "markdown": "$\\displaystyle \\frac{x+2}{x-5} + \\frac{x-3}{x+4} - \\frac{2x^2 - 3x - 2}{x^2 - x - 20}$", "answer_latex": [ "$\\displaystyle \\frac{x + 25}{x^{2} - x - 20}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x + 25}{x^{2} - x - 20}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x + 2)/(x - 5) + (x - 3)/(x + 4) - (2*x**2 - 3*x - 2)/(x**2 - x - 20)", "answer_expr": "(x + 25)/(x**2 - x - 20)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 3)/(x + 4) - (2*x**2 - 3*x - 2)/(x**2 - x - 20) + (x + 2)/(x - 5)" ], "shape": [ "identity: 2 - (N*x + N*x**N + N)/(N - x + x**N)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/24", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 24", "problem_latex": "$\\displaystyle \\frac{m - n}{mn} + \\frac{p - m}{mp} +\n\\frac{n-p}{np}$", "markdown": "$\\displaystyle \\frac{m - n}{mn} + \\frac{p - m}{mp} + \\frac{n-p}{np}$", "answer_latex": [ "0." ], "answer_markdown": [ "0." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-6.6819117752304891154e-52", "0.0" ], "problem_expr": "(m - n)/(m*n) + (p - m)/(m*p) + (n - p)/(n*p)", "answer_expr": "0" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (b - x)/(b*x) + (-a + x)/(a*x) + (a - b)/(a*b)" ], "shape": [ "identity: (b - x)/(b*x) + (-a + x)/(a*x) + (a - b)/(a*b)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/25", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 25", "problem_latex": "$\\displaystyle \\frac{a+b}{ab} - \\frac{a-c}{ac} -\n\\frac{c-b}{bc}$", "markdown": "$\\displaystyle \\frac{a+b}{ab} - \\frac{a-c}{ac} - \\frac{c-b}{bc}$", "answer_latex": [ "$\\displaystyle \\frac{2}{a}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2}{a}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a + b)/(a*b) - (a - c)/(a*c) - (c - b)/(b*c)", "answer_expr": "2/a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -(-b + x)/(b*x) + (a + x)/(a*x) - (-a + b)/(a*b)" ], "shape": [ "identity: -(-b + x)/(b*x) + (a + x)/(a*x) - (-a + b)/(a*b)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/26", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 26", "problem_latex": "$\\displaystyle \\frac{x^2 - yz}{(x+y)(x+z)} + \\frac{x^2 -\nxz}{(y+z)(y+x)} + \\frac{z^2}{(z+x)(z+y)}$", "markdown": "$\\displaystyle \\frac{x^2 - yz}{(x+y)(x+z)} + \\frac{x^2 - xz}{(y+z)(y+x)} + \\frac{z^2}{(z+x)(z+y)}$", "answer_latex": [ "$\\displaystyle \\frac{x^{2} + x z - y z}{(x + z)(y + z)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^{2} + x z - y z}{(x + z)(y + z)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2 - y*z)/((x + y)*(x + z)) + (x**2 - x*z)/((y + z)*(y + x)) + z**2/((z + x)*(z + y))", "answer_expr": "(x**2 + x*z - y*z)/((x + z)*(y + z))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: b**2/((a + b)*(b + x)) + (-a*b + x**2)/((a + x)*(b + x)) + (-b*x + x**2)/((a + b)*(a + x))" ], "shape": [ "identity: b**N/((a + b)*(b + x)) + (-a*b + x**N)/((a + x)*(b + x)) + (-b*x + x**N)/((a + b)*(a + x))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand", "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/27", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 27", "problem_latex": "$\\displaystyle \\frac{m^2 - bx}{(m+b)(m+x)} - \\frac{mx -\nb^2}{(b+x)(b+m)} - \\frac{mb - x^2}{(x+m)(x+b)}$", "markdown": "$\\displaystyle \\frac{m^2 - bx}{(m+b)(m+x)} - \\frac{mx - b^2}{(b+x)(b+m)} - \\frac{mb - x^2}{(x+m)(x+b)}$", "answer_latex": [ "0." ], "answer_markdown": [ "0." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(m**2 - b*x)/((m + b)*(m + x)) - (m*x - b**2)/((b + x)*(b + m)) - (m*b - x**2)/((x + m)*(x + b))", "answer_expr": "0" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a*b + x**2)/((a + x)*(b + x)) - (a*x - b**2)/((a + b)*(b + x)) - (-a**2 + b*x)/((a + b)*(a + x))" ], "shape": [ "identity: (-a*b + x**N)/((a + x)*(b + x)) - (a*x - b**N)/((a + b)*(b + x)) - (-a**N + b*x)/((a + b)*(a + x))" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/28", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 28", "problem_latex": "$x$ is how many times $y$?", "markdown": "$x$ is how many times $y$?", "answer_latex": [ "$\\displaystyle \\frac{x}{y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x}{y}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "x/y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/29", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 29", "problem_latex": "If $a$ is $\\frac{2}{5}$ of a number, what is $\\frac{1}{5}$\nof the number?", "markdown": "If $a$ is $\\frac{2}{5}$ of a number, what is $\\frac{1}{5}$ of the number?", "answer_latex": [ "$\\displaystyle \\frac{a}{2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a}{2}$." ], "checks": [ { "task": "solve", "verdict": "FLAG-MISMATCH", "judge_why": "the equations leave [{N: 5*a/2}]", "problem_expr": null, "answer_expr": "{R: a/2}" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "solve: (Eq(x, a/5), Eq(b, 2*a/5))" ], "shape": [ "solve: (Eq(x, N*a), Eq(b, N*a))" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/3", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 3", "problem_latex": "$\\displaystyle \\frac{2x}{3}-\\frac{3x}{4}-\\frac{4x}{5}$.", "markdown": "$\\displaystyle \\frac{2x}{3}-\\frac{3x}{4}-\\frac{4x}{5}$.", "answer_latex": [ "$\\displaystyle \\frac{43 x}{60}$." ], "answer_markdown": [ "$\\displaystyle \\frac{43 x}{60}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-1.4133333333333333333", "1.1466666666666666667" ], "problem_expr": "2*x/3 - 3*x/4 - 4*x/5", "answer_expr": "43*x/60" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: -53*x/60" ], "shape": [ "identity: N*x" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/30", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 30", "problem_latex": "If $x$ is $\\frac{3}{7}$ of a number, what is the number?", "markdown": "If $x$ is $\\frac{3}{7}$ of a number, what is the number?", "answer_latex": [ "$\\displaystyle \\frac{7 x}{3}$." ], "answer_markdown": [ "$\\displaystyle \\frac{7 x}{3}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{N: 7*x/3}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a, 3*x/7)" ], "shape": [ "solve: Eq(a, N*x)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/31", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 31, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 31", "problem_latex": "Seven years ago $A$ was four times as old as $B$. If $B$ is\n$x$ years old, what is $A$'s present age?", "markdown": "Seven years ago $A$ was four times as old as $B$. If $B$ is $x$ years old, what is $A$’s present age?", "answer_latex": [ "$4 x - 21$." ], "answer_markdown": [ "$4 x - 21$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{A: 4*x - 21}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x - 7, 4*a - 28)" ], "shape": [ "solve: Eq(N + x, N*a + N)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/4", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 4", "problem_latex": "$\\displaystyle \\frac{4a}{b}+\\frac{3x}{2m}$.", "markdown": "$\\displaystyle \\frac{4a}{b}+\\frac{3x}{2m}$.", "answer_latex": [ "$\\displaystyle \\frac{4 a m + 3 b x}{2 b m}$." ], "answer_markdown": [ "$\\displaystyle \\frac{4 a m + 3 b x}{2 b m}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "7.6495937161430119177", "6.7957475622968580715" ], "problem_expr": "4*a/b + 3*x/(2*m)", "answer_expr": "(4*a*m + 3*b*x)/(2*b*m)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: 3*c/(2*b) + 4*x/a" ], "shape": [ "identity: N*c/b + N*x/a" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/5", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 5", "problem_latex": "$\\displaystyle \\frac{2x}{3}-x+\\frac{3x}{5}$.", "markdown": "$\\displaystyle \\frac{2x}{3}-x+\\frac{3x}{5}$.", "answer_latex": [ "$\\displaystyle \\frac{4 x}{15}$." ], "answer_markdown": [ "$\\displaystyle \\frac{4 x}{15}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "2*x/3 - x + 3*x/5", "answer_expr": "4*x/15" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*x/15" ], "shape": [ "identity: N*x" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/6", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 6", "problem_latex": "$\\displaystyle \\frac{m^2}{n^2}-2+\\frac{n^2}{m^2}$.", "markdown": "$\\displaystyle \\frac{m^2}{n^2}-2+\\frac{n^2}{m^2}$.", "answer_latex": [ "$\\displaystyle \\frac{m^{4} - 2 m^{2} n^{2} + n^{4}}{m^{2}\nn^{2}}$." ], "answer_markdown": [ "$\\displaystyle \\frac{m^{4} - 2 m^{2} n^{2} + n^{4}}{m^{2} n^{2}}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "m**2/n**2 - 2 + n**2/m**2", "answer_expr": "(m**4 - 2*m**2*n**2 + n**4)/(m**2*n**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a**2/x**2 - 2 + x**2/a**2" ], "shape": [ "identity: N + 2*a**N*x**N" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/7", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 7", "problem_latex": "$\\displaystyle \\frac{x}{mn}-\\frac{x+mn}{3n}+2m$.", "markdown": "$\\displaystyle \\frac{x}{mn}-\\frac{x+mn}{3n}+2m$.", "answer_latex": [ "$\\displaystyle \\frac{3 x - m x + 5 m^{2} n}{3 m n}$." ], "answer_markdown": [ "$\\displaystyle \\frac{3 x - m x + 5 m^{2} n}{3 m n}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x/(m*n) - (x + m*n)/(3*n) + 2*m", "answer_expr": "(3*x - m*x + 5*m**2*n)/(3*m*n)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a - (a*b + x)/(3*b) + x/(a*b)" ], "shape": [ "identity: N*a + N*(a*b + x)/b + x/(a*b)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/8", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 8", "problem_latex": "$\\displaystyle \\frac{2b+x}{3x}+\\frac{5b-4x}{9x}$.", "markdown": "$\\displaystyle \\frac{2b+x}{3x}+\\frac{5b-4x}{9x}$.", "answer_latex": [ "$\\displaystyle \\frac{11 b - x}{9 x}$." ], "answer_markdown": [ "$\\displaystyle \\frac{11 b - x}{9 x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*b + x)/(3*x) + (5*b - 4*x)/(9*x)", "answer_expr": "(11*b - x)/(9*x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a + x)/(3*x) + (5*a - 4*x)/(9*x)" ], "shape": [ "identity: N*(N*a + x)/x + N*(N*a + N*x)/x" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-44/9", "set": "boyden-first-book-in-algebra-1895/ex-44", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 44, problem 9", "problem_latex": "$\\displaystyle\n\\frac{3m-a}{am}+\\frac{b-2m}{bm}-\\frac{3b-2a}{ab}$.", "markdown": "$\\displaystyle \\frac{3m-a}{am}+\\frac{b-2m}{bm}-\\frac{3b-2a}{ab}$.", "answer_latex": [ "0." ], "answer_markdown": [ "0." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "1.0022867662845733673e-51", "0.0" ], "problem_expr": "(3*m - a)/(a*m) + (b - 2*m)/(b*m) - (3*b - 2*a)/(a*b)", "answer_expr": "0" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (3*b - x)/(b*x) - (3*a - 2*x)/(a*x) + (a - 2*b)/(a*b)" ], "shape": [ "identity: (N*b - x)/(b*x) - (N*a + N*x)/(a*x) + (N*b + a)/(a*b)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/1", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 1", "problem_latex": "$\\displaystyle \\frac{2x}{x^2-4} + \\frac{1}{2-x} +\n\\frac{1}{2+x}$.", "markdown": "$\\displaystyle \\frac{2x}{x^2-4} + \\frac{1}{2-x} + \\frac{1}{2+x}$.", "answer_latex": [ "$\\displaystyle \\frac{2}{x + 2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2}{x + 2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "2*x/(x**2 - 4) + 1/(2 - x) + 1/(2 + x)", "answer_expr": "2/(x + 2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a/(a**2 - 4) + 1/(a + 2) + 1/(-a + 2)" ], "shape": [ "identity: N*a/(N + a**N) + 1/(N + a) + 1/(N - a)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/10", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 10", "problem_latex": "$\\displaystyle\n\\frac{1}{(z-a)(z-y)}+\\frac{1}{(a-z)(a-y)}+\\frac{1}{(y-z)(y-a)}$.", "markdown": "$\\displaystyle \\frac{1}{(z-a)(z-y)}+\\frac{1}{(a-z)(a-y)}+\\frac{1}{(y-z)(y-a)}$.", "answer_latex": [ "0." ], "answer_markdown": [ "0." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "1/((z - a)*(z - y)) + 1/((a - z)*(a - y)) + 1/((y - z)*(y - a))", "answer_expr": "0" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 1/((a - b)*(a - c)) + 1/((-a + c)*(-b + c)) + 1/((-a + b)*(b - c))" ], "shape": [ "identity: 1/((a - b)*(a - c)) + 1/((-a + c)*(-b + c)) + 1/((-a + b)*(b - c))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/11", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 11", "problem_latex": "$\\displaystyle\n\\frac{1}{(1-x)(1-y)}-\\frac{x^2}{(x-1)(y-x)}-\\frac{y^2}{(y-1)(x-y)}$.", "markdown": "$\\displaystyle \\frac{1}{(1-x)(1-y)}-\\frac{x^2}{(x-1)(y-x)}-\\frac{y^2}{(y-1)(x-y)}$.", "answer_latex": [ "1." ], "answer_markdown": [ "1." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "1/((1 - x)*(1 - y)) - x**2/((x - 1)*(y - x)) - y**2/((y - 1)*(x - y))", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**2/((-a + b)*(a - 1)) - b**2/((a - b)*(b - 1)) + 1/((-a + 1)*(-b + 1))" ], "shape": [ "identity: -a**N/((-a + b)*(a - 1)) - b**N/((a - b)*(b - 1)) + 1/((-a + 1)*(-b + 1))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/12", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 12", "problem_latex": "$\\displaystyle a-\\frac{a^2}{a+1}-\\frac{a}{1-a}$.", "markdown": "$\\displaystyle a-\\frac{a^2}{a+1}-\\frac{a}{1-a}$.", "answer_latex": [ "$\\displaystyle \\frac{2 a^{2}}{a^{2} - 1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2 a^{2}}{a^{2} - 1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "a - a**2/(a + 1) - a/(1 - a)", "answer_expr": "2*a**2/(a**2 - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**2/(a + 1) + a - a/(-a + 1)" ], "shape": [ "identity: a - a/(-a + 1) - a**N/(a + 1)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/13", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 13", "problem_latex": "$\\displaystyle 1-a+a^2-a^3+\\frac{a}{1+a}$.", "markdown": "$\\displaystyle 1-a+a^2-a^3+\\frac{a}{1+a}$.", "answer_latex": [ "$\\displaystyle \\frac{1 + a - a^{4}}{1 + a}$." ], "answer_markdown": [ "$\\displaystyle \\frac{1 + a - a^{4}}{1 + a}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "1 - a + a**2 - a**3 + a/(1 + a)", "answer_expr": "(1 + a - a**4)/(1 + a)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -a**3 + a**2 - a + a/(a + 1) + 1" ], "shape": [ "identity: -a + a/(a + 1) + 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/14", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 14", "problem_latex": "$\\displaystyle\n\\frac{1}{x^2-7x+12}-\\frac{2}{x^2-6x+8}+\\frac{2}{x^2-5x+6}$.", "markdown": "$\\displaystyle \\frac{1}{x^2-7x+12}-\\frac{2}{x^2-6x+8}+\\frac{2}{x^2-5x+6}$.", "answer_latex": [ "$\\displaystyle \\frac{1}{(x - 2)(x - 3)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{1}{(x - 2)(x - 3)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "1/(x**2 - 7*x + 12) - 2/(x**2 - 6*x + 8) + 2/(x**2 - 5*x + 6)", "answer_expr": "1/((x - 2)*(x - 3))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2/(a**2 - 5*a + 6) - 2/(a**2 - 6*a + 8) + 1/(a**2 - 7*a + 12)" ], "shape": [ "identity: 2*N/(N*a + N + a**N) + 1/(N*a + N + a**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/15", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 15", "problem_latex": "What will $a$ pounds of rice cost if $b$ pounds costs 43\\\\\ncents?", "markdown": "What will $a$ pounds of rice cost if $b$ pounds costs 43 cents?", "answer_latex": [ "$\\displaystyle \\frac{43 a}{b}$." ], "answer_markdown": [ "$\\displaystyle \\frac{43 a}{b}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{C: 43*a/b}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x/a, 43/b)" ], "shape": [ "solve: Eq(x/a, N/b)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/16", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 16", "problem_latex": "$x$ is $\\frac{4}{9}$ of what number?", "markdown": "$x$ is $\\frac{4}{9}$ of what number?", "answer_latex": [ "$\\displaystyle \\frac{9 x}{4}$." ], "answer_markdown": [ "$\\displaystyle \\frac{9 x}{4}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{N: 9*x/4}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a, 4*x/9)" ], "shape": [ "solve: Eq(a, N*x)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/17", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 17", "problem_latex": "$m$ is $\\frac{5}{x}$ of what number?", "markdown": "$m$ is $\\frac{5}{x}$ of what number?", "answer_latex": [ "$\\displaystyle \\frac{m x}{5}$." ], "answer_markdown": [ "$\\displaystyle \\frac{m x}{5}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{N: m*x/5}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a, 5*x/b)" ], "shape": [ "solve: Eq(a, N*x/b)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/18", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 18", "problem_latex": "$y$ is $\\frac{a}{b}$ of what number?", "markdown": "$y$ is $\\frac{a}{b}$ of what number?", "answer_latex": [ "$\\displaystyle \\frac{b y}{a}$." ], "answer_markdown": [ "$\\displaystyle \\frac{b y}{a}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{N: b*y/a}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(c, a*x/b)" ], "shape": [ "solve: Eq(c, a*x/b)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/2", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 2", "problem_latex": "$\\displaystyle \\frac{3a}{a^2-9} + \\frac{1}{3-a} -\n\\frac{1}{3+a}$.", "markdown": "$\\displaystyle \\frac{3a}{a^2-9} + \\frac{1}{3-a} - \\frac{1}{3+a}$.", "answer_latex": [ "$\\displaystyle \\frac{a}{a^{2} - 9}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a}{a^{2} - 9}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "3*a/(a**2 - 9) + 1/(3 - a) - 1/(3 + a)", "answer_expr": "a/(a**2 - 9)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*a/(a**2 - 9) - 1/(a + 3) + 1/(-a + 3)" ], "shape": [ "identity: N*a/(N + a**N) - 1/(N + a) + 1/(N - a)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/3", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 3", "problem_latex": "$\\displaystyle m^2 - \\frac{am^2}{a-m} - \\frac{am^2}{m+a} -\n\\frac{2a^2m^2}{m^2-a^2}$.", "markdown": "$\\displaystyle m^2 - \\frac{am^2}{a-m} - \\frac{am^2}{m+a} - \\frac{2a^2m^2}{m^2-a^2}$.", "answer_latex": [ "$m^{2}$." ], "answer_markdown": [ "$m^{2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "m**2 - a*m**2/(a - m) - a*m**2/(m + a) - 2*a**2*m**2/(m**2 - a**2)", "answer_expr": "m**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -2*a**2*b**2/(-a**2 + b**2) - a*b**2/(a + b) - a*b**2/(a - b) + b**2" ], "shape": [ "identity: N*a**N*b**N/(-a**N + b**N) - a*b**N/(a + b) - a*b**N/(a - b) + b**N" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/4", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 4", "problem_latex": "$\\displaystyle\n\\frac{20a-4}{4a^2-1}+\\frac{3}{1-2a}-\\frac{6}{1-2a}$.", "markdown": "$\\displaystyle \\frac{20a-4}{4a^2-1}+\\frac{3}{1-2a}-\\frac{6}{1-2a}$.", "answer_latex": [ "$\\displaystyle \\frac{1}{2 a + 1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{1}{2 a + 1}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "2.0451528952504879636", "0.13448275862068965517" ], "problem_expr": "(20*a - 4)/(4*a**2 - 1) + 3/(1 - 2*a) - 6/(1 - 2*a)", "answer_expr": "1/(2*a + 1)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (20*a - 4)/(4*a**2 - 1) - 3/(-2*a + 1)" ], "shape": [ "identity: N/(N*a + 1) + (N*a + N)/(N*a**N - 1)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/5", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 5", "problem_latex": "$\\displaystyle \\frac{1}{x-y} + \\frac{3y^3}{y^3-x^3} -\n\\frac{1}{3(1+a)}$.", "markdown": "$\\displaystyle \\frac{1}{x-y} + \\frac{3y^3}{y^3-x^3} - \\frac{1}{3(1+a)}$.", "answer_latex": [ "$\\displaystyle \\frac{3 y}{x^{2} + x y + y^{2}}$." ], "answer_markdown": [ "$\\displaystyle \\frac{3 y}{x^{2} + x y + y^{2}}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "2.1289662169509025165", "1.2896439381607978101" ], "problem_expr": "1/(x - y) + 3*y**3/(y**3 - x**3) - 1/(3*(1 + a))", "answer_expr": "3*y/(x**2 + x*y + y**2)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: 3*c**3/(-b**3 + c**3) + 1/(b - c) - 1/(3*a + 3)" ], "shape": [ "identity: N*c**N/(-b**N + c**N) - 1/(N*a + N) + 1/(b - c)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/6", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 6", "problem_latex": "$\\displaystyle\n\\frac{a+3}{6(a^2-1)}+\\frac{1}{2(1-a)}+\\frac{1}{3(1+a)}$.", "markdown": "$\\displaystyle \\frac{a+3}{6(a^2-1)}+\\frac{1}{2(1-a)}+\\frac{1}{3(1+a)}$.", "answer_latex": [ "$\\displaystyle - \\frac{1}{3(a^{2} - 1)}$." ], "answer_markdown": [ "$\\displaystyle - \\frac{1}{3(a^{2} - 1)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a + 3)/(6*(a**2 - 1)) + 1/(2*(1 - a)) + 1/(3*(1 + a))", "answer_expr": "-1/(3*(a**2 - 1))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a + 3)/(6*a**2 - 6) + 1/(3*a + 3) + 1/(-2*a + 2)" ], "shape": [ "identity: (N + a)/(N*a**N + N) + 2/(N*a + N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/7", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 7", "problem_latex": "$\\displaystyle\n\\frac{1}{5(3b-y^2)}-\\frac{1}{2(3b+y^2)}-\\frac{11b-7y^2}{10(y^4-9b^2)}$.", "markdown": "$\\displaystyle \\frac{1}{5(3b-y^2)}-\\frac{1}{2(3b+y^2)}-\\frac{11b-7y^2}{10(y^4-9b^2)}$.", "answer_latex": [ "$\\displaystyle - \\frac{b}{5(y^{4} - 9 b^{2})}$." ], "answer_markdown": [ "$\\displaystyle - \\frac{b}{5(y^{4} - 9 b^{2})}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "1/(5*(3*b - y**2)) - 1/(2*(3*b + y**2)) - (11*b - 7*y**2)/(10*(y**4 - 9*b**2))", "answer_expr": "-b/(5*(y**4 - 9*b**2))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -(11*a - 7*b**2)/(-90*a**2 + 10*b**4) + 1/(15*a - 5*b**2) - 1/(6*a + 2*b**2)" ], "shape": [ "identity: -(N*a + N*b**N)/(N*a**N + N*b**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/8", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 8", "problem_latex": "$\\displaystyle\n\\frac{3}{(1-x)(3-x)}+\\frac{1}{(2-x)(x-3)}-\\frac{1}{(x-1)(x-2)}$.", "markdown": "$\\displaystyle \\frac{3}{(1-x)(3-x)}+\\frac{1}{(2-x)(x-3)}-\\frac{1}{(x-1)(x-2)}$.", "answer_latex": [ "$\\displaystyle \\frac{1}{(1 - x)(3 - x)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{1}{(1 - x)(3 - x)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "3/((1 - x)*(3 - x)) + 1/((2 - x)*(x - 3)) - 1/((x - 1)*(x - 2))", "answer_expr": "1/((1 - x)*(3 - x))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -1/((a - 2)*(a - 1)) + 1/((-a + 2)*(a - 3)) + 3/((-a + 1)*(-a + 3))" ], "shape": [ "identity: N/((-a + 1)*(N - a)) - 1/((N + a)*(a - 1)) + 1/((N - a)*(N + a))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-45/9", "set": "boyden-first-book-in-algebra-1895/ex-45", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 45, problem 9", "problem_latex": "$\\displaystyle\n\\frac{a}{(a-b)(b-c)}+\\frac{1}{c-a}-\\frac{a-b}{(c-a)(c-b)}$.", "markdown": "$\\displaystyle \\frac{a}{(a-b)(b-c)}+\\frac{1}{c-a}-\\frac{a-b}{(c-a)(c-b)}$.", "answer_latex": [ "$\\displaystyle \\frac{b}{(b - c)(a - b)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{b}{(b - c)(a - b)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "a/((a - b)*(b - c)) + 1/(c - a) - (a - b)/((c - a)*(c - b))", "answer_expr": "b/((b - c)*(a - b))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a/((a - b)*(b - c)) - (a - b)/((-a + c)*(-b + c)) + 1/(-a + c)" ], "shape": [ "identity: a/((a - b)*(b - c)) - (a - b)/((-a + c)*(-b + c)) + 1/(-a + c)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/1", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 1", "problem_latex": "$\\displaystyle \\frac{a}{b^2}$ by $x$.", "markdown": "$\\displaystyle \\frac{a}{b^2}$ by $x$.", "answer_latex": [ "$\\displaystyle \\frac{ax}{b^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{ax}{b^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a/b**2)*x", "answer_expr": "a*x/b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: b*x/a**2" ], "shape": [ "identity: a**N*b*x" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/10", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 10", "problem_latex": "$\\displaystyle \\frac{a^2-4a-21}{a^2-3a-10}$ by $a-5$.", "markdown": "$\\displaystyle \\frac{a^2-4a-21}{a^2-3a-10}$ by $a-5$.", "answer_latex": [ "$\\displaystyle \\frac{a^2-4a-21}{a+2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a^2-4a-21}{a+2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a**2-4*a-21)/(a**2-3*a-10))*(a-5)", "answer_expr": "(a**2-4*a-21)/(a+2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 5)*(x**2 - 4*x - 21)/(x**2 - 3*x - 10)" ], "shape": [ "identity: N + x" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/11", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 11", "problem_latex": "$\\displaystyle x+y-\\frac{4xy}{x+y}$ by $x+y$.", "markdown": "$\\displaystyle x+y-\\frac{4xy}{x+y}$ by $x+y$.", "answer_latex": [ "$x^2-2xy+y^2$." ], "answer_markdown": [ "$x^2-2xy+y^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x+y-4*x*y/(x+y))*(x+y)", "answer_expr": "x**2-2*x*y+y**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a + x)*(-4*a*x/(a + x) + a + x)" ], "shape": [ "identity: (a + x)*(N*a*x/(a + x) + a + x)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/12", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 12", "problem_latex": "$\\displaystyle a-b+\\frac{4ab}{a-b}$ by $a-b$.", "markdown": "$\\displaystyle a-b+\\frac{4ab}{a-b}$ by $a-b$.", "answer_latex": [ "$a^2+2ab+b^2$." ], "answer_markdown": [ "$a^2+2ab+b^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a-b+4*a*b/(a-b))*(a-b)", "answer_expr": "a**2+2*a*b+b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a + x)*(4*a*x/(-a + x) - a + x)" ], "shape": [ "identity: (-a + x)*(N*a*x/(-a + x) - a + x)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/13", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 13", "problem_latex": "$\\displaystyle \\frac{1}{x-y+z}+\\frac{2z}{(x-y)^2-z^2}$ by\n$x^2-xy-xz$.", "markdown": "$\\displaystyle \\frac{1}{x-y+z}+\\frac{2z}{(x-y)^2-z^2}$ by $x^2-xy-xz$.", "answer_latex": [ "$x$." ], "answer_markdown": [ "$x$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1/(x-y+z) + 2*z/((x-y)**2-z**2))*(x**2-x*y-x*z)", "answer_expr": "x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*b/(-b**2 + (-a + x)**2) + 1/(-a + 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"verdicts": [ "PASS" ] }, "form": [ "identity: (-2*a/(-a**2 + (b + x)**2) + 1/(-a + b + x))*(a*b + b**2 + b*x)" ], "shape": [ "identity: (N*a/(-a**N + (b + x)**N) + 1/(-a + b + x))*(a*b + b*x + b**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/15", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 15", "problem_latex": "How many units of the value of $\\frac{1}{5}$ are there in 2?", "markdown": "How many units of the value of $\\frac{1}{5}$ are there in 2?", "answer_latex": [ "$10$." ], "answer_markdown": [ "$10$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 10.0, printed 10 (half-unit 0.5; correctly rounded at the printed digits: 10.0)", 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"boyden-first-book-in-algebra-1895/ex-46/2", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 2", "problem_latex": "$\\displaystyle \\frac{3a^2bc}{7x^2y^3}$ by $y^2$.", "markdown": "$\\displaystyle \\frac{3a^2bc}{7x^2y^3}$ by $y^2$.", "answer_latex": [ "$\\displaystyle \\frac{3a^2 bc}{7x^2 y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{3a^2 bc}{7x^2 y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3*a**2*b*c/(7*x**2*y**3))*y**2", "answer_expr": "3*a**2*b*c/(7*x**2*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*a*b*x**2/(7*c**2*d)" ], "shape": [ "identity: N*a*b*c**N*x**N/d" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/3", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 3", "problem_latex": "$\\displaystyle \\frac{1}{2c^2d}$ by $a^2d$.", "markdown": "$\\displaystyle \\frac{1}{2c^2d}$ by $a^2d$.", "answer_latex": [ "$\\displaystyle \\frac{a^2}{2c^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a^2}{2c^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1/(2*c**2*d))*(a**2*d)", "answer_expr": "a**2/(2*c**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: x**2/(2*a**2)" ], "shape": [ "identity: N*a**N*x**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/4", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 4", "problem_latex": "$\\displaystyle \\frac{4abc^2}{9x^2y}$ by $3xy$.", "markdown": "$\\displaystyle \\frac{4abc^2}{9x^2y}$ by $3xy$.", "answer_latex": [ "$\\displaystyle \\frac{4abc^2}{3x}$." ], "answer_markdown": [ "$\\displaystyle \\frac{4abc^2}{3x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*a*b*c**2/(9*x**2*y))*(3*x*y)", "answer_expr": "4*a*b*c**2/(3*x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*a*b**2*x/(3*c)" ], "shape": [ "identity: N*a*b**N*x/c" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/5", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 5", "problem_latex": "$\\displaystyle \\frac{3mn}{2x^2y^2}$ by $6x^2y$.", "markdown": "$\\displaystyle \\frac{3mn}{2x^2y^2}$ by $6x^2y$.", "answer_latex": [ "$\\displaystyle \\frac{9mn}{y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{9mn}{y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3*m*n/(2*x**2*y**2))*(6*x**2*y)", "answer_expr": "9*m*n/y" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 9*a*x/b" ], "shape": [ "identity: N*a*x/b" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/6", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 6", "problem_latex": "$\\displaystyle \\frac{x-y}{2mn}$ by $3x$.", "markdown": "$\\displaystyle \\frac{x-y}{2mn}$ by $3x$.", "answer_latex": [ "$\\displaystyle \\frac{3x(x-y)}{2mn}$." ], "answer_markdown": [ "$\\displaystyle \\frac{3x(x-y)}{2mn}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x-y)/(2*m*n))*(3*x)", "answer_expr": "3*x*(x-y)/(2*m*n)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*x*(-c + x)/(2*a*b)" ], "shape": [ "identity: N*x*(-c + x)/(a*b)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/7", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 7", "problem_latex": "$\\displaystyle \\frac{2a-b}{3x^2-xy}$ by $x$.", "markdown": "$\\displaystyle \\frac{2a-b}{3x^2-xy}$ by $x$.", "answer_latex": [ "$\\displaystyle \\frac{2a-b}{3x-y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2a-b}{3x-y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((2*a-b)/(3*x**2-x*y))*x", "answer_expr": "(2*a-b)/(3*x-y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: b*(-a + 2*x)/(3*b**2 - b*c)" ], "shape": [ "identity: b*(N*x - a)/(N*b**N - b*c)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/8", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 8", "problem_latex": "$\\displaystyle \\frac{x^2}{x^3-y^3}$ by $x-y$.", "markdown": "$\\displaystyle \\frac{x^2}{x^3-y^3}$ by $x-y$.", "answer_latex": [ "$\\displaystyle \\frac{x^2}{x^2+xy+y^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2}{x^2+xy+y^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2/(x**3-y**3))*(x-y)", "answer_expr": "x**2/(x**2+x*y+y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: x**2*(-a + x)/(-a**3 + x**3)" ], "shape": [ "identity: x**N*(-a + x)/(-a**N + x**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-46/9", "set": "boyden-first-book-in-algebra-1895/ex-46", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 46, problem 9", "problem_latex": "$\\displaystyle \\frac{3x+3y}{x-y}$ by $x^2-y^2$.", "markdown": "$\\displaystyle \\frac{3x+3y}{x-y}$ by $x^2-y^2$.", "answer_latex": [ "$3\\left(x+y\\right)^2$." ], "answer_markdown": [ "$3\\left(x+y\\right)^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((3*x+3*y)/(x-y))*(x**2-y**2)", "answer_expr": "3*(x+y)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (3*a + 3*x)*(-a**2 + x**2)/(-a + x)" ], "shape": [ "identity: (-a**N + x**N)*(N*a + N*x)/(-a + x)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/1", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 1", "problem_latex": "$\\displaystyle \\frac{a^2x}{b}$ by $ax$.", "markdown": "$\\displaystyle \\frac{a^2x}{b}$ by $ax$.", "answer_latex": [ "$\\displaystyle \\frac{a}{b}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a}{b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**2*x/b)/(a*x)", "answer_expr": "a/b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a/b" ], "shape": [ "identity: a/b" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/10", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 10", "problem_latex": "$\\displaystyle \\frac{x^2+5x-14}{x^2-7x+12}$ by $x-2$.", "markdown": "$\\displaystyle \\frac{x^2+5x-14}{x^2-7x+12}$ by $x-2$.", "answer_latex": [ "$\\displaystyle \\frac{x+7}{x^2-7x+12}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x+7}{x^2-7x+12}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x**2+5*x-14)/(x**2-7*x+12))/(x-2)", "answer_expr": "(x+7)/(x**2-7*x+12)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 + 5*a - 14)/((a - 2)*(a**2 - 7*a + 12))" ], "shape": [ "identity: 1/(N + a)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/11", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 11", "problem_latex": "$\\displaystyle ax+bx+a+b+\\frac{a+b}{3x}$ by $a+b$.", "markdown": "$\\displaystyle ax+bx+a+b+\\frac{a+b}{3x}$ by $a+b$.", "answer_latex": [ "$\\displaystyle x+1+\\frac{1}{3x}$." ], "answer_markdown": [ "$\\displaystyle x+1+\\frac{1}{3x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a*x+b*x+a+b+(a+b)/(3*x))/(a+b)", "answer_expr": "x+1+1/(3*x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a*c + a + b*c + b + (a + b)/(3*c))/(a + b)" ], "shape": [ "identity: (N*(a + b)/c + a*c + a + b*c + b)/(a + b)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/12", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 12", "problem_latex": "Multiply $\\displaystyle \\frac{x^2-5x+6}{x^2+3x-4}$ by $x-1$.", "markdown": "Multiply $\\displaystyle \\frac{x^2-5x+6}{x^2+3x-4}$ by $x-1$.", "answer_latex": [ "$\\displaystyle \\frac{x^2-5x+6}{x+4}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2-5x+6}{x+4}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x**2-5*x+6)/(x**2+3*x-4))*(x-1)", "answer_expr": "(x**2-5*x+6)/(x+4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a - 1)*(a**2 - 5*a + 6)/(a**2 + 3*a - 4)" ], "shape": [ "identity: a - 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/13", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 13", "problem_latex": "Divide $\\displaystyle \\frac {5 b c^2}{6 a x^3} $ by $10 a b\nc$.", "markdown": "Divide $\\displaystyle \\frac {5 b c^2}{6 a x^3} $ by $10 a b c$.", "answer_latex": [ "$\\displaystyle \\frac{c}{12a^2 x^3}$." ], "answer_markdown": [ "$\\displaystyle \\frac{c}{12a^2 x^3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(5*b*c**2/(6*a*x**3))/(10*a*b*c)", "answer_expr": "c/(12*a**2*x**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: b/(12*a**2*c**3)" ], "shape": [ "identity: N*a**N*b*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/14", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 14", "problem_latex": "Multiply $\\displaystyle 1 + \\frac{3ac}{4 x^2 y} $ by $ 2 a\nc $.", "markdown": "Multiply $\\displaystyle 1 + \\frac{3ac}{4 x^2 y} $ by $ 2 a c $.", "answer_latex": [ "$\\displaystyle 2ac+\\frac{3a^2 c^2}{2x^2 y}$." ], "answer_markdown": [ "$\\displaystyle 2ac+\\frac{3a^2 c^2}{2x^2 y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1+3*a*c/(4*x**2*y))*(2*a*c)", "answer_expr": "2*a*c+3*a**2*c**2/(2*x**2*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a*b*(3*a*b/(4*c**2*d) + 1)" ], "shape": [ "identity: N*a*b*(N*a*b*c**N/d + 1)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/15", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 15", "problem_latex": "Divide $\\displaystyle \\frac{5 x^2 y - 5 y^3}{2 x^2 z} $ by\n$ 4 x + 4 y $.", "markdown": "Divide $\\displaystyle \\frac{5 x^2 y - 5 y^3}{2 x^2 z} $ by $ 4 x + 4 y $.", "answer_latex": [ "$\\displaystyle \\frac{5y(x-y)}{8x^2 z}$." ], "answer_markdown": [ "$\\displaystyle \\frac{5y(x-y)}{8x^2 z}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((5*x**2*y-5*y**3)/(2*x**2*z))/(4*x+4*y)", "answer_expr": "5*y*(x-y)/(8*x**2*z)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (5*a**2*b - 5*b**3)/(2*a**2*c*(4*a + 4*b))" ], "shape": [ "identity: N*a**N*(N*a**N*b + N*b**N)/(c*(N*a + N*b))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/16", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 16", "problem_latex": "Divide $\\displaystyle \\frac{4 x^2 y}{3 m n^2} $ by $ 6 a x\ny $.", "markdown": "Divide $\\displaystyle \\frac{4 x^2 y}{3 m n^2} $ by $ 6 a x y $.", "answer_latex": [ "$\\displaystyle \\frac{2x}{9amn^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2x}{9amn^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*x**2*y/(3*m*n**2))/(6*a*x*y)", "answer_expr": "2*x/(9*a*m*n**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*d/(9*a*b*c**2)" ], "shape": [ "identity: N*c**N*d/(a*b)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/17", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 17", "problem_latex": "A can do a piece of-work in $2 \\frac{1}{3}$ days, and B in\n$2\\frac{1}{2}$ days. How much of the work can they both together\ndo in one day?", "markdown": "A can do a piece of-work in $2 \\frac{1}{3}$ days, and B in $2\\frac{1}{2}$ days. How much of the work can they both together do in one day?", "answer_latex": [ "$\\displaystyle \\frac{29}{35}$." ], "answer_markdown": [ "$\\displaystyle \\frac{29}{35}$." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 0.828571428571, printed 29/35 (half-unit 1.0e-40; correctly rounded at the printed digits: 0.828571428571)", "problem_expr": "1/Rational(7,3) + 1/Rational(5,2)", "answer_expr": "29/35" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 29/35" ], "shape": [ "evaluate: N" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": "X#\\frac{29}{35},5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/18", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 18", "problem_latex": "If C can do a piece of work in $m$ days, and D works half as\nfast as G, how much of the work can D do in one day?", "markdown": "If C can do a piece of work in $m$ days, and D works half as fast as G, how much of the work can D do in one day?", "answer_latex": [ "$\\displaystyle \\frac{1}{2m}$." ], "answer_markdown": [ "$\\displaystyle \\frac{1}{2m}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "1/(2*m)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/2", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 2", "problem_latex": "$\\displaystyle \\frac{3m^2n}{2xy}$ by $2x$.", "markdown": "$\\displaystyle \\frac{3m^2n}{2xy}$ by $2x$.", "answer_latex": [ "$\\displaystyle \\frac{3m^2 n}{4x^2 y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{3m^2 n}{4x^2 y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(3*m**2*n/(2*x*y))/(2*x)", "answer_expr": "3*m**2*n/(4*x**2*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*a**2*b/(4*c**2*d)" ], "shape": [ "identity: N*a**N*b*c**N/d" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/3", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 3", "problem_latex": "$\\displaystyle \\frac{18cd^5}{5x}$ by $6cd^3$.", "markdown": "$\\displaystyle \\frac{18cd^5}{5x}$ by $6cd^3$.", "answer_latex": [ "$\\displaystyle \\frac{3d^2}{5x}$." ], "answer_markdown": [ "$\\displaystyle \\frac{3d^2}{5x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(18*c*d**5/(5*x))/(6*c*d**3)", "answer_expr": "3*d**2/(5*x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 3*a**2/(5*b)" ], "shape": [ "identity: N*a**N/b" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/4", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 4", "problem_latex": "$\\displaystyle \\frac{6x^2y}{m}$ by $9mn$.", "markdown": "$\\displaystyle \\frac{6x^2y}{m}$ by $9mn$.", "answer_latex": [ "$\\displaystyle \\frac{2x^2 y}{3m^2 n}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2x^2 y}{3m^2 n}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(6*x**2*y/m)/(9*m*n)", "answer_expr": "2*x**2*y/(3*m**2*n)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*c**2*d/(3*a**2*b)" ], "shape": [ "identity: N*a**N*c**N*d/b" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/5", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 5", "problem_latex": "$\\displaystyle \\frac{a}{c+d}$ by $3x$.", "markdown": "$\\displaystyle \\frac{a}{c+d}$ by $3x$.", "answer_latex": [ "$\\displaystyle \\frac{a}{3x(c+d)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a}{3x(c+d)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a/(c+d))/(3*x)", "answer_expr": "a/(3*x*(c+d))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a/(3*d*(b + c))" ], "shape": [ "identity: N*a/(d*(b + c))" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/6", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 6", "problem_latex": "$\\displaystyle \\frac{3x^3-3xy}{2m^2n}$ by $3x$.", "markdown": "$\\displaystyle \\frac{3x^3-3xy}{2m^2n}$ by $3x$.", "answer_latex": [ "$\\displaystyle \\frac{x^2-y}{2m^2n}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2-y}{2m^2n}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((3*x**3-3*x*y)/(2*m**2*n))/(3*x)", "answer_expr": "(x**2-y)/(2*m**2*n)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (3*c**3 - 3*c*d)/(6*a**2*b*c)" ], "shape": [ "identity: N*a**N*(N*c*d + N*c**N)/(b*c)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/7", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 7", "problem_latex": "$\\displaystyle \\frac{2ab-2b^4}{5x^2yz}$ by $2ab$.", "markdown": "$\\displaystyle \\frac{2ab-2b^4}{5x^2yz}$ by $2ab$.", "answer_latex": [ "$\\displaystyle \\frac{a-b^3}{5ax^2yz}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a-b^3}{5ax^2yz}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((2*a*b-2*b**4)/(5*x**2*y*z))/(2*a*b)", "answer_expr": "(a-b**3)/(5*a*x**2*y*z)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a*b - 2*b**4)/(10*a*b*c**2*d*e)" ], "shape": [ "identity: N*c**N*(N*a*b + N*b**N)/(a*b*d*e)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/8", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 8", "problem_latex": "$\\displaystyle \\frac{5(a^2-b^2)}{xy}$ by $a-b$.", "markdown": "$\\displaystyle \\frac{5(a^2-b^2)}{xy}$ by $a-b$.", "answer_latex": [ "$\\displaystyle \\frac{5(a+b)}{xy}$." ], "answer_markdown": [ "$\\displaystyle \\frac{5(a+b)}{xy}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(5*(a**2-b**2)/(x*y))/(a-b)", "answer_expr": "5*(a+b)/(x*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (5*a**2 - 5*b**2)/(c*d*(a - b))" ], "shape": [ "identity: (N*a**N + N*b**N)/(c*d*(a - b))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-47/9", "set": "boyden-first-book-in-algebra-1895/ex-47", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 47, problem 9", "problem_latex": "$\\displaystyle \\frac{m+n}{2m^2-2mn}$ by $m^2-n^2$.", "markdown": "$\\displaystyle \\frac{m+n}{2m^2-2mn}$ by $m^2-n^2$.", "answer_latex": [ "$\\displaystyle \\frac{1}{2m\\left(m-n\\right)^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{1}{2m\\left(m-n\\right)^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((m+n)/(2*m**2-2*m*n))/(m**2-n**2)", "answer_expr": "1/(2*m*(m-n)**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a + b)/((a**2 - b**2)*(2*a**2 - 2*a*b))" ], "shape": [ "identity: (a + b)/((a**N - b**N)*(N*a*b + N*a**N))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/1", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 1", "problem_latex": "$\\displaystyle \\frac{7a^2b^2c}{18x^2y^2z} \\times\n\\frac{9xyz^2}{28abc^2}$", "markdown": "$\\displaystyle \\frac{7a^2b^2c}{18x^2y^2z} \\times \\frac{9xyz^2}{28abc^2}$", "answer_latex": [ "$\\displaystyle \\frac{abz}{8cxy}$." ], "answer_markdown": [ "$\\displaystyle \\frac{abz}{8cxy}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(7*a**2*b**2*c/(18*x**2*y**2*z))*(9*x*y*z**2/(28*a*b*c**2))", "answer_expr": "a*b*z/(8*c*x*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: a*b*f/(8*c*d*e)" ], "shape": [ "identity: N*a*b*f/(c*d*e)" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/10", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 10", "problem_latex": "$\\displaystyle \\frac{m^2 - 25}{m^2 + 2m - 15} \\times\n\\frac{m^4 - 27m}{m^2 - 5m}$", "markdown": "$\\displaystyle \\frac{m^2 - 25}{m^2 + 2m - 15} \\times \\frac{m^4 - 27m}{m^2 - 5m}$", "answer_latex": [ "$m^2+3m+9$." ], "answer_markdown": [ "$m^2+3m+9$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((m**2 - 25)/(m**2 + 2*m - 15))*((m**4 - 27*m)/(m**2 - 5*m))", "answer_expr": "m**2 + 3*m + 9" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - 25)*(a**4 - 27*a)/((a**2 - 5*a)*(a**2 + 2*a - 15))" ], "shape": [ "identity: (N + a**N)/(N*a + N + a**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/11", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 11", "problem_latex": "$\\displaystyle \\frac{a^3 - a^2y + ay^2}{x - 3} \\times\n\\frac{ax + xy - 3a -3y}{a^3 + y^3}$", "markdown": "$\\displaystyle \\frac{a^3 - a^2y + ay^2}{x - 3} \\times \\frac{ax + xy - 3a -3y}{a^3 + y^3}$", "answer_latex": [ "$a$." ], "answer_markdown": [ "$a$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a**3 - a**2*y + a*y**2)/(x - 3))*((a*x + x*y - 3*a - 3*y)/(a**3 + y**3))", "answer_expr": "a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3 - a**2*c + a*c**2)*(a*b - 3*a + b*c - 3*c)/((a**3 + c**3)*(b - 3))" ], "shape": [ "identity: (a*c**N - a**N*c + a**N)*(N*a + N*c + a*b + b*c)/((N + b)*(a**N + c**N))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/12", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 12", "problem_latex": "$\\displaystyle \\frac{x^3 + x^2 - x - 1}{x^2 + 6x + 9} \\times\n\\frac{x^2 + 2x - 3}{2x^3 + 4x^2 + 2x}$", "markdown": "$\\displaystyle \\frac{x^3 + x^2 - x - 1}{x^2 + 6x + 9} \\times \\frac{x^2 + 2x - 3}{2x^3 + 4x^2 + 2x}$", "answer_latex": [ "$\\displaystyle \\frac{\\left(x-1\\right)^2}{2x(x+3)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{\\left(x-1\\right)^2}{2x(x+3)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x**3 + x**2 - x - 1)/(x**2 + 6*x + 9))*((x**2 + 2*x - 3)/(2*x**3 + 4*x**2 + 2*x))", "answer_expr": "(x - 1)**2/(2*x*(x + 3))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 + 2*a - 3)*(a**3 + a**2 - a - 1)/((a**2 + 6*a + 9)*(2*a**3 + 4*a**2 + 2*a))" ], "shape": [ "identity: (-a + 2*a**N - 1)/(N*a + 2*N*a**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/13", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 13", "problem_latex": "$\\displaystyle \\frac{a^3 - a^2 - a + 1}{a^2 + 4a + 4} \\times\n\\frac{a^2 + 3a + 2}{3a^3 - 6a^2 + 3a}$", "markdown": "$\\displaystyle \\frac{a^3 - a^2 - a + 1}{a^2 + 4a + 4} \\times \\frac{a^2 + 3a + 2}{3a^3 - 6a^2 + 3a}$", "answer_latex": [ "$\\displaystyle \\frac{\\left(a+1\\right)^2}{3a(a+2)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{\\left(a+1\\right)^2}{3a(a+2)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a**3 - a**2 - a + 1)/(a**2 + 4*a + 4))*((a**2 + 3*a + 2)/(3*a**3 - 6*a**2 + 3*a))", "answer_expr": "(a + 1)**2/(3*a*(a + 2))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 + 3*a + 2)*(a**3 - a**2 - a + 1)/((a**2 + 4*a + 4)*(3*a**3 - 6*a**2 + 3*a))" ], "shape": [ "identity: (-a + 1)/(N*a + 2*N*a**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/14", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 14", "problem_latex": "$\\displaystyle (m + \\frac{mn}{m - n})(n - \\frac{mn}{m + n})$", "markdown": "$\\displaystyle (m + \\frac{mn}{m - n})(n - \\frac{mn}{m + n})$", "answer_latex": [ "$\\displaystyle \\frac{m^2 n^2}{m^2-n^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{m^2 n^2}{m^2-n^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(m + m*n/(m - n))*(n - m*n/(m + n))", "answer_expr": "m**2*n**2/(m**2 - n**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a*b/(a - b) + a)*(-a*b/(a + b) + b)" ], "shape": [ "identity: (a*b/(a - b) + a)*(-a*b/(a + b) + b)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/15", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 15", "problem_latex": "A grocer purchased $y$ pounds of tea for \\$25. Another\ngrocer purchased 4 pounds less for the same money. What was the\nprice per pound which each paid?", "markdown": "A grocer purchased $y$ pounds of tea for $25. Another grocer purchased 4 pounds less for the same money. What was the price per pound which each paid?", "answer_latex": [ "$\\displaystyle \\frac{25}{y}$; $\\displaystyle \\frac{25}{y-4}$ dols." ], "answer_markdown": [ "$\\displaystyle \\frac{25}{y}$; $\\displaystyle \\frac{25}{y-4}$ dols." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{p: 25/y, q: 25/(y - 4)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b*x, 25), Eq(a*(b - 4), 25))" ], "shape": [ "solve: (Eq(b*x, N), Eq(a*(N + b), N))" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/16", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 16", "problem_latex": "What is $\\displaystyle \\frac{a}{3}$ of $\\displaystyle \n\\frac{2}{c}$?", "markdown": "What is $\\displaystyle \\frac{a}{3}$ of $\\displaystyle \\frac{2}{c}$?", "answer_latex": [ "$\\displaystyle \\frac{2a}{3c}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2a}{3c}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a/3)*(2/c)", "answer_expr": "2*a/(3*c)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*a/(3*b)" ], "shape": [ "identity: N*a/b" ], "same_problem_in": [ "wentworth-first-steps-in-algebra-1894/ex-42/7" ], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/17", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 17", "problem_latex": "Two numbers differ by 28, and one is eight-ninths of the\nother. What are the numbers?", "markdown": "Two numbers differ by 28, and one is eight-ninths of the other. What are the numbers?", "answer_latex": [ "$252$; $224$." ], "answer_markdown": [ "$252$; $224$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 252, y: 224}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 8*x/9), Eq(-a + x, 28))" ], "shape": [ "solve: (Eq(a, N*x), Eq(-a + x, N))" ], "same_problem_in": [], "needs": [ "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/2", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 2", "problem_latex": "$\\displaystyle \\frac{9a^2b^2}{8nx^3y^2} \\times\n\\frac{5x^2y^2}{2am^2n} \\times \\frac{24m^2n^2x}{90ab^2}$", "markdown": "$\\displaystyle \\frac{9a^2b^2}{8nx^3y^2} \\times \\frac{5x^2y^2}{2am^2n} \\times \\frac{24m^2n^2x}{90ab^2}$", "answer_latex": [ "$ \\frac{2}{3}$." ], "answer_markdown": [ "$ \\frac{2}{3}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "0.75", "0.66666666666666666667" ], "problem_expr": "(9*a**2*b**2/(8*n*x**3*y**2))*(5*x**2*y**2/(2*a*m**2*n))*(24*m**2*n**2*x/(90*a*b**2))", "answer_expr": "2/3" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: 3/4" ], "shape": [ "identity: N" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.simplify", "core.arith", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/3", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 3", "problem_latex": "$\\displaystyle \\frac{x^2 - 16y^2}{xy - 4y^2} \\times\n\\frac{2y}{x + 4y}$", "markdown": "$\\displaystyle \\frac{x^2 - 16y^2}{xy - 4y^2} \\times \\frac{2y}{x + 4y}$", "answer_latex": [ "$2$." ], "answer_markdown": [ "$2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x**2 - 16*y**2)/(x*y - 4*y**2))*(2*y/(x + 4*y))", "answer_expr": "2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*b*(a**2 - 16*b**2)/((a + 4*b)*(a*b - 4*b**2))" ], "shape": [ "identity: N*b*(N*b**N + a**N)/((N*b + a)*(N*b**N + a*b))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/4", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 4", "problem_latex": "$\\displaystyle \\frac{3a - b}{2b} \\times \\frac{18ab +\n6b^2}{9a^2 - b^2}$", "markdown": "$\\displaystyle \\frac{3a - b}{2b} \\times \\frac{18ab + 6b^2}{9a^2 - b^2}$", "answer_latex": [ "$3$." ], "answer_markdown": [ "$3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((3*a - b)/(2*b))*((18*a*b + 6*b**2)/(9*a**2 - b**2))", "answer_expr": "3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (3*a - b)*(18*a*b + 6*b**2)/(2*b*(9*a**2 - b**2))" ], "shape": [ "identity: N*(N*a - b)*(N*a*b + N*b**N)/(b*(N*a**N - b**N))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/5", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 5", "problem_latex": "$\\displaystyle \\frac{abd + cd^2}{a^2d - abc} \\times \\frac{acd\n- bc^2}{ab^2 + bcd}$", "markdown": "$\\displaystyle \\frac{abd + cd^2}{a^2d - abc} \\times \\frac{acd - bc^2}{ab^2 + bcd}$", "answer_latex": [ "$\\displaystyle \\frac{cd}{ab}$." ], "answer_markdown": [ "$\\displaystyle \\frac{cd}{ab}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a*b*d + c*d**2)/(a**2*d - a*b*c))*((a*c*d - b*c**2)/(a*b**2 + b*c*d))", "answer_expr": "c*d/(a*b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a*b*d + c*d**2)*(a*c*d - b*c**2)/((a*b**2 + b*c*d)*(a**2*d - a*b*c))" ], "shape": [ "identity: (a*b*d + c*d**N)*(a*c*d - b*c**N)/((a*b**N + b*c*d)*(-a*b*c + a**N*d))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/6", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 6", "problem_latex": "$\\displaystyle \\frac{2ax - 4y}{mn^2 + any} \\times \\frac{mny +\nay^2}{a^2x - 2ay}$", "markdown": "$\\displaystyle \\frac{2ax - 4y}{mn^2 + any} \\times \\frac{mny + ay^2}{a^2x - 2ay}$", "answer_latex": [ "$\\displaystyle \\frac{2y}{an}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2y}{an}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((2*a*x - 4*y)/(m*n**2 + a*n*y))*((m*n*y + a*y**2)/(a**2*x - 2*a*y))", "answer_expr": "2*y/(a*n)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a*d - 4*e)*(a*e**2 + b*c*e)/((a**2*d - 2*a*e)*(a*c*e + b*c**2))" ], "shape": [ "identity: (a*e**N + b*c*e)*(N*a*d + N*e)/((N*a*e + a**N*d)*(a*c*e + b*c**N))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/7", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 7", "problem_latex": "$\\displaystyle \\frac{x^2 - x - 6}{x^2 + x - 2} \\times\n\\frac{x^2 + 3x - 4}{x^2 - 2x - 3}$", "markdown": "$\\displaystyle \\frac{x^2 - x - 6}{x^2 + x - 2} \\times \\frac{x^2 + 3x - 4}{x^2 - 2x - 3}$", "answer_latex": [ "$\\displaystyle \\frac{x+4}{x+1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x+4}{x+1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x**2 - x - 6)/(x**2 + x - 2))*((x**2 + 3*x - 4)/(x**2 - 2*x - 3))", "answer_expr": "(x + 4)/(x + 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - a - 6)*(a**2 + 3*a - 4)/((a**2 - 2*a - 3)*(a**2 + a - 2))" ], "shape": [ "identity: (N - a + a**N)/(N + a + a**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/8", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 8", "problem_latex": "$\\displaystyle \\frac{a^2 + 2a - 3}{a^2 + a - 2} \\times\n\\frac{a^2 + 7a + 10}{a + 3}$", "markdown": "$\\displaystyle \\frac{a^2 + 2a - 3}{a^2 + a - 2} \\times \\frac{a^2 + 7a + 10}{a + 3}$", "answer_latex": [ "$a+5$." ], "answer_markdown": [ "$a+5$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a**2 + 2*a - 3)/(a**2 + a - 2))*((a**2 + 7*a + 10)/(a + 3))", "answer_expr": "a + 5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 + 2*a - 3)*(a**2 + 7*a + 10)/((a + 3)*(a**2 + a - 2))" ], "shape": [ "identity: (N*a + N + a**N)**2/((N + a)*(N + a + a**N))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-48/9", "set": "boyden-first-book-in-algebra-1895/ex-48", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 48, problem 9", "problem_latex": "$\\displaystyle \\frac{x^4 - 64x}{3x^2 - 2x} \\times \\frac{9x^2\n- 4}{x^2 - 4x}$", "markdown": "$\\displaystyle \\frac{x^4 - 64x}{3x^2 - 2x} \\times \\frac{9x^2 - 4}{x^2 - 4x}$", "answer_latex": [ "$\\displaystyle\n\\frac{(x^2+4x+16)(3x+2)}{x}$." ], "answer_markdown": [ "$\\displaystyle \\frac{(x^2+4x+16)(3x+2)}{x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x**4 - 64*x)/(3*x**2 - 2*x))*((9*x**2 - 4)/(x**2 - 4*x))", "answer_expr": "(x**2 + 4*x + 16)*(3*x + 2)/x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (9*a**2 - 4)*(a**4 - 64*a)/((a**2 - 4*a)*(3*a**2 - 2*a))" ], "shape": [ "identity: (N*a**N + N)/(N*a + N*a**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/1", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 1", "problem_latex": "$\\displaystyle \\frac{18a^6b^2c}{35x^3y^3z}\\div\n\\frac{3a^4b}{5x^2yz}$.", "markdown": "$\\displaystyle \\frac{18a^6b^2c}{35x^3y^3z}\\div \\frac{3a^4b}{5x^2yz}$.", "answer_latex": [ "$\\displaystyle \\frac{6a^2bc}{7xy^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{6a^2bc}{7xy^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(18*a**6*b**2*c/(35*x**3*y**3*z))/(3*a**4*b/(5*x**2*y*z))", "answer_expr": "6*a**2*b*c/(7*x*y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 6*a**2*b*c/(7*d*e**2)" ], "shape": [ "identity: N*a**N*b*c*e**N/d" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/10", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 10", "problem_latex": "$\\displaystyle\n\\frac{x^2-y^2}{x^2+y^2}\\times\\frac{x^4-y^4}{(x-y)^3}\\div\n\\frac{(x+y)^2}{x-y}$.", "markdown": "$\\displaystyle \\frac{x^2-y^2}{x^2+y^2}\\times\\frac{x^4-y^4}{(x-y)^3}\\div \\frac{(x+y)^2}{x-y}$.", "answer_latex": [ "$1$." ], "answer_markdown": [ "$1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x**2-y**2)/(x**2+y**2))*((x**4-y**4)/(x-y)**3)/((x+y)**2/(x-y))", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - b**2)*(a**4 - b**4)/((a - b)**2*(a + b)**2*(a**2 + b**2))" ], "shape": [ "identity: (a - b)**N*(a + b)**N*(a**N - b**N)**2/(a**N + b**N)" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-49/9" ], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/11", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 11", "problem_latex": "$\\displaystyle \\frac{a^2-2a-8}{a^2+2a-15}\\div\n\\frac{a^2+5a+6}{a^2-4a+3}\\div \\frac{a^2-5a+4}{a^2+8a+15}$.", "markdown": "$\\displaystyle \\frac{a^2-2a-8}{a^2+2a-15}\\div \\frac{a^2+5a+6}{a^2-4a+3}\\div \\frac{a^2-5a+4}{a^2+8a+15}$.", "answer_latex": [ "$1$." ], "answer_markdown": [ "$1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a**2-2*a-8)/(a**2+2*a-15))/((a**2+5*a+6)/(a**2-4*a+3))/((a**2-5*a+4)/(a**2+8*a+15))", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - 4*a + 3)*(a**2 - 2*a - 8)*(a**2 + 8*a + 15)/((a**2 - 5*a + 4)*(a**2 + 2*a - 15)*(a**2 + 5*a + 6))" ], "shape": [ "identity: 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/12", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 12", "problem_latex": "$\\displaystyle \\frac{x^2-9x+20}{x^2-5x-14}\\div\n\\frac{x^2-7x+12}{x^2-x-42}\\times\\frac{x^2-x-6}{x^2+11x+30}$.", "markdown": "$\\displaystyle \\frac{x^2-9x+20}{x^2-5x-14}\\div \\frac{x^2-7x+12}{x^2-x-42}\\times\\frac{x^2-x-6}{x^2+11x+30}$.", "answer_latex": [ "$\\displaystyle \\frac{x-5}{x+5}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x-5}{x+5}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x**2-9*x+20)/(x**2-5*x-14))/((x**2-7*x+12)/(x**2-x-42))*((x**2-x-6)/(x**2+11*x+30))", "answer_expr": "(x-5)/(x+5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - 9*a + 20)*(a**2 - a - 42)*(a**2 - a - 6)/((a**2 - 7*a + 12)*(a**2 - 5*a - 14)*(a**2 + 11*a + 30))" ], "shape": [ "identity: (N - a + a**N)**2/(N*a + N + a**N)**2" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/13", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 13", "problem_latex": "$\\displaystyle \\frac{a^2 - a - 2}{a^2 + 2a - 8} \\times\n\\frac{a^2 + 5a}{ab + b} \\div \\frac{a^2 - 25}{a^2 - a - 20}$.", "markdown": "$\\displaystyle \\frac{a^2 - a - 2}{a^2 + 2a - 8} \\times \\frac{a^2 + 5a}{ab + b} \\div \\frac{a^2 - 25}{a^2 - a - 20}$.", "answer_latex": [ "$\\displaystyle \\frac{a}{b}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a}{b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a**2-a-2)/(a**2+2*a-8))*((a**2+5*a)/(a*b+b))/((a**2-25)/(a**2-a-20))", "answer_expr": "a/b" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 + 5*a)*(a**2 - a - 20)*(a**2 - a - 2)/((a**2 - 25)*(a*b + b)*(a**2 + 2*a - 8))" ], "shape": [ "identity: (N*a + a**N)*(N - a + a**N)**2/((N + a**N)*(a*b + b)*(N*a + N + a**N))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/14", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 14", "problem_latex": "$\\displaystyle \\frac{m - 2}{2m - 14} \\times \\frac{m^2 - 5m -\n14}{2m^2 + 4m} \\times \\frac{4m^2}{m^2 - 4} \\div \\frac{2mn -\n14n}{m^2 - 5m - 14}$.", "markdown": "$\\displaystyle \\frac{m - 2}{2m - 14} \\times \\frac{m^2 - 5m - 14}{2m^2 + 4m} \\times \\frac{4m^2}{m^2 - 4} \\div \\frac{2mn - 14n}{m^2 - 5m - 14}$.", "answer_latex": [ "$\\displaystyle \\frac{m}{2n}$." ], "answer_markdown": [ "$\\displaystyle \\frac{m}{2n}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((m-2)/(2*m-14))*((m**2-5*m-14)/(2*m**2+4*m))*((4*m**2)/(m**2-4))/((2*m*n-14*n)/(m**2-5*m-14))", "answer_expr": "m/(2*n)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*a**2*(a - 2)*(a**2 - 5*a - 14)**2/((2*a - 14)*(a**2 - 4)*(2*a**2 + 4*a)*(2*a*b - 14*b))" ], "shape": [ "identity: N*a**N*(N + a)*(N*a + N + a**N)**N/((N + a**N)*(N*a + N)*(N*a + N*a**N)*(N*a*b + N*b))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/15", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 15", "problem_latex": "$ \\displaystyle \\left(\\frac{a+1}{a-1} + 1\\right)\n\\left(\\frac{a-1}{a+1} + 1\\right)\n \\div\n \\left(\\frac{a+1}{a-1} - 1\\right) \\left(1 - \\frac{a-1}{a+1}\\right)$.", "markdown": "$ \\displaystyle \\left(\\frac{a+1}{a-1} + 1\\right) \\left(\\frac{a-1}{a+1} + 1\\right) \\div \\left(\\frac{a+1}{a-1} - 1\\right) \\left(1 - \\frac{a-1}{a+1}\\right)$.", "answer_latex": [ "$a^2$." ], "answer_markdown": [ "$a^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a+1)/(a-1)+1)*((a-1)/(a+1)+1)/(((a+1)/(a-1)-1)*(1-(a-1)/(a+1)))", "answer_expr": "a**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (1 + (a + 1)/(a - 1))*((a - 1)/(a + 1) + 1)/((-1 + (a + 1)/(a - 1))*(-(a - 1)/(a + 1) + 1))" ], "shape": [ "identity: (1 + (a + 1)/(a - 1))*((a - 1)/(a + 1) + 1)/((-1 + (a + 1)/(a - 1))*(-(a - 1)/(a + 1) + 1))" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/16", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 16", "problem_latex": "$\\displaystyle \\left(1 + \\frac{x}{1-x}\\right) \\left(1 -\n\\frac{x}{1+x}\\right) \\div \\left(1 + \\frac{1+x}{1-x}\\right) \\left(1\n- \\frac{1-x}{1+x}\\right)$.", "markdown": "$\\displaystyle \\left(1 + \\frac{x}{1-x}\\right) \\left(1 - \\frac{x}{1+x}\\right) \\div \\left(1 + \\frac{1+x}{1-x}\\right) \\left(1 - \\frac{1-x}{1+x}\\right)$.", "answer_latex": [ "$\\displaystyle \\frac{1}{4x}$." ], "answer_markdown": [ "$\\displaystyle \\frac{1}{4x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((1+x/(1-x))*(1-x/(1+x)))/((1+(1+x)/(1-x))*(1-(1-x)/(1+x)))", "answer_expr": "1/(4*x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/(-a + 1) + 1)*(-a/(a + 1) + 1)/((1 + (a + 1)/(-a + 1))*(-(-a + 1)/(a + 1) + 1))" ], "shape": [ "identity: (a/(-a + 1) + 1)*(-a/(a + 1) + 1)/((1 + (a + 1)/(-a + 1))*(-(-a + 1)/(a + 1) + 1))" ], "same_problem_in": [], "needs": [ "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/17", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 17", "problem_latex": "How much times 7 is 21?", "markdown": "How much times 7 is 21?", "answer_latex": [ "$3$." ], "answer_markdown": [ "$3$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(7*x, 21)", "answer_expr": "{x: 3}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(7*x, 21)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "21 ENTER 7 ÷" ], "constants": [ { "value": "21", "source": "the 21 in 'How much times 7 is 21?'" }, { "value": "7", "source": "the 7 in 'How much times 7 is 21?'" } ], "calculator_value": "+3E+0", "printed_value": "3", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/18", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 18", "problem_latex": "How much times $\\frac{3}{14}$ is $\\frac{6}{7}$?", "markdown": "How much times $\\frac{3}{14}$ is $\\frac{6}{7}$?", "answer_latex": [ "$4$." ], "answer_markdown": [ "$4$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x*Rational(3, 14), Rational(6, 7))", "answer_expr": "{x: 4}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*x/14, 6/7)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "6 ENTER 14 ×", "7 ÷", "3 ÷" ], "calculator_value": "+4E+0", "printed_value": "4", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/19", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 19", "problem_latex": "How much times $\\displaystyle \\frac{c}{d}$ is $\\displaystyle\n\\frac{x}{4}$?", "markdown": "How much times $\\displaystyle \\frac{c}{d}$ is $\\displaystyle \\frac{x}{4}$?", "answer_latex": [ "$\\displaystyle \\frac{dx}{4c}$." ], "answer_markdown": [ "$\\displaystyle \\frac{dx}{4c}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(y*c/d, x/4)", "answer_expr": "{y: d*x/(4*c)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a*x/b, c/4)" ], "shape": [ "solve: Eq(a*x/b, N*c)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/2", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 2", "problem_latex": "$\\displaystyle \\frac{7axy^2}{8m^2n}\\div\n\\frac{2xz^3}{3ab^2m}$.", "markdown": "$\\displaystyle \\frac{7axy^2}{8m^2n}\\div \\frac{2xz^3}{3ab^2m}$.", "answer_latex": [ "$\\displaystyle\n\\frac{21ab^2y^2}{16mnz^3}$." ], "answer_markdown": [ "$\\displaystyle \\frac{21ab^2y^2}{16mnz^3}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "94.101215915020349404", "33.458210103118346455" ], "problem_expr": "(7*a*x*y**2/(8*m**2*n))/(2*x*z**3/(3*a*b**2*m))", "answer_expr": "21*a*b**2*y**2/(16*m*n*z**3)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: 21*a**2*b**2*e**2/(16*c*d*f**3)" ], "shape": [ "identity: N*a**N*b**N*e**N*f**N/(c*d)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/20", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 20", "problem_latex": "How much times $\\displaystyle \\frac{5bz}{7mx^3}$ is\n$\\displaystyle \\frac{3xy^2z}{4amn^2}$?", "markdown": "How much times $\\displaystyle \\frac{5bz}{7mx^3}$ is $\\displaystyle \\frac{3xy^2z}{4amn^2}$?", "answer_latex": [ "$\\displaystyle \\frac{21x^4y^2}{20abn^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{21x^4y^2}{20abn^2}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(w*5*b*z/(7*m*x**3), 3*x*y**2*z/(4*a*m*n**2))", "answer_expr": "{w: 21*x**4*y**2/(20*a*b*n**2)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(5*b*g*x/(7*c*e**3), 3*e*f**2*g/(4*a*c*d**2))" ], "shape": [ "solve: Eq(N*b*e**N*g*x/c, N*d**N*e*f**N*g/(a*c))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/3", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 3", "problem_latex": "$\\displaystyle \\frac{4x^2y^3z^4}{3a^2b^3c^4}\\div\n\\frac{3x^4y^3z^2}{4a^4b^3c^2}$.", "markdown": "$\\displaystyle \\frac{4x^2y^3z^4}{3a^2b^3c^4}\\div \\frac{3x^4y^3z^2}{4a^4b^3c^2}$.", "answer_latex": [ "$\\displaystyle\n\\frac{16a^2z^2}{9c^2x^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{16a^2z^2}{9c^2x^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*x**2*y**3*z**4/(3*a**2*b**3*c**4))/(3*x**4*y**3*z**2/(4*a**4*b**3*c**2))", "answer_expr": "16*a**2*z**2/(9*c**2*x**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 16*a**2*d**2/(9*b**2*c**2)" ], "shape": [ "identity: N*a**N*b**N*c**N*d**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/4", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 4", "problem_latex": "$\\displaystyle \\frac{2am^3n^2}{3x^3yz^2}\\div\n\\frac{3a^3mn^2}{2x^3yz^2}$.", "markdown": "$\\displaystyle \\frac{2am^3n^2}{3x^3yz^2}\\div \\frac{3a^3mn^2}{2x^3yz^2}$.", "answer_latex": [ "$\\displaystyle\n\\frac{4m^2y^2}{9a^2x^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{4m^2y^2}{9a^2x^2}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "2.3008156342739298828", "15.957941662429840444" ], "problem_expr": "(2*a*m**3*n**2/(3*x**3*y*z**2))/(3*a**3*m*n**2/(2*x**3*y*z**2))", "answer_expr": "4*m**2*y**2/(9*a**2*x**2)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: 4*b**2/(9*a**2)" ], "shape": [ "identity: N*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/5", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 5", "problem_latex": "$\\displaystyle \\frac{x^2-7x+10}{x^2}\\div\n\\frac{x^2-4}{x^2+5x}$.", "markdown": "$\\displaystyle \\frac{x^2-7x+10}{x^2}\\div \\frac{x^2-4}{x^2+5x}$.", "answer_latex": [ "$\\displaystyle \\frac{x^2-25}{x^2+2x}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2-25}{x^2+2x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x**2-7*x+10)/x**2)/((x**2-4)/(x**2+5*x))", "answer_expr": "(x**2-25)/(x**2+2*x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 + 5*a)*(a**2 - 7*a + 10)/(a**2*(a**2 - 4))" ], "shape": [ "identity: a**N*(N*a + a**N)*(N*a + N + a**N)/(N + a**N)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/6", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 6", "problem_latex": "$\\displaystyle \\frac{x-6}{x-3}\\div \\frac{x^2-3x}{x^2-5x}$.", "markdown": "$\\displaystyle \\frac{x-6}{x-3}\\div \\frac{x^2-3x}{x^2-5x}$.", "answer_latex": [ "$\\displaystyle \\frac{(x-5)(x-6)}{(x-3)(x-3)}$." ], "answer_markdown": [ "$\\displaystyle \\frac{(x-5)(x-6)}{(x-3)(x-3)}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x-6)/(x-3))/((x**2-3*x)/(x**2-5*x))", "answer_expr": "(x-5)*(x-6)/((x-3)*(x-3))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a - 6)*(a**2 - 5*a)/((a - 3)*(a**2 - 3*a))" ], "shape": [ "identity: 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/7", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 7", "problem_latex": "$\\displaystyle \\frac{x-2}{x-7}\\div\n\\frac{x^2-9x+20}{x^2-10x+21}\\div \\frac{x^2-4x+3}{x^2-5x+4}$.", "markdown": "$\\displaystyle \\frac{x-2}{x-7}\\div \\frac{x^2-9x+20}{x^2-10x+21}\\div \\frac{x^2-4x+3}{x^2-5x+4}$.", "answer_latex": [ "$\\displaystyle \\frac{x-2}{x-5}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x-2}{x-5}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((x-2)/(x-7))/((x**2-9*x+20)/(x**2-10*x+21))/((x**2-4*x+3)/(x**2-5*x+4))", "answer_expr": "(x-2)/(x-5)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a - 2)*(a**2 - 10*a + 21)*(a**2 - 5*a + 4)/((a - 7)*(a**2 - 9*a + 20)*(a**2 - 4*a + 3))" ], "shape": [ "identity: 1" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/8", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 8", "problem_latex": "$\\displaystyle \\frac{a^2-7a}{a-8}\\div\n\\frac{a^2+10a+24}{a^2-14a+48}\\div \\frac{a^2-7a+6}{a^2+3a-4}$.", "markdown": "$\\displaystyle \\frac{a^2-7a}{a-8}\\div \\frac{a^2+10a+24}{a^2-14a+48}\\div \\frac{a^2-7a+6}{a^2+3a-4}$.", "answer_latex": [ "$\\displaystyle \\frac{a(a-7)}{a+6}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a(a-7)}{a+6}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a**2-7*a)/(a-8))/((a**2+10*a+24)/(a**2-14*a+48))/((a**2-7*a+6)/(a**2+3*a-4))", "answer_expr": "a*(a-7)/(a+6)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - 7*a)*(a**2 - 14*a + 48)*(a**2 + 3*a - 4)/((a - 8)*(a**2 - 7*a + 6)*(a**2 + 10*a + 24))" ], "shape": [ "identity: (N*a + a**N)/(N + a)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-49/9", "set": "boyden-first-book-in-algebra-1895/ex-49", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 49, problem 9", "problem_latex": "$\\displaystyle \\frac{a+b}{(a-b)^2}div\n\\frac{a^2+b^2}{a^2-b^2}\\times\\frac{a^4-b^4}{(a+b)^3}$.", "markdown": "$\\displaystyle \\frac{a+b}{(a-b)^2}div \\frac{a^2+b^2}{a^2-b^2}\\times\\frac{a^4-b^4}{(a+b)^3}$.", "answer_latex": [ "$1$." ], "answer_markdown": [ "$1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a+b)/(a-b)**2)/((a**2+b**2)/(a**2-b**2))*((a**4-b**4)/(a+b)**3)", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - b**2)*(a**4 - b**4)/((a - b)**2*(a + b)**2*(a**2 + b**2))" ], "shape": [ "identity: (a - b)**N*(a + b)**N*(a**N - b**N)**2/(a**N + b**N)" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-49/10" ], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/1", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 1", "problem_latex": "Mary bought some blue ribbon at 7 cents a yard, and three\ntimes as much white ribbon at 5 cents a yard, paying \\$1.10 for\nthe whole. How many yards of each kind did she buy?", "markdown": "Mary bought some blue ribbon at 7 cents a yard, and three times as much white ribbon at 5 cents a yard, paying $1.10 for the whole. How many yards of each kind did she buy?", "answer_latex": [ "Blue, 5 yds.; white, 15 yds." ], "answer_markdown": [ "Blue, 5 yds.; white, 15 yds." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{b: 5, w: 15}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 3*x), Eq(5*a + 7*x, 110))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/10", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 10", "problem_latex": "I sold three houses, of equal value, and a barn for\n\\$16,800. If the barn brought \\$1200 less than a house, what was\nthe price of each?", "markdown": "I sold three houses, of equal value, and a barn for $16,800. If the barn brought $1200 less than a house, what was the price of each?", "answer_latex": [ "House, \\$4500; barn, \\$3300." ], "answer_markdown": [ "House, $4500; barn, $3300." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{h: 4500, b: 3300}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x - 1200), Eq(a + 3*x, 16800))" ], "shape": [ "solve: (Eq(a, N + x), Eq(N*x + a, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/11", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 11", "problem_latex": "Five lots, two of one size and three of another, aggregate\n63,000 feet. Each of the two is 1500 feet larger than each of the\nthree. What is the size of the lots?", "markdown": "Five lots, two of one size and three of another, aggregate 63,000 feet. Each of the two is 1500 feet larger than each of the three. What is the size of the lots?", "answer_latex": [ "12,000; 13,500 ft." ], "answer_markdown": [ "12,000; 13,500 ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 13500, y: 12000}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, a + 1500), Eq(3*a + 2*x, 63000))" ], "shape": [ "solve: (Eq(x, N + a), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/12", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 12", "problem_latex": "Four pumps, two of one size and two of another, can pump 106\ngallons per minute. If the smaller pumps 5 gallons less per minute\nthan the larger, how much does each pump per minute?", "markdown": "Four pumps, two of one size and two of another, can pump 106 gallons per minute. If the smaller pumps 5 gallons less per minute than the larger, how much does each pump per minute?", "answer_latex": [ "29 gal.; 24 gal." ], "answer_markdown": [ "29 gal.; 24 gal." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{L: 29, S: 24}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x - 5), Eq(2*a + 2*x, 106))" ], "shape": [ "solve: (Eq(a, N + x), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/13", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 13", "problem_latex": "Johnson and May enter into a partnership in which Johnson's\ninterest is four times as great as May's. Johnson's profit was\n\\$4500 more than May's profit. What was the profit of each?", "markdown": "Johnson and May enter into a partnership in which Johnson’s interest is four times as great as May’s. Johnson’s profit was $4500 more than May’s profit. What was the profit of each?", "answer_latex": [ "Johnson, \\$6000; May, \\$1500." ], "answer_markdown": [ "Johnson, $6000; May, $1500." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{J: 6000, M: 1500}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 4*a), Eq(-a + x, 4500))" ], "shape": [ "solve: (Eq(x, N*a), Eq(-a + x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/14", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 14", "problem_latex": "Three electric cars are carrying 79 persons. In the first\ncar there are 17 more people than in the second and 15 less than\nin the third. How many persons in each car?", "markdown": "Three electric cars are carrying 79 persons. In the first car there are 17 more people than in the second and 15 less than in the third. How many persons in each car?", "answer_latex": [ "27; 10; 42." ], "answer_markdown": [ "27; 10; 42." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{F: 27, S: 10, T: 42}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, a + 17), Eq(x, b - 15), Eq(a + b + x, 79))" ], "shape": [ "solve: (Eq(x, N + a), Eq(x, N + b), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/15", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 15", "problem_latex": "Divide 71 into three parts so that the second part shall be\n5 more than four times the first part, and the third part three\ntimes the second.", "markdown": "Divide 71 into three parts so that the second part shall be 5 more than four times the first part, and the third part three times the second.", "answer_latex": [ "3; 17; 51." ], "answer_markdown": [ "3; 17; 51." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 3, b: 17, c: 51}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 4*x + 5), Eq(b, 3*a), Eq(a + b + x, 71))" ], "shape": [ "solve: (Eq(a, N*x + N), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/16", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 16", "problem_latex": "I bought a certain number of barrels of apples and three\ntimes as many boxes of oranges for \\$33. I paid \\$2 a barrel for\nthe apples, and \\$3 a box for the oranges. How many of each did I\nbuy?", "markdown": "I bought a certain number of barrels of apples and three times as many boxes of oranges for $33. I paid $2 a barrel for the apples, and $3 a box for the oranges. How many of each did I buy?", "answer_latex": [ "3 bbls.; 9 boxes." ], "answer_markdown": [ "3 bbls.; 9 boxes." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{b: 3, o: 9}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 3*x), Eq(3*a + 2*x, 33))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/17", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 17", "problem_latex": "Divide the number 288 into three parts, so that the third\npart shall be twice the second, and the second five times the\nfirst.", "markdown": "Divide the number 288 into three parts, so that the third part shall be twice the second, and the second five times the first.", "answer_latex": [ "18; 90; 180." ], "answer_markdown": [ "18; 90; 180." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{f: 18, s: 90, t: 180}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 5*x), Eq(b, 2*a), Eq(a + b + x, 288))" ], "shape": [ "solve: (Eq(a, N*x), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/18", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 18", "problem_latex": "Find two numbers whose sum is 216 and whose difference is\n48.", "markdown": "Find two numbers whose sum is 216 and whose difference is 48.", "answer_latex": [ "84; 132." ], "answer_markdown": [ "84; 132." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 132, y: 84}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(-a + x, 48), Eq(a + x, 216))" ], "shape": [ "solve: (Eq(-a + x, N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/2", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 2", "problem_latex": "Twice a certain number added to five times the double of\nthat number gives for the sum 36. What is the number?", "markdown": "Twice a certain number added to five times the double of that number gives for the sum 36. What is the number?", "answer_latex": [ "3." ], "answer_markdown": [ "3." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(12*x, 36)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": "X=3", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "2 ENTER 5 ENTER 2 × +", "36 x↔y ÷" ], "constants": [ { "value": "2", "source": "the 'twice' in 'Twice a certain number' (2x)" }, { "value": "5", "source": "the 'five times' in 'five times the double of that number'" }, { "value": "2", "source": "the 'double' in 'the double of that number' (2x); the working is 2x + 5(2x) = 12x = 36, so x = 36 ÷ 12" } ], "calculator_value": "+3E+0", "printed_value": "3", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/3", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 3", "problem_latex": "Mr. James Cobb walked a certain length of time at the rate\nof 4 miles an hour, and then rode four times as long at the rate\nof 10 miles an hour, to finish a journey of 88 miles. How long did\nhe walk and how long did he ride?", "markdown": "Mr. James Cobb walked a certain length of time at the rate of 4 miles an hour, and then rode four times as long at the rate of 10 miles an hour, to finish a journey of 88 miles. How long did he walk and how long did he ride?", "answer_latex": [ "Walked 2 hrs.; rode 8 hrs." ], "answer_markdown": [ "Walked 2 hrs.; rode 8 hrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{w: 2, r: 8}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 4*x), Eq(10*a + 4*x, 88))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/4", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 4", "problem_latex": "A man bought 3 books and 2 lamps for \\$14. The price of a\nlamp was twice that of a book. What was the cost of each?", "markdown": "A man bought 3 books and 2 lamps for $14. The price of a lamp was twice that of a book. What was the cost of each?", "answer_latex": [ "Book, \\$2; lamp, \\$4." ], "answer_markdown": [ "Book, $2; lamp, $4." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{b: 2, l: 4}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(2*a + 3*x, 14))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/5", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 5", "problem_latex": "George bought an equal number of apples, oranges, and\nbananas for \\$1.08; each apple cost 2 cents, each orange 4 cents,\nand each banana 3 cents. How many of each did he buy?", "markdown": "George bought an equal number of apples, oranges, and bananas for $1.08; each apple cost 2 cents, each orange 4 cents, and each banana 3 cents. How many of each did he buy?", "answer_latex": [ "12." ], "answer_markdown": [ "12." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "12" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(9*x, 108)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": "X=12", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "108 ENTER 2 ENTER 4 + 3 +", "÷" ], "calculator_value": "+12E+0", "printed_value": "12", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/6", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 6", "problem_latex": "I bought some 2-cent stamps and twice as many 5-cent stamps,\npaying for the whole \\$1.44. How many stamps of each kind did I\nbuy?", "markdown": "I bought some 2-cent stamps and twice as many 5-cent stamps, paying for the whole $1.44. How many stamps of each kind did I buy?", "answer_latex": [ "12 twos; 24 fives." ], "answer_markdown": [ "12 twos; 24 fives." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{s: 12, f: 24}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(5*a + 2*x, 144))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/7", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 7", "problem_latex": "I bought 2 pounds of coffee and 1 pound of tea for \\$1.31;\nthe price of a pound of tea was equal to that of 2 pounds of\ncoffee and 3 cents more. What was the cost of each per pound?", "markdown": "I bought 2 pounds of coffee and 1 pound of tea for $1.31; the price of a pound of tea was equal to that of 2 pounds of coffee and 3 cents more. What was the cost of each per pound?", "answer_latex": [ "Tea, 67; coffee, 32." ], "answer_markdown": [ "Tea, 67; coffee, 32." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{c: 32, t: 67}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x + 3), Eq(a + 2*x, 131))" ], "shape": [ "solve: (Eq(a, N*x + N), Eq(N*x + a, N))" ], "same_problem_in": [], "needs": [ "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/8", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 8", "problem_latex": "A lady bought 2 pounds of crackers and 3 pounds of\ngingersnaps for \\$1.11. If a pound of gingersnaps cost 7 cents\nmore than a pound of crackers, what was the price of each?", "markdown": "A lady bought 2 pounds of crackers and 3 pounds of gingersnaps for $1.11. If a pound of gingersnaps cost 7 cents more than a pound of crackers, what was the price of each?", "answer_latex": [ "Crackers,18 gingersnaps, 25" ], "answer_markdown": [ "Crackers,18 gingersnaps, 25" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{k: 18, g: 25}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 7), Eq(3*a + 2*x, 111))" ], "shape": [ "solve: (Eq(a, N + x), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-5/9", "set": "boyden-first-book-in-algebra-1895/ex-5", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 5, problem 9", "problem_latex": "A man bought 3 lamps and 2 vases for \\$6. If a vase cost 50\ncents less than 2 lamps, what was the price of each?", "markdown": "A man bought 3 lamps and 2 vases for $6. If a vase cost 50 cents less than 2 lamps, what was the price of each?", "answer_latex": [ "Lamp, \\$1; vase, \\$1.50." ], "answer_markdown": [ "Lamp, $1; vase, $1.50." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{l: 1, v: Rational(3, 2)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x - 1/2), Eq(2*a + 3*x, 6))" ], "shape": [ "solve: (Eq(a, N*x + N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/1", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 1", "problem_latex": "$\\displaystyle \\left(\\frac{2x^2}{ab^3}\\right)^2$.", "markdown": "$\\displaystyle \\left(\\frac{2x^2}{ab^3}\\right)^2$.", "answer_latex": [ "$\\displaystyle \\frac{4x^4}{a^2b^6}$." ], "answer_markdown": [ "$\\displaystyle \\frac{4x^4}{a^2b^6}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*x**2/(a*b**3))**2", "answer_expr": "4*x**4/(a**2*b**6)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*c**4/(a**2*b**6)" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/10", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 10", "problem_latex": "$\\displaystyle \\sqrt{ \\frac{ 36m^2n^8 }{ 121a^4b^6 } }$.", "markdown": "$\\displaystyle \\sqrt{ \\frac{ 36m^2n^8 }{ 121a^4b^6 } }$.", "answer_latex": [ "$\\displaystyle \\frac{6mn^4}{11a^2b^3}$." ], "answer_markdown": [ "$\\displaystyle \\frac{6mn^4}{11a^2b^3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "sqrt(36*m**2*n**8/(121*a**4*b**6))", "answer_expr": "6*m*n**4/(11*a**2*b**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 6*d**4*sqrt(1/(a**4*b**6))*Abs(c)/11" ], "shape": [ "identity: N*d**N*(a**N*b**N)**N*Abs(c)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/11", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 11", "problem_latex": "$\\displaystyle \\sqrt[4]{ \\frac{ 256x^4y^8 }{ 81a^4b^{12} }\n}$.", "markdown": "$\\displaystyle \\sqrt[4]{ \\frac{ 256x^4y^8 }{ 81a^4b^{12} } }$.", "answer_latex": [ "$\\displaystyle \\frac{4xy^2}{3ab^3}$." ], "answer_markdown": [ "$\\displaystyle \\frac{4xy^2}{3ab^3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(256*x**4*y**8/(81*a**4*b**12))**Rational(1,4)", "answer_expr": "4*x*y**2/(3*a*b**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 4*d**2*(1/(a**4*b**12))**(1/4)*Abs(c)/3" ], "shape": [ "identity: N*d**N*(a**N*b**N)**N*Abs(c)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/12", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 12", "problem_latex": "$\\displaystyle \\sqrt[5]{ - \\frac{32x^5y^10}{ 243m^10n^15 }\n}$.", "markdown": "$\\displaystyle \\sqrt[5]{ - \\frac{32x^5y^10}{ 243m^10n^15 } }$.", "answer_latex": [ "$\\displaystyle -\\frac{2xy^2}{3m^2n^3}$." ], "answer_markdown": [ "$\\displaystyle -\\frac{2xy^2}{3m^2n^3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "-(32*x**5*y**10/(243*m**10*n**15))**Rational(1,5)", "answer_expr": "-2*x*y**2/(3*m**2*n**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -2*d**2*(c**5/(a**10*b**15))**(1/5)/3" ], "shape": [ "identity: N*d**N*(a**N*b**N*c**N)**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/13", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 13", "problem_latex": "$\\displaystyle \\sqrt[3]{ -\\frac{ 27x^6(a-b)^9 }{ 64a^6b^{12}\n} }$.", "markdown": "$\\displaystyle \\sqrt[3]{ -\\frac{ 27x^6(a-b)^9 }{ 64a^6b^{12} } }$.", "answer_latex": [ "$\\displaystyle -\\frac{3x^2\\left(a-b\\right)^3}{4a^2b^4}$." ], "answer_markdown": [ "$\\displaystyle -\\frac{3x^2\\left(a-b\\right)^3}{4a^2b^4}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "-(27*x**6*(a-b)**9/(64*a**6*b**12))**Rational(1,3)", "answer_expr": "-3*x**2*(a-b)**3/(4*a**2*b**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -3*c**2*((a - b)**9/(a**6*b**12))**(1/3)/4" ], "shape": [ "identity: N*c**N*(a**N*b**N*(a - b)**N)**N" ], "same_problem_in": [], "needs": [ "cas.root.poly", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/14", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 14", "problem_latex": "$\\displaystyle \\sqrt{ \\frac{ 4x^2 + 12xy + 9y^2 }{ 16x^4y^8\n} }$.", "markdown": "$\\displaystyle \\sqrt{ \\frac{ 4x^2 + 12xy + 9y^2 }{ 16x^4y^8 } }$.", "answer_latex": [ "$\\displaystyle \\frac{2x+3y}{4x^2y^4}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2x+3y}{4x^2y^4}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "sqrt((4*x**2 + 12*x*y + 9*y**2)/(16*x**4*y**8))", "answer_expr": "(2*x+3*y)/(4*x**2*y**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: sqrt((4*a**2 + 12*a*b + 9*b**2)/(a**4*b**8))/4" ], "shape": [ "identity: N*(a**N*b**N*(N*a*b + N*a**N + N*b**N))**N" ], "same_problem_in": [], "needs": [ "cas.root.poly", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/15", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 15", "problem_latex": "$\\displaystyle \\sqrt{ \\frac{ 8x^2(x+y)^5 }{ 50y^4(x+y) } }$.", "markdown": "$\\displaystyle \\sqrt{ \\frac{ 8x^2(x+y)^5 }{ 50y^4(x+y) } }$.", "answer_latex": [ "$\\displaystyle \\frac{2x\\left(x+y\\right)^2}{5y^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2x\\left(x+y\\right)^2}{5y^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "sqrt(8*x**2*(x+y)**5/(50*y**4*(x+y)))", "answer_expr": "2*x*(x+y)**2/(5*y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*(a + b)**2*Abs(a)/(5*b**2)" ], "shape": [ "identity: N*b**N*(a + b)**N*Abs(a)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/16", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 16", "problem_latex": "$\\displaystyle \\sqrt[3]{ -\\frac{ 81a^3(a-b)^7 }{ 24b^9(a-b)\n} }$.", "markdown": "$\\displaystyle \\sqrt[3]{ -\\frac{ 81a^3(a-b)^7 }{ 24b^9(a-b) } }$.", "answer_latex": [ "$\\displaystyle -\\frac{3a \\left(a-b \\right)^2}{2b^3}$." ], "answer_markdown": [ "$\\displaystyle -\\frac{3a \\left(a-b \\right)^2}{2b^3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "-(81*a**3*(a-b)**7/(24*b**9*(a-b)))**Rational(1,3)", "answer_expr": "-3*a*(a-b)**2/(2*b**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -3*(a**3/b**9)**(1/3)*(a - b)**2/2" ], "shape": [ "identity: N*(a**N*b**N)**N*(a - b)**N" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.root.poly", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/17", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 17", "problem_latex": "$\\displaystyle \\left( \\frac{x}{y} + \\frac{a}{b} \\right)\n \\left( \\frac{x}{y} - \\frac{a}{b} \\right)$.", "markdown": "$\\displaystyle \\left( \\frac{x}{y} + \\frac{a}{b} \\right) \\left( \\frac{x}{y} - \\frac{a}{b} \\right)$.", "answer_latex": [ "$\\displaystyle \\frac{x^2}{y^2}-\\frac{a^2}{b^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2}{y^2}-\\frac{a^2}{b^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x/y + a/b)*(x/y - a/b)", "answer_expr": "x**2/y**2 - a**2/b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a/b + c/d)*(a/b + c/d)" ], "shape": [ "identity: (-a/b + c/d)*(a/b + c/d)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/18", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 18", "problem_latex": "$\\displaystyle \\left(\\frac{a}{b} - \\frac{c}{d} \\right)\n \\left( \\frac{a}{b} + \\frac{c}{d} \\right)$.", "markdown": "$\\displaystyle \\left(\\frac{a}{b} - \\frac{c}{d} \\right) \\left( \\frac{a}{b} + \\frac{c}{d} \\right)$.", "answer_latex": [ "$\\displaystyle \\frac{a^2}{b^2}-\\frac{c^2}{d^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a^2}{b^2}-\\frac{c^2}{d^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a/b - c/d)*(a/b + c/d)", "answer_expr": "a**2/b**2 - c**2/d**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/b - c/d)*(a/b + c/d)" ], "shape": [ "identity: (a/b - c/d)*(a/b + c/d)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/19", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 19", "problem_latex": "$\\displaystyle 3ab\\left(\\frac{2x}{ab}+ \\frac{x^2}{2mn}-\n\\frac{ax}{3mb}\\right)$.", "markdown": "$\\displaystyle 3ab\\left(\\frac{2x}{ab}+ \\frac{x^2}{2mn}- \\frac{ax}{3mb}\\right)$.", "answer_latex": [ "$6x+\\frac{3abx^2y}{2mn}-\\frac{a^2x}{m}$." ], "answer_markdown": [ "$6x+\\frac{3abx^2y}{2mn}-\\frac{a^2x}{m}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "8.3273875963131946483", "10.115642703980744712" ], "problem_expr": "3*a*b*(2*x/(a*b) + x**2/(2*m*n) - a*x/(3*m*b))", "answer_expr": "6*x + 3*a*b*x**2*y/(2*m*n) - a**2*x/m" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: 3*a*b*(-a*e/(3*b*c) + e**2/(2*c*d) + 2*e/(a*b))" ], "shape": [ "identity: N*a*b*(N*a*e/(b*c) + N*e**N/(c*d) + N*e/(a*b))" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/2", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 2", "problem_latex": "$\\displaystyle \\left(\\frac{a^2b^3}{4y}\\right)^3$.", "markdown": "$\\displaystyle \\left(\\frac{a^2b^3}{4y}\\right)^3$.", "answer_latex": [ "$\\displaystyle \\frac{a^3b^9}{64y^3}$" ], "answer_markdown": [ "$\\displaystyle \\frac{a^3b^9}{64y^3}$" ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "7949.5335942750843076", "1214.9511238841191801" ], "problem_expr": "(a**2*b**3/(4*y))**3", "answer_expr": "a**3*b**9/(64*y**3)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: a**6*b**9/(64*c**3)" ], "shape": [ "identity: N*a**N*b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/20", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 20", "problem_latex": "$\\displaystyle \\frac{x^2}{yz}\n \\left( \\frac{2x}{3} - \\frac{3y^2z}{2x} + \\frac{x^2y}{m^2z} \\right)$.", "markdown": "$\\displaystyle \\frac{x^2}{yz} \\left( \\frac{2x}{3} - \\frac{3y^2z}{2x} + \\frac{x^2y}{m^2z} \\right)$.", "answer_latex": [ "$\\displaystyle\n\\frac{2x^3}{3yz}-\\frac{3xy}{2}+\\frac{x^4}{m^2z^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2x^3}{3yz}-\\frac{3xy}{2}+\\frac{x^4}{m^2z^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2/(y*z)*(2*x/3 - 3*y**2*z/(2*x) + x**2*y/(m**2*z))", "answer_expr": "2*x**3/(3*y*z) - 3*x*y/2 + x**4/(m**2*z**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: b**2*(2*b/3 - 3*c**2*d/(2*b) + b**2*c/(a**2*d))/(c*d)" ], "shape": [ "identity: b**N*(N*b + N*c**N*d/b + a**N*b**N*c/d)/(c*d)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/21", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 21", "problem_latex": "$\\displaystyle \\left( \\frac{a^4}{b^4} + \\frac{c^4}{d^4}\n\\right)\n \\left( \\frac{a^2}{b^2} + \\frac{c^2}{d^2} \\right)\n \\left( \\frac{ a }{ b } + \\frac{ c }{ d } \\right)\n \\left( \\frac{ a }{ b } - \\frac{ c }{ d } \\right)$.", "markdown": "$\\displaystyle \\left( \\frac{a^4}{b^4} + \\frac{c^4}{d^4} \\right) \\left( \\frac{a^2}{b^2} + \\frac{c^2}{d^2} \\right) \\left( \\frac{ a }{ b } + \\frac{ c }{ d } \\right) \\left( \\frac{ a }{ b } - \\frac{ c }{ d } \\right)$.", "answer_latex": [ "$\\displaystyle \\frac{a^8}{b^8}-\\frac{c^8}{d^8}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a^8}{b^8}-\\frac{c^8}{d^8}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**4/b**4 + c**4/d**4)*(a**2/b**2 + c**2/d**2)*(a/b + c/d)*(a/b - c/d)", "answer_expr": "a**8/b**8 - c**8/d**8" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/b - c/d)*(a/b + c/d)*(a**2/b**2 + c**2/d**2)*(a**4/b**4 + c**4/d**4)" ], "shape": [ "identity: (a/b - c/d)*(a/b + c/d)*(a**N*b**N + c**N*d**N)**2" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/22", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 22", "problem_latex": "$\\displaystyle \\left( \\frac{x^2}{16} + \\frac{9y^2}{25m^1}\n\\right)\n \\left( \\frac{x}{4} + \\frac{3y}{5m} \\right)\n \\left( \\frac{x}{4} - \\frac{3y}{5m} \\right)$.", "markdown": "$\\displaystyle \\left( \\frac{x^2}{16} + \\frac{9y^2}{25m^1} \\right) \\left( \\frac{x}{4} + \\frac{3y}{5m} \\right) \\left( \\frac{x}{4} - \\frac{3y}{5m} \\right)$.", "answer_latex": [ "$\\displaystyle \\frac{x^4}{256} - \\frac{81y^4}{625m^4}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^4}{256} - \\frac{81y^4}{625m^4}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "0.009259199193788525608", "0.0075832811688408007822" ], "problem_expr": "(x**2/16 + 9*y**2/(25*m))*(x/4 + 3*y/(5*m))*(x/4 - 3*y/(5*m))", "answer_expr": "x**4/256 - 81*y**4/(625*m**4)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: (b/4 - 3*c/(5*a))*(b/4 + 3*c/(5*a))*(b**2/16 + 9*c**2/(25*a))" ], "shape": [ "identity: (N*b + N*c/a)**2*(N*b**N + N*c**N/a)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/23", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 23", "problem_latex": "$\\displaystyle \\left( \\frac{x}{y} + 1 \\right)\n \\left( \\frac{x^2}{y^2} - \\frac{x}{y} + 1 \\right)$.", "markdown": "$\\displaystyle \\left( \\frac{x}{y} + 1 \\right) \\left( \\frac{x^2}{y^2} - \\frac{x}{y} + 1 \\right)$.", "answer_latex": [ "$\\displaystyle \\frac{x^3}{y^3}+1$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^3}{y^3}+1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x/y + 1)*(x**2/y**2 - x/y + 1)", "answer_expr": "x**3/y**3 + 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/b + 1)*(a**2/b**2 - a/b + 1)" ], "shape": [ "identity: (a/b + 1)*(-a/b + a**N*b**N + 1)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/24", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 24", "problem_latex": "$\\displaystyle \\left( \\frac{a}{b} - 1 \\right)\n \\left( \\frac{a^2}{b^2} + \\frac{a}{b} + 1 \\right)$.", "markdown": "$\\displaystyle \\left( \\frac{a}{b} - 1 \\right) \\left( \\frac{a^2}{b^2} + \\frac{a}{b} + 1 \\right)$.", "answer_latex": [ "$\\displaystyle \\frac{a^3}{b^3}-1$." ], "answer_markdown": [ "$\\displaystyle \\frac{a^3}{b^3}-1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a/b - 1)*(a**2/b**2 + a/b + 1)", "answer_expr": "a**3/b**3 - 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/b - 1)*(a**2/b**2 + a/b + 1)" ], "shape": [ "identity: (a/b - 1)*(a/b + a**N*b**N + 1)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/25", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 25", "problem_latex": "$\\displaystyle \\left( \\frac{x}{y} - \\frac{3a^2}{2b}\n\\right)$.", "markdown": "$\\displaystyle \\left( \\frac{x}{y} - \\frac{3a^2}{2b} \\right)$.", "answer_latex": [ "$\\displaystyle \\frac{x^2}{y^2}-\\frac{3a^2x}{by}+\\frac{9a^4}{4b^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2}{y^2}-\\frac{3a^2x}{by}+\\frac{9a^4}{4b^2}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-4.3861363618499654153", "19.238192184742450749" ], "problem_expr": "x/y - 3*a**2/(2*b)", "answer_expr": "x**2/y**2 - 3*a**2*x/(b*y) + 9*a**4/(4*b**2)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: -3*a**2/(2*b) + c/d" ], "shape": [ "identity: N*a**N/b + c/d" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/26", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 26", "problem_latex": "$\\displaystyle \\left( \\frac{2y}{c^2} + \\frac{9}{2d}\n\\right)^2$.", "markdown": "$\\displaystyle \\left( \\frac{2y}{c^2} + \\frac{9}{2d} \\right)^2$.", "answer_latex": [ "$\\displaystyle \\frac{4y^2}{c^4}+\\frac{18y}{c^2d}+\\frac{81}{4d^2}$." ], "answer_markdown": [ "$\\displaystyle \\frac{4y^2}{c^4}+\\frac{18y}{c^2d}+\\frac{81}{4d^2}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*y/c**2 + 9/(2*d))**2", "answer_expr": "4*y**2/c**4 + 18*y/(c**2*d) + 81/(4*d**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (9/(2*b) + 2*c/a**2)**2" ], "shape": [ "identity: (N*a**N*c + N/b)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/27", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 27", "problem_latex": "$\\displaystyle \\left( \\frac{a}{b} + 2 \\right) \\left(\n\\frac{a}{b} - 5 \\right)$.", "markdown": "$\\displaystyle \\left( \\frac{a}{b} + 2 \\right) \\left( \\frac{a}{b} - 5 \\right)$.", "answer_latex": [ "$\\displaystyle \\frac{a^2}{b^2}-\\frac{3a}{b}-10$." ], "answer_markdown": [ "$\\displaystyle \\frac{a^2}{b^2}-\\frac{3a}{b}-10$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a/b + 2)*(a/b - 5)", "answer_expr": "a**2/b**2 - 3*a/b - 10" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/b - 5)*(a/b + 2)" ], "shape": [ "identity: (N + a/b)**2" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/28", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 28", "problem_latex": "$\\displaystyle \\left( \\frac{x}{y} - \\frac{a}{b} \\right)^3$.", "markdown": "$\\displaystyle \\left( \\frac{x}{y} - \\frac{a}{b} \\right)^3$.", "answer_latex": [ "$\\displaystyle \\frac{x^3}{y^3}-\\frac{3ax^2}{by^2}+\n \\frac{3a^2x}{b^2y}-\\frac{a^3}{b^3}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^3}{y^3}-\\frac{3ax^2}{by^2}+ \\frac{3a^2x}{b^2y}-\\frac{a^3}{b^3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x/y - a/b)**3", "answer_expr": "x**3/y**3 - 3*a*x**2/(b*y**2) + 3*a**2*x/(b**2*y) - a**3/b**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-a/b + c/d)**3" ], "shape": [ "identity: (-a/b + c/d)**N" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/29", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 29", "problem_latex": "$\\displaystyle \\frac{x^4}{a^2} - \\frac{b^2}{y^4}$", "markdown": "$\\displaystyle \\frac{x^4}{a^2} - \\frac{b^2}{y^4}$", "answer_latex": [ "$\\displaystyle \\left(\\frac{x^2}{a}-\\frac{b}{y^2}\\right)\\left(\\frac{x^2}{a}+\n \\frac{b}{y^2}\\right)$." ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{x^2}{a}-\\frac{b}{y^2}\\right)\\left(\\frac{x^2}{a}+ \\frac{b}{y^2}\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**4/a**2 - b**2/y**4", "answer_expr": "(x**2/a - b/y**2)*(x**2/a + b/y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -b**2/d**4 + c**4/a**2" ], "shape": [ "factor: a**N*c**N - b**N*d**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/3", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 3", "problem_latex": "$\\displaystyle \\left(-\\frac{2xy}{3a^2m^3}\\right)^5)$.", "markdown": "$\\displaystyle \\left(-\\frac{2xy}{3a^2m^3}\\right)^5)$.", "answer_latex": [ "$\\displaystyle -\\frac{32x^5y^5}{243a^{10}m^{15}}$." ], "answer_markdown": [ "$\\displaystyle -\\frac{32x^5y^5}{243a^{10}m^{15}}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-2*x*y/(3*a**2*m**3))**5", "answer_expr": "-32*x**5*y**5/(243*a**10*m**15)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: -32*c**5*d**5/(243*a**10*b**15)" ], "shape": [ "identity: N*a**N*b**N*c**N*d**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/30", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 30", "problem_latex": "$\\displaystyle \\frac{a^2}{b^4} - \\frac{x^8}{y^2}$", "markdown": "$\\displaystyle \\frac{a^2}{b^4} - \\frac{x^8}{y^2}$", "answer_latex": [ "$\\displaystyle\n\\left(\\frac{a}{b^2}-\\frac{x^4}{y}\\right)\\left(\\frac{a}{b^2}+\n \\frac{x^4}{y}\\right)$" ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{a}{b^2}-\\frac{x^4}{y}\\right)\\left(\\frac{a}{b^2}+ \\frac{x^4}{y}\\right)$" ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**2/b**4 - x**8/y**2", "answer_expr": "(a/b**2 - x**4/y)*(a/b**2 + x**4/y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2/b**4 - c**8/d**2" ], "shape": [ "factor: a**N*b**N - c**N*d**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/31", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 31, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 31", "problem_latex": "$\\frac{a^4}{m^4} - \\frac{b^4}{x^4}$", "markdown": "$\\frac{a^4}{m^4} - \\frac{b^4}{x^4}$", "answer_latex": [ "$\\displaystyle \\left(\\frac{a^2}{m^2}+\\frac{b^2}{x^2}\\right)\n \\left(\\frac{a}{m}+\\frac{b}{x}\\right)\n \\left(\\frac{a}{m}-\\frac{b}{x}\\right)$." ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{a^2}{m^2}+\\frac{b^2}{x^2}\\right) \\left(\\frac{a}{m}+\\frac{b}{x}\\right) \\left(\\frac{a}{m}-\\frac{b}{x}\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**4/m**4 - b**4/x**4", "answer_expr": "(a**2/m**2 + b**2/x**2)*(a/m + b/x)*(a/m - b/x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**4/c**4 - b**4/d**4" ], "shape": [ "factor: a**N*c**N - b**N*d**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/32", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 32, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 32", "problem_latex": "$\\displaystyle \\frac{8a^3}{y^3} + \\frac{b^3}{c^3}$", "markdown": "$\\displaystyle \\frac{8a^3}{y^3} + \\frac{b^3}{c^3}$", "answer_latex": [ "$\\displaystyle \\left(\\frac{2a}{y}+\\frac{b}{c}\\right)\n \\left(\\frac{4a^2}{y^2}-\\frac{2ab}{cy}+\\frac{b^2}{c^2}\\right)$." ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{2a}{y}+\\frac{b}{c}\\right) \\left(\\frac{4a^2}{y^2}-\\frac{2ab}{cy}+\\frac{b^2}{c^2}\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "8*a**3/y**3 + b**3/c**3", "answer_expr": "(2*a/y + b/c)*(4*a**2/y**2 - 2*a*b/(c*y) + b**2/c**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 8*a**3/d**3 + b**3/c**3" ], "shape": [ "factor: N*a**N*d**N + b**N*c**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/33", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 33, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 33", "problem_latex": "$\\displaystyle \\frac{x^3}{27a^3} - \\frac{y^3}{c^3}$", "markdown": "$\\displaystyle \\frac{x^3}{27a^3} - \\frac{y^3}{c^3}$", "answer_latex": [ "$\\displaystyle \\left(\\frac{x}{3a}-\\frac{y}{c}\\right)\\left(\\frac{x^2}{9a^2}+\n \\frac{xy}{3ac}+\\frac{y^2}{c^2}\\right)$." ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{x}{3a}-\\frac{y}{c}\\right)\\left(\\frac{x^2}{9a^2}+ \\frac{xy}{3ac}+\\frac{y^2}{c^2}\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**3/(27*a**3) - y**3/c**3", "answer_expr": "(x/(3*a) - y/c)*(x**2/(9*a**2) + x*y/(3*a*c) + y**2/c**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -d**3/b**3 + c**3/(27*a**3)" ], "shape": [ "factor: N*a**N*c**N - b**N*d**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/34", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 34, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 34", "problem_latex": "$\\displaystyle \\frac{81a^4}{b^4} - \\frac{x^4y^4}{625z^4}$", "markdown": "$\\displaystyle \\frac{81a^4}{b^4} - \\frac{x^4y^4}{625z^4}$", "answer_latex": [ "$\\displaystyle\n\\left(\\frac{9a^2}{b^2}+\\frac{x^2y^2}{25z^2}\\right)\n \\left(\\frac{3a}{b}+\\frac{xy}{5z}\\right)\n \\left(\\frac{3a}{b}-\\frac{xy}{5z}\\right)$." ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{9a^2}{b^2}+\\frac{x^2y^2}{25z^2}\\right) \\left(\\frac{3a}{b}+\\frac{xy}{5z}\\right) \\left(\\frac{3a}{b}-\\frac{xy}{5z}\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "81*a**4/b**4 - x**4*y**4/(625*z**4)", "answer_expr": "(9*a**2/b**2 + x**2*y**2/(25*z**2))*(3*a/b + x*y/(5*z))*(3*a/b - x*y/(5*z))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 81*a**4/b**4 - c**4*d**4/(625*e**4)" ], "shape": [ "factor: N*a**N*b**N + N*c**N*d**N*e**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/35", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 35, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 35", "problem_latex": "$\\displaystyle \\frac{m^2}{y^2} + \\frac{2m}{y} - 15$", "markdown": "$\\displaystyle \\frac{m^2}{y^2} + \\frac{2m}{y} - 15$", "answer_latex": [ "$\\displaystyle\n\\left(\\frac{m}{y}-5\\right)\\left(\\frac{m}{y}+3\\right)$." ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{m}{y}-5\\right)\\left(\\frac{m}{y}+3\\right)$." ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "-11.522188860090957993", "-15.986524524426622329" ], "problem_expr": "m**2/y**2 + 2*m/y - 15", "answer_expr": "(m/y - 5)*(m/y + 3)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: a**2/b**2 + 2*a/b - 15" ], "shape": [ "factor: N*a/b + N + a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/36", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 36, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 36", "problem_latex": "$\\displaystyle \\frac{x^2}{a^2} - \\frac{2x}{a} - 8$", "markdown": "$\\displaystyle \\frac{x^2}{a^2} - \\frac{2x}{a} - 8$", "answer_latex": [ "$\\displaystyle\n\\left(\\frac{x}{a}-4\\right)\\left(\\frac{x}{a}+2\\right)$." ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{x}{a}-4\\right)\\left(\\frac{x}{a}+2\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2/a**2 - 2*x/a - 8", "answer_expr": "(x/a - 4)*(x/a + 2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -8 - 2*b/a + b**2/a**2" ], "shape": [ "factor: N + N*b/a + a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/37", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 37, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 37", "problem_latex": "$\\displaystyle \\frac{y^2}{4} + 2 + \\frac{4}{y^2}$", "markdown": "$\\displaystyle \\frac{y^2}{4} + 2 + \\frac{4}{y^2}$", "answer_latex": [ "$\\displaystyle \\left(\\frac{y}{2}+\\frac{2}{y}\\right)^2$." ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{y}{2}+\\frac{2}{y}\\right)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "y**2/4 + 2 + 4/y**2", "answer_expr": "(y/2 + 2/y)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2/4 + 2 + 4/a**2" ], "shape": [ "factor: 2*N*a**N + N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/38", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 38, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 38", "problem_latex": "$\\displaystyle \\frac{x^2}{a^2} + \\frac{a^2}{x^2} - 2$", "markdown": "$\\displaystyle \\frac{x^2}{a^2} + \\frac{a^2}{x^2} - 2$", "answer_latex": [ "$\\displaystyle \\left(\\frac{x}{a}-\\frac{a}{x}\\right)^2$." ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{x}{a}-\\frac{a}{x}\\right)^2$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2/a**2 + a**2/x**2 - 2", "answer_expr": "(x/a - a/x)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: a**2/b**2 - 2 + b**2/a**2" ], "shape": [ "factor: N + 2*a**N*b**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/39", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 39, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 39", "problem_latex": "A dog can take 2 leaps of $a$ feet each in a second. How\nmany feet can he go in 9 seconds?", "markdown": "A dog can take 2 leaps of $a$ feet each in a second. How many feet can he go in 9 seconds?", "answer_latex": [ "$18a$ ft." ], "answer_markdown": [ "$18a$ ft." ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "symbolic printed value '18a' equals 18*a", "problem_expr": "2*a*9", "answer_expr": "18*a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: 18*a" ], "shape": [ "evaluate: N*a" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": "X#18a,5E-1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/4", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 4", "problem_latex": "$\\displaystyle \\left(\\frac{x(a-b)}{3a^2b}\\right)^4$.", "markdown": "$\\displaystyle \\left(\\frac{x(a-b)}{3a^2b}\\right)^4$.", "answer_latex": [ "$\\displaystyle \\frac{x^4 \\left(a-b \\right)^4}{81a^8b^4}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^4 \\left(a-b \\right)^4}{81a^8b^4}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x*(a-b)/(3*a**2*b))**4", "answer_expr": "x**4*(a-b)**4/(81*a**8*b**4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: c**4*(a - b)**4/(81*a**8*b**4)" ], "shape": [ "identity: N*a**N*b**N*c**N*(a - b)**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/40", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 40, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 40", "problem_latex": "How many weeks would it take to build a stone wall if\n$\\frac{1}{a}$ of it can be built in one day?", "markdown": "How many weeks would it take to build a stone wall if $\\frac{1}{a}$ of it can be built in one day?", "answer_latex": [ "$\\displaystyle \\frac{a}{6}$ weeks." ], "answer_markdown": [ "$\\displaystyle \\frac{a}{6}$ weeks." ], "checks": [ { "task": "evaluate", "verdict": "FLAG-MISMATCH", "judge_why": "symbolic printed value 'a/6' differs from a/7", "problem_expr": "a/7", "answer_expr": "a/6" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "evaluate: a/7" ], "shape": [ "evaluate: N*a" ], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/5", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 5", "problem_latex": "$\\displaystyle \\left(-\n\\frac{5x^2y(a+b^2)^2}{2ab^3(x^2-y)^3}\\right)^3$.", "markdown": "$\\displaystyle \\left(- \\frac{5x^2y(a+b^2)^2}{2ab^3(x^2-y)^3}\\right)^3$.", "answer_latex": [ "$\\displaystyle -\\frac{125x^5y^3\\left(a+b^2\\right)^6}{8a^3b^9\n\\left(x^2-y \\right)^9}$." ], "answer_markdown": [ "$\\displaystyle -\\frac{125x^5y^3\\left(a+b^2\\right)^6}{8a^3b^9 \\left(x^2-y \\right)^9}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "545.45595396221714342", "477.2739597169400005" ], "problem_expr": "(-5*x**2*y*(a+b**2)**2/(2*a*b**3*(x**2-y)**3))**3", "answer_expr": "-125*x**5*y**3*(a+b**2)**6/(8*a**3*b**9*(x**2-y)**9)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: -125*c**6*d**3*(a + b**2)**6/(8*a**3*b**9*(c**2 - d)**9)" ], "shape": [ "identity: N*a**N*b**N*c**N*d**N*(a + b**N)**N*(c**N - d)**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/6", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 6", "problem_latex": "$\\displaystyle \\left(-\n\\frac{3am^4(2a+3b)^3}{4x^2y^2(m-n)^2}\\right)^3$.", "markdown": "$\\displaystyle \\left(- \\frac{3am^4(2a+3b)^3}{4x^2y^2(m-n)^2}\\right)^3$.", "answer_latex": [ "$\\displaystyle -\\frac{27a^3m^{12} \\left( 2a+3b \\right)\n^9}{64x^6y^9 \\left( m-n \\right) ^6}$." ], "answer_markdown": [ "$\\displaystyle -\\frac{27a^3m^{12} \\left( 2a+3b \\right) ^9}{64x^6y^9 \\left( m-n \\right) ^6}$." ], "checks": [ { "task": "identity", "verdict": "FLAG-MISMATCH", "judge_why": [ "-39968891168.23426314", "-1353516032.5900621881" ], "problem_expr": "(-3*a*m**4*(2*a+3*b)**3/(4*x**2*y**2*(m-n)**2))**3", "answer_expr": "-27*a**3*m**12*(2*a+3*b)**9/(64*x**6*y**9*(m-n)**6)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "identity: -27*a**3*c**12*(2*a + 3*b)**9/(64*e**6*f**6*(c - d)**6)" ], "shape": [ "identity: N*a**N*c**N*e**N*f**N*(c - d)**N*(N*a + N*b)**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/7", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 7", "problem_latex": "$\\displaystyle \\left( -\\frac{ 3a^5xy^2z^3 }{ 2bc^4d^4 }\n\\right)^4$.", "markdown": "$\\displaystyle \\left( -\\frac{ 3a^5xy^2z^3 }{ 2bc^4d^4 } \\right)^4$.", "answer_latex": [ "$\\displaystyle\n\\frac{81a^{20}x^4y^8z^{12}}{16b^4c^{16}d^{16}}$." ], "answer_markdown": [ "$\\displaystyle \\frac{81a^{20}x^4y^8z^{12}}{16b^4c^{16}d^{16}}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-3*a**5*x*y**2*z**3/(2*b*c**4*d**4))**4", "answer_expr": "81*a**20*x**4*y**8*z**12/(16*b**4*c**16*d**16)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 81*a**20*e**4*f**8*g**12/(16*b**4*c**16*d**16)" ], "shape": [ "identity: N*a**N*b**N*c**N*d**N*e**N*f**N*g**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/8", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 8", "problem_latex": "$\\displaystyle \\left( -\\frac{ 4x^7y^2z^3 }{ 3ab^6d^3 }\n\\right)^4$.", "markdown": "$\\displaystyle \\left( -\\frac{ 4x^7y^2z^3 }{ 3ab^6d^3 } \\right)^4$.", "answer_latex": [ "$\\displaystyle\n\\frac{256x^{28}y^8z^{12}}{81a^4b^{24}d^{12}}$." ], "answer_markdown": [ "$\\displaystyle \\frac{256x^{28}y^8z^{12}}{81a^4b^{24}d^{12}}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(-4*x**7*y**2*z**3/(3*a*b**6*d**3))**4", "answer_expr": "256*x**28*y**8*z**12/(81*a**4*b**24*d**12)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 256*d**28*e**8*f**12/(81*a**4*b**24*c**12)" ], "shape": [ "identity: N*a**N*b**N*c**N*d**N*e**N*f**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-50/9", "set": "boyden-first-book-in-algebra-1895/ex-50", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 50, problem 9", "problem_latex": "$\\displaystyle \\sqrt[3]{ \\frac{ 8a^3b^6 }{ 27m^6n^9 } }$.", "markdown": "$\\displaystyle \\sqrt[3]{ \\frac{ 8a^3b^6 }{ 27m^6n^9 } }$.", "answer_latex": [ "$\\displaystyle \\frac{2ab^2}{3m^2n^3}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2ab^2}{3m^2n^3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(8*a**3*b**6/(27*m**6*n**9))**Rational(1,3)", "answer_expr": "2*a*b**2/(3*m**2*n**3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*b**2*(a**3/(c**6*d**9))**(1/3)/3" ], "shape": [ "identity: N*b**N*(a**N*c**N*d**N)**N" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/1", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 1", "problem_latex": "$\\displaystyle \\frac{1+\\frac{a}{b}}{\\frac{x}{b}-1}$.", "markdown": "$\\displaystyle \\frac{1+\\frac{a}{b}}{\\frac{x}{b}-1}$.", "answer_latex": [ "$\\displaystyle \\frac{b+a}{x-b}$." ], "answer_markdown": [ "$\\displaystyle \\frac{b+a}{x-b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1 + a/b)/(x/b - 1)", "answer_expr": "(b + a)/(x - b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/b + 1)/(-1 + c/b)" ], "shape": [ "identity: (a/b + 1)/(-1 + c/b)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/10", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 10", "problem_latex": "$\\frac{1+a+a^2}{1+\\frac{1}{a}+\\frac{1}{a^2}}$.", "markdown": "$\\frac{1+a+a^2}{1+\\frac{1}{a}+\\frac{1}{a^2}}$.", "answer_latex": [ "$a^2$." ], "answer_markdown": [ "$a^2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1 + a + a**2)/(1 + 1/a + 1/a**2)", "answer_expr": "a**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 + a + 1)/(1 + 1/a + a**(-2))" ], "shape": [ "identity: (a + a**N + 1)/(a**N + 1 + 1/a)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/11", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 11", "problem_latex": "$\\displaystyle \\frac{x-3-\\frac{2}{x-4}}{x-1+\\frac{2}{x-4}}$.", "markdown": "$\\displaystyle \\frac{x-3-\\frac{2}{x-4}}{x-1+\\frac{2}{x-4}}$.", "answer_latex": [ "$\\displaystyle \\frac{x-5}{x-3}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x-5}{x-3}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - 3 - 2/(x - 4))/(x - 1 + 2/(x - 4))", "answer_expr": "(x - 5)/(x - 3)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a - 3 - 2/(a - 4))/(a - 1 + 2/(a - 4))" ], "shape": [ "identity: (N + N/(N + a) + a)/(N/(N + a) + a - 1)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/12", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 12", "problem_latex": "$\\displaystyle\n\\frac{\\frac{a}{a+b}+\\frac{a}{a-b}}{\\frac{2a}{a^2-b^2}}$.", "markdown": "$\\displaystyle \\frac{\\frac{a}{a+b}+\\frac{a}{a-b}}{\\frac{2a}{a^2-b^2}}$.", "answer_latex": [ "$a$." ], "answer_markdown": [ "$a$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a/(a + b) + a/(a - b))/(2*a/(a**2 - b**2))", "answer_expr": "a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**2 - b**2)*(a/(a + b) + a/(a - b))/(2*a)" ], "shape": [ "identity: N*(a**N - b**N)*(a/(a + b) + a/(a - b))/a" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/13", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 13", "problem_latex": "$\\displaystyle\n\\frac{\\frac{a+1}{a-1}+\\frac{a-1}{a+1}}{\\frac{a+1}{a-1}-\\frac{a-1}{a+1}}$.", "markdown": "$\\displaystyle \\frac{\\frac{a+1}{a-1}+\\frac{a-1}{a+1}}{\\frac{a+1}{a-1}-\\frac{a-1}{a+1}}$.", "answer_latex": [ "$\\displaystyle \\frac{a^2+1}{2a}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a^2+1}{2a}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a + 1)/(a - 1) + (a - 1)/(a + 1))/((a + 1)/(a - 1) - (a - 1)/(a + 1))", "answer_expr": "(a**2 + 1)/(2*a)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: ((a - 1)/(a + 1) + (a + 1)/(a - 1))/(-(a - 1)/(a + 1) + (a + 1)/(a - 1))" ], "shape": [ "identity: ((a - 1)/(a + 1) + (a + 1)/(a - 1))/(-(a - 1)/(a + 1) + (a + 1)/(a - 1))" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/14", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 14", "problem_latex": "$\\displaystyle\n\\frac{\\frac{a^3+b^3}{a^2-b^2}}{\\frac{a^2-ab+b^2}{a-b}}$.", "markdown": "$\\displaystyle \\frac{\\frac{a^3+b^3}{a^2-b^2}}{\\frac{a^2-ab+b^2}{a-b}}$.", "answer_latex": [ "$1$." ], "answer_markdown": [ "$1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a**3 + b**3)/(a**2 - b**2))/((a**2 - a*b + b**2)/(a - b))", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a - b)*(a**3 + b**3)/((a**2 - b**2)*(a**2 - a*b + b**2))" ], "shape": [ "identity: (a - b)*(a**N + b**N)/((a**N - b**N)*(-a*b + a**N + b**N))" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/15", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 15", "problem_latex": "$\\displaystyle 1-\\frac{1}{1+\\frac{2}{a-2}}$.", "markdown": "$\\displaystyle 1-\\frac{1}{1+\\frac{2}{a-2}}$.", "answer_latex": [ "$\\displaystyle \\frac{2}{a}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2}{a}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "1 - 1/(1 + 2/(a - 2))", "answer_expr": "2/a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 1 - 1/(1 + 2/(a - 2))" ], "shape": [ "identity: 1 - 1/(N/(N + a) + 1)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/16", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 16", "problem_latex": "$\\displaystyle\n\\frac{\\frac{a+2b}{b}-\\frac{a}{a+b}}{\\frac{a+2b}{a+b}+\\frac{a}{b}}$.", "markdown": "$\\displaystyle \\frac{\\frac{a+2b}{b}-\\frac{a}{a+b}}{\\frac{a+2b}{a+b}+\\frac{a}{b}}$.", "answer_latex": [ "$l$." ], "answer_markdown": [ "$l$." ], "checks": [ { "task": "identity", "verdict": "FLAG-PARSE", "judge_why": "undeclared symbols ['l']", "problem_expr": "((a + 2*b)/b - a/(a + b))/((a + 2*b)/(a + b) + a/b)", "answer_expr": "1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-PARSE" ] }, "form": [ "identity: (-a/(a + b) + (a + 2*b)/b)/(a/b + (a + 2*b)/(a + b))" ], "shape": [ "identity: (-a/(a + b) + (N*b + a)/b)/(a/b + (N*b + a)/(a + b))" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/17", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 17", "problem_latex": "How many pounds of pepper can be bought for $y$ dollars, if\n$x$ pounds cost $2x$ dimes?", "markdown": "How many pounds of pepper can be bought for $y$ dollars, if $x$ pounds cost $2x$ dimes?", "answer_latex": [ "$5y$ lbs." ], "answer_markdown": [ "$5y$ lbs." ], "checks": [ { "task": "solve", "verdict": "FLAG-MISMATCH", "judge_why": "the equations leave [{x: 0, y: 0}]", "problem_expr": null, "answer_expr": "{p: 5*y}" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "solve: (Eq(a*x, 10*c), Eq(a*b, 2*b))" ], "shape": [ "solve: (Eq(a*x, N*c), Eq(a*b, N*b))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/18a", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 18, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 18a", "problem_latex": "How many inches in $y$ feet? How many yards?", "markdown": "How many inches in $y$ feet? How many yards?", "answer_latex": [ "12y in." ], "answer_markdown": [ "12y in." ], "checks": [ { "task": "evaluate", "verdict": "FLAG-EXTRACTION", "judge_why": "evaluate: SyntaxError: invalid syntax (, line 1)", "problem_expr": "12*y", "answer_expr": "12*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "evaluate: 12*a" ], "shape": [ "evaluate: N*a" ], "same_problem_in": [], "needs": [ "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/18b", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 18, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 18b", "problem_latex": "How many inches in $y$ feet? How many yards?", "markdown": "How many inches in $y$ feet? How many yards?", "answer_latex": [ "$\\displaystyle \\frac{y}{3}$ yds." ], "answer_markdown": [ "$\\displaystyle \\frac{y}{3}$ yds." ], "checks": [ { "task": "evaluate", "verdict": "FLAG-MISMATCH", "judge_why": "symbolic printed value '\\\\displaystyle \\\\frac{y}{3} yds' differs from y/3", "problem_expr": "y/3", "answer_expr": "y/3" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "evaluate: a/3" ], "shape": [ "evaluate: N*a" ], "same_problem_in": [], "needs": [ "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/19", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 19", "problem_latex": "A man bought $x$ pounds of beef at $x$ cents a pound,\nand handed the butcher a $y$-dollar bill. How many cents\nchange should he receive?", "markdown": "A man bought $x$ pounds of beef at $x$ cents a pound, and handed the butcher a $y$-dollar bill. How many cents change should he receive?", "answer_latex": [ "$100y-x^2$ cts." ], "answer_markdown": [ "$100y-x^2$ cts." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{c: 100*y - x**2}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a**2 + x, 100*b)" ], "shape": [ "solve: Eq(a**N + x, N*b)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/2", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 2", "problem_latex": "$\\displaystyle \\frac{x+\\frac{a}{y}}{m-\\frac{b}{y}}$.", "markdown": "$\\displaystyle \\frac{x+\\frac{a}{y}}{m-\\frac{b}{y}}$.", "answer_latex": [ "$\\displaystyle \\frac{xy+a}{my-b}$." ], "answer_markdown": [ "$\\displaystyle \\frac{xy+a}{my-b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x + a/y)/(m - b/y)", "answer_expr": "(x*y + a)/(m*y - b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/e + d)/(-b/e + c)" ], "shape": [ "identity: (a/e + d)/(-b/e + c)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/20", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 20", "problem_latex": "$x$ times $I$ is how many times $m$?", "markdown": "$x$ times $I$ is how many times $m$?", "answer_latex": [ "$\\displaystyle \\frac{lx}{m}$." ], "answer_markdown": [ "$\\displaystyle \\frac{lx}{m}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{k: I*x/m}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(b*x, a*c)" ], "shape": [ "solve: Eq(b*x, a*c)" ], "same_problem_in": [], "needs": [ "core.eqn" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/3", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 3", "problem_latex": "$\\displaystyle \\frac{x}{a+\\frac{b}{c}}$.", "markdown": "$\\displaystyle \\frac{x}{a+\\frac{b}{c}}$.", "answer_latex": [ "$\\displaystyle \\frac{cx}{ac+b}$." ], "answer_markdown": [ "$\\displaystyle \\frac{cx}{ac+b}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "x/(a + b/c)", "answer_expr": "c*x/(a*c + b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: d/(a + b/c)" ], "shape": [ "identity: d/(a + b/c)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/4", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 4", "problem_latex": "$\\displaystyle \\frac{x-\\frac{1}{x^2}}{1-\\frac{1}{x}}$.", "markdown": "$\\displaystyle \\frac{x-\\frac{1}{x^2}}{1-\\frac{1}{x}}$.", "answer_latex": [ "$\\displaystyle \\frac{x^2+x+1}{x}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2+x+1}{x}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - 1/x**2)/(1 - 1/x)", "answer_expr": "(x**2 + x + 1)/x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a - 1/a**2)/(1 - 1/a)" ], "shape": [ "identity: (a - a**N)/(1 - 1/a)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/5", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 5", "problem_latex": "$\\displaystyle \\frac{\\frac{a}{b}-\\frac{b}{a}}{a-b}$.", "markdown": "$\\displaystyle \\frac{\\frac{a}{b}-\\frac{b}{a}}{a-b}$.", "answer_latex": [ "$\\displaystyle \\frac{a+b}{ab}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a+b}{ab}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a/b - b/a)/(a - b)", "answer_expr": "(a + b)/(a*b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/b - b/a)/(a - b)" ], "shape": [ "identity: (a/b - b/a)/(a - b)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/6", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 6", "problem_latex": "$\\displaystyle \\frac{1+m^3}{1+\\frac{1}{m}}$.", "markdown": "$\\displaystyle \\frac{1+m^3}{1+\\frac{1}{m}}$.", "answer_latex": [ "$m(m^2-m+1)$." ], "answer_markdown": [ "$m(m^2-m+1)$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1 + m**3)/(1 + 1/m)", "answer_expr": "m*(m**2 - m + 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3 + 1)/(1 + 1/a)" ], "shape": [ "identity: (a**N + 1)/(1 + 1/a)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/7", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 7", "problem_latex": "$\\displaystyle\n\\frac{\\frac{x}{y}-\\frac{z}{x}}{\\frac{a}{y}-\\frac{b}{x}}$.", "markdown": "$\\displaystyle \\frac{\\frac{x}{y}-\\frac{z}{x}}{\\frac{a}{y}-\\frac{b}{x}}$.", "answer_latex": [ "$\\displaystyle \\frac{x^2-yz}{ax-by}$." ], "answer_markdown": [ "$\\displaystyle \\frac{x^2-yz}{ax-by}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x/y - z/x)/(a/y - b/x)", "answer_expr": "(x**2 - y*z)/(a*x - b*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (c/d - e/c)/(a/d - b/c)" ], "shape": [ "identity: (c/d - e/c)/(a/d - b/c)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/8", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 8", "problem_latex": "$\\displaystyle \\frac{\\frac{ab}{c}-3d}{3c-\\frac{ab}{d}}$.", "markdown": "$\\displaystyle \\frac{\\frac{ab}{c}-3d}{3c-\\frac{ab}{d}}$.", "answer_latex": [ "$\\displaystyle -\\frac{d}{c}$." ], "answer_markdown": [ "$\\displaystyle -\\frac{d}{c}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a*b/c - 3*d)/(3*c - a*b/d)", "answer_expr": "-d/c" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a*b/c - 3*d)/(-a*b/d + 3*c)" ], "shape": [ "identity: (N*d + a*b/c)/(N*c - a*b/d)" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-51/9", "set": "boyden-first-book-in-algebra-1895/ex-51", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 51, problem 9", "problem_latex": "$\\displaystyle \\frac{1+\\frac{1}{a-1}}{1-\\frac{1}{a+1}}$.", "markdown": "$\\displaystyle \\frac{1+\\frac{1}{a-1}}{1-\\frac{1}{a+1}}$.", "answer_latex": [ "$\\displaystyle \\frac{a+1}{a-1}$." ], "answer_markdown": [ "$\\displaystyle \\frac{a+1}{a-1}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1 + 1/(a - 1))/(1 - 1/(a + 1))", "answer_expr": "(a + 1)/(a - 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (1 + 1/(a - 1))/(1 - 1/(a + 1))" ], "shape": [ "identity: (1 + 1/(a - 1))/(1 - 1/(a + 1))" ], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/1", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 1", "problem_latex": "Divide $x^3 - 19x + 6x^7 + 20 + 8x^2 + 16x^4-x^6-11x^5$\nby $x^2 + 4-3x+2x^3$.", "markdown": "Divide $x^3 - 19x + 6x^7 + 20 + 8x^2 + 16x^4-x^6-11x^5$ by $x^2 + 4-3x+2x^3$.", "answer_latex": [ "$3x^4-2x^3-x+5$." ], "answer_markdown": [ "$3x^4-2x^3-x+5$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**3 - 19*x + 6*x**7 + 20 + 8*x**2 + 16*x**4 - x**6 - 11*x**5)/(x**2 + 4 - 3*x + 2*x**3)", "answer_expr": "3*x**4 - 2*x**3 - x + 5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (6*x**7 - x**6 - 11*x**5 + 16*x**4 + x**3 + 8*x**2 - 19*x + 20)/(2*x**3 + x**2 - 3*x + 4)" ], "shape": [ "identity: (N*x + 4*N*x**N + N)/(N*x + N*x**N + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/10", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 10", "problem_latex": "$\\displaystyle \\frac{x - 3}{x - 2} + \\frac{2 (1 - x)}{x^2 -\n6x + 8} - \\frac{x - 1}{x - 4}$.", "markdown": "$\\displaystyle \\frac{x - 3}{x - 2} + \\frac{2 (1 - x)}{x^2 - 6x + 8} - \\frac{x - 1}{x - 4}$.", "answer_latex": [ "$\\displaystyle -\\frac{6}{x-4}$." ], "answer_markdown": [ "$\\displaystyle -\\frac{6}{x-4}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - 3)/(x - 2) + 2*(1 - x)/(x**2 - 6*x + 8) - (x - 1)/(x - 4)", "answer_expr": "-6/(x - 4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-2*x + 2)/(x**2 - 6*x + 8) + (x - 3)/(x - 2) - (x - 1)/(x - 4)" ], "shape": [ "identity: (N*x + N)/(N*x + N + x**N) + 1 - (x - 1)/(N + x)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/11", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 11", "problem_latex": "$\\displaystyle \\frac{1}{(2 - x)(3 - x)} - \\frac{2}{(x - 1)(x\n- 3)} + \\frac{1}{(x - 1)(x - 2)}$.", "markdown": "$\\displaystyle \\frac{1}{(2 - x)(3 - x)} - \\frac{2}{(x - 1)(x - 3)} + \\frac{1}{(x - 1)(x - 2)}$.", "answer_latex": [ "$0$." ], "answer_markdown": [ "$0$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "1/((2 - x)*(3 - x)) - 2/((x - 1)*(x - 3)) + 1/((x - 1)*(x - 2))", "answer_expr": "0" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 1/((x - 2)*(x - 1)) - 2/((x - 3)*(x - 1)) + 1/((-x + 2)*(-x + 3))" ], "shape": [ "identity: N/((N + x)*(x - 1)) + 1/((N + x)*(x - 1)) + (N - x)**(-2)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/12", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 12", "problem_latex": "$\\displaystyle \\frac{x^2 + xy}{x - y} \\times \\frac{x^3 -\n3x^2y + 3xy^2 - y^3}{x^2 - y^2} \\div \\frac{2xy - 2y^2}{3}$.", "markdown": "$\\displaystyle \\frac{x^2 + xy}{x - y} \\times \\frac{x^3 - 3x^2y + 3xy^2 - y^3}{x^2 - y^2} \\div \\frac{2xy - 2y^2}{3}$.", "answer_latex": [ "$\\displaystyle \\frac{3x}{2y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{3x}{2y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2 + x*y)/(x - y) * (x**3 - 3*x**2*y + 3*x*y**2 - y**3)/(x**2 - y**2) / ((2*x*y - 2*y**2)/3)", "answer_expr": "3*x/(2*y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a*x + x**2)*(-a**3 + 3*a**2*x - 3*a*x**2 + x**3)/((-a + x)*(-a**2 + x**2)*(-2*a**2/3 + 2*a*x/3))" ], "shape": [ "identity: (a*x + x**N)*(N*a*x**N + N*a**N*x - a**N + x**N)/((-a + x)*(-a**N + x**N)*(N*a*x + N*a**N))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/13", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 13", "problem_latex": "$\\displaystyle \\left( \\frac{1}{m} + \\frac{1}{n} \\right) (a +\nb) - \\left( \\frac{a + b}{m} \\right) - \\left( \\frac{a - b}{n}\n\\right)$.", "markdown": "$\\displaystyle \\left( \\frac{1}{m} + \\frac{1}{n} \\right) (a + b) - \\left( \\frac{a + b}{m} \\right) - \\left( \\frac{a - b}{n} \\right)$.", "answer_latex": [ "$\\displaystyle \\frac{2b}{n}$." ], "answer_markdown": [ "$\\displaystyle \\frac{2b}{n}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(1/m + 1/n)*(a + b) - (a + b)/m - (a - b)/n", "answer_expr": "2*b/n" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a + x)*(1/c + 1/b) - (-a + x)/c - (a + x)/b" ], "shape": [ "identity: (a + x)*(1/c + 1/b) - (-a + x)/c - (a + x)/b" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/14", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 14", "problem_latex": "$\\displaystyle \\left( x - \\frac{1}{1 + \\frac{2}{x - 1}}\n\\right) \\div \\frac{x + \\frac{1}{x}}{\\frac{1}{x} + 1}$.", "markdown": "$\\displaystyle \\left( x - \\frac{1}{1 + \\frac{2}{x - 1}} \\right) \\div \\frac{x + \\frac{1}{x}}{\\frac{1}{x} + 1}$.", "answer_latex": [ "$1$." ], "answer_markdown": [ "$1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - 1/(1 + 2/(x - 1)))/((x + 1/x)/(1/x + 1))", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (1 + 1/x)*(x - 1/(1 + 2/(x - 1)))/(x + 1/x)" ], "shape": [ "identity: (1 + 1/x)*(x - 1/(N/(x - 1) + 1))/(x + 1/x)" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/15", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 15", "problem_latex": "$\\displaystyle \\frac{\\frac{a}{b} + \\frac{b}{a} -\n1}{\\frac{a^2}{b^2} + \\frac{a}{b} + 1} \\times \\frac{1 +\n\\frac{b}{a}}{a - b} \\div \\frac{1 + \\frac{b^3}{a^3}}{\\frac{a^2}{b}\n- \\frac{b^2}{a}}$.", "markdown": "$\\displaystyle \\frac{\\frac{a}{b} + \\frac{b}{a} - 1}{\\frac{a^2}{b^2} + \\frac{a}{b} + 1} \\times \\frac{1 + \\frac{b}{a}}{a - b} \\div \\frac{1 + \\frac{b^3}{a^3}}{\\frac{a^2}{b} - \\frac{b^2}{a}}$.", "answer_latex": [ "$1$." ], "answer_markdown": [ "$1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((a/b + b/a - 1)/(a**2/b**2 + a/b + 1))*((1 + b/a)/(a - b))/((1 + b**3/a**3)/(a**2/b - b**2/a))", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a/x + 1)*(-a**2/x + x**2/a)*(a/x - 1 + x/a)/((-a + x)*(a**3/x**3 + 1)*(1 + x/a + x**2/a**2))" ], "shape": [ "identity: (a/x + 1)*(-a**N/x + x**N/a)*(a/x - 1 + x/a)/((-a + x)*(a**N*x**N + 1)*(a**N*x**N + 1 + x/a))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/16", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 16", "problem_latex": "Prove that $3(a + b)(a + c)(b + c) = (a + b + c)^3 - (a^3 +\nb^3 + c^3)$.", "markdown": "Prove that $3(a + b)(a + c)(b + c) = (a + b + c)^3 - (a^3 + b^3 + c^3)$.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/17", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 17", "problem_latex": "How many sevenths in $6xy$?", "markdown": "How many sevenths in $6xy$?", "answer_latex": [ "$42xy$." ], "answer_markdown": [ "$42xy$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "42*x*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/18", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 18", "problem_latex": "Divide $\\displaystyle 2x^5 - \\frac{x^4}{12} +\n2\\frac{3}{4}x^3 - 2x^2 - x$ by $3x^2 + x$.", "markdown": "Divide $\\displaystyle 2x^5 - \\frac{x^4}{12} + 2\\frac{3}{4}x^3 - 2x^2 - x$ by $3x^2 + x$.", "answer_latex": [ "$\\displaystyle \\frac{2x^3}{3} - \\frac{x^2}{4} + x - 1$." ], "answer_markdown": [ "$\\displaystyle \\frac{2x^3}{3} - \\frac{x^2}{4} + x - 1$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*x**5 - x**4/12 + (2 + Rational(3, 4))*x**3 - 2*x**2 - x)/(3*x**2 + x)", "answer_expr": "2*x**3/3 - x**2/4 + x - 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*x**5 - x**4/12 + 11*x**3/4 - 2*x**2 - x)/(3*x**2 + x)" ], "shape": [ "identity: (4*N*x**N - x)/(N*x**N + x)" ], "same_problem_in": [], "needs": [ "cas.pdiv", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/2", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 2", "problem_latex": "Find two numbers whose sum is 100 and whose\ndifference is 10.", "markdown": "Find two numbers whose sum is 100 and whose difference is 10.", "answer_latex": [ "$45$; $55$." ], "answer_markdown": [ "$45$; $55$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 45, y: 55}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a - x, 10), Eq(a + x, 100))" ], "shape": [ "solve: (Eq(a - x, N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/3", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 3", "problem_latex": "Find the G.C.F. of $x^4-1$, $x^5+ x^4-x^3-x^2 + x + 1$, and\n$x^2 - x - 2$.", "markdown": "Find the G.C.F. of $x^4-1$, $x^5+ x^4-x^3-x^2 + x + 1$, and $x^2 - x - 2$.", "answer_latex": [ "$x+1$." ], "answer_markdown": [ "$x+1$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "x + 1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (x**4 - 1, x**2 - x - 2, x**5 + x**4 - x**3 - x**2 + x + 1)" ], "shape": [ "hcf: (x**N - 1, N - x + x**N, x + 1)" ], "same_problem_in": [], "needs": [ "cas.pgcd" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/4a", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 4, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 4a", "problem_latex": "Factor $x^{10} - 14x^5y + 49y^2$, $a^9-b^9$, $3a^2-3a-216$.", "markdown": "Factor $x^{10} - 14x^5y + 49y^2$, $a^9-b^9$, $3a^2-3a-216$.", "answer_latex": [ "$(x^5-7y)^2$" ], "answer_markdown": [ "$(x^5-7y)^2$" ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**10 - 14*x**5*y + 49*y**2", "answer_expr": "(x**5 - 7*y)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 49*a**2 - 14*a*x**5 + x**10" ], "shape": [ "factor: N*a*x**N + N*a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/4b", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 4, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 4b", "problem_latex": "Factor $x^{10} - 14x^5y + 49y^2$, $a^9-b^9$, $3a^2-3a-216$.", "markdown": "Factor $x^{10} - 14x^5y + 49y^2$, $a^9-b^9$, $3a^2-3a-216$.", "answer_latex": [ "$(a-b)(a^2+ab+b^2)(a^6+a^3b^3+b^6)$" ], "answer_markdown": [ "$(a-b)(a^2+ab+b^2)(a^6+a^3b^3+b^6)$" ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a**9 - b**9", "answer_expr": "(a - b)*(a**2 + a*b + b**2)*(a**6 + a**3*b**3 + b**6)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -a**9 + x**9" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/4c", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 4, "part": "c", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 4c", "problem_latex": "Factor $x^{10} - 14x^5y + 49y^2$, $a^9-b^9$, $3a^2-3a-216$.", "markdown": "Factor $x^{10} - 14x^5y + 49y^2$, $a^9-b^9$, $3a^2-3a-216$.", "answer_latex": [ "$3(a-9)(a+8)$." ], "answer_markdown": [ "$3(a-9)(a+8)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "3*a**2 - 3*a - 216", "answer_expr": "3*(a - 9)*(a + 8)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 3*x**2 - 3*x - 216" ], "shape": [ "factor: N*x + N*x**N + N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/5", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 5", "problem_latex": "Reduce $\\displaystyle\n\\frac{(2a+2b)(a^2-b^2)}{(a^2+2ab+b^2)(a-b)}$ to lowest terms.", "markdown": "Reduce $\\displaystyle \\frac{(2a+2b)(a^2-b^2)}{(a^2+2ab+b^2)(a-b)}$ to lowest terms.", "answer_latex": [ "$2$." ], "answer_markdown": [ "$2$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "2*(a + b)*(a**2 - b**2)/((a**2 + 2*a*b + b**2)*(a - b))", "answer_expr": "2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (2*a + 2*x)*(-a**2 + x**2)/((-a + x)*(a**2 + 2*a*x + x**2))" ], "shape": [ "identity: (-a**N + x**N)*(N*a + N*x)/((-a + x)*(N*a*x + a**N + x**N))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/6", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 6", "problem_latex": "Factor $\\displaystyle\n\\frac{16x^4}{a^4b^4}-\\frac{c^4}{81y^4}$.", "markdown": "Factor $\\displaystyle \\frac{16x^4}{a^4b^4}-\\frac{c^4}{81y^4}$.", "answer_latex": [ "$\\displaystyle \n\\left(\\frac{4x^2}{a^2b^2}+\\frac{c^2}{9y^2}\\right)\n \\left(\\frac{2x}{ab}+\\frac{c}{3y}\\right)\n \\left(\\frac{2x}{ab}-\\frac{c}{3y}\\right)$." ], "answer_markdown": [ "$\\displaystyle \\left(\\frac{4x^2}{a^2b^2}+\\frac{c^2}{9y^2}\\right) \\left(\\frac{2x}{ab}+\\frac{c}{3y}\\right) \\left(\\frac{2x}{ab}-\\frac{c}{3y}\\right)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "16*x**4/(a**4*b**4) - c**4/(81*y**4)", "answer_expr": "(4*x**2/(a**2*b**2) + c**2/(9*y**2))*(2*x/(a*b) + c/(3*y))*(2*x/(a*b) - c/(3*y))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -c**4/(81*d**4) + 16*x**4/(a**4*b**4)" ], "shape": [ "factor: N*a**N*b**N*x**N + N*c**N*d**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/7", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 7", "problem_latex": "If $x$ and $y$ stand for the digits of a number of two\nplaces, what will represent the number?", "markdown": "If $x$ and $y$ stand for the digits of a number of two places, what will represent the number?", "answer_latex": [ "$10x+y$." ], "answer_markdown": [ "$10x+y$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "10*x + y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/8", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 8", "problem_latex": "Find the L.C.M. of $a^2-5a + 6$, $a^2-16$, $a^2-9$, $a^2- 7a\n+ 12$, and $a^2 - 4$.", "markdown": "Find the L.C.M. of $a^2-5a + 6$, $a^2-16$, $a^2-9$, $a^2- 7a + 12$, and $a^2 - 4$.", "answer_latex": [ "$(a^2-16)(a^2-9)(a^2-4)$." ], "answer_markdown": [ "$(a^2-16)(a^2-9)(a^2-4)$." ], "checks": [ { "task": "lcm", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "(a**2 - 16)*(a**2 - 9)*(a**2 - 4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "lcm: (x**2 - 16, x**2 - 9, x**2 - 4, x**2 - 7*x + 12, x**2 - 5*x + 6)" ], "shape": [ "lcm: (N + x**N, N + x**N, N + x**N, N*x + N + x**N, N*x + N + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-52/9", "set": "boyden-first-book-in-algebra-1895/ex-52", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 52, problem 9", "problem_latex": "If one picture costs $a$ cents, how many can be bought\nfor $x$ dollars?", "markdown": "If one picture costs $a$ cents, how many can be bought for $x$ dollars?", "answer_latex": [ "$\\displaystyle \\frac{100x}{a}$." ], "answer_markdown": [ "$\\displaystyle \\frac{100x}{a}$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "100*x/a" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/1", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 1", "problem_latex": "$22-6x=34-12x$.", "markdown": "$22-6x=34-12x$.", "answer_latex": [ "$x = 2$." ], "answer_markdown": [ "$x = 2$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(22 - 6*x, 34 - 12*x)", "answer_expr": "2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-6*x + 22, -12*x + 34)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": "X=2", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "34 ENTER 22 −", "ENTER 12 ENTER 6 −", "÷" ], "constants": [ { "value": "12", "source": "the coefficient of x in 34 − 12x; the working moves 12x to the left-hand side and gives 12x − 6x = 34 − 22, so the coefficient difference is 12 − 6" }, { "value": "6", "source": "the coefficient of x in 22 − 6x; the difference 12 − 6 leaves 6x = 12" } ], "calculator_value": "+2E+0", "printed_value": "2", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/10", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 10", "problem_latex": "$21x-57=6x-14x+30$.", "markdown": "$21x-57=6x-14x+30$.", "answer_latex": [ "$x = 3$." ], "answer_markdown": [ "$x = 3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(21*x - 57, 6*x - 14*x + 30)", "answer_expr": "3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(21*x - 57, -8*x + 30)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": "X=3", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "30 ENTER 57 +", "21 ENTER 6 ENTER 14 − −", "÷" ], "constants": [ { "value": "21", "source": "the 21 in 'Solve: 21x-57=6x-14x+30' (coefficient of x on the left)" }, { "value": "57", "source": "the 57 in 'Solve: 21x-57=6x-14x+30' (constant on the left, moved across as +57)" }, { "value": "6", "source": "the 6 in 'Solve: 21x-57=6x-14x+30' (coefficient of x on the right)" }, { "value": "14", "source": "the 14 in 'Solve: 21x-57=6x-14x+30' (coefficient of x on the right, combined with 6)" }, { "value": "30", "source": "the 30 in 'Solve: 21x-57=6x-14x+30' (constant on the right, moved across as +30)" } ], "calculator_value": "+3E+0", "printed_value": "3", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/11", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 11", "problem_latex": "$5x-27-11x+16=98-40x-41$.", "markdown": "$5x-27-11x+16=98-40x-41$.", "answer_latex": [ "$x = 2$." ], "answer_markdown": [ "$x = 2$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(5*x - 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1)*(x + 4)*(x - 2), x*(x - 2)*(x + 2))", "answer_expr": "4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq((x - 2)*(x - 1)*(x + 4), x*(x - 2)*(x + 2))" ], "shape": [ "solve: Eq((N + x)**2*(x - 1), x*(N + x)**2)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.solve.poly", "core.eqn" ], "expectation": "X=4", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/18", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 18", "problem_latex": "$(x-5)(x+3)-(x-7)(x-2)-2(x-1)=-12$.", "markdown": "$(x-5)(x+3)-(x-7)(x-2)-2(x-1)=-12$.", "answer_latex": [ "$x = 3$." ], "answer_markdown": [ "$x = 3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x - 5)*(x + 3) - (x - 7)*(x - 2) - 2*(x - 1), -12)", "answer_expr": "3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-2*x - (x - 7)*(x - 2) + (x - 5)*(x + 3) + 2, -12)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn" ], "expectation": "X=3", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/19", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 19", "problem_latex": "$(x+2)^{2}-(x-1)^{2}=5(2x+3)$.", "markdown": "$(x+2)^{2}-(x-1)^{2}=5(2x+3)$.", "answer_latex": [ "$x = -3$." ], "answer_markdown": [ "$x = -3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x + 2)**2 - (x - 1)**2, 5*(2*x + 3))", "answer_expr": "-3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-(x - 1)**2 + (x + 2)**2, 10*x + 15)" ], "shape": [ "solve: Eq((N + x)**N - (x - 1)**N, N*x + N)" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn" ], "expectation": "X=-3", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/2", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 2", "problem_latex": "$5x-4=10x+ 11$.", "markdown": "$5x-4=10x+ 11$.", "answer_latex": [ "$x = -3$." ], "answer_markdown": [ "$x = -3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(5*x - 4, 10*x + 11)", "answer_expr": "-3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(5*x - 4, 10*x + 11)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": "X=-3", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "11 ENTER 4 +", "5 ENTER 10 − ÷" ], "constants": [ { "value": "4", "source": "the −4 on the left side of 5x − 4 = 10x + 11, moved across as +4" }, { "value": "5", "source": "the coefficient of x on the left side, 5x" }, { "value": "10", "source": "the coefficient of x on the right side, 10x" } ], "calculator_value": "-3E+0", "printed_value": "-3", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/20", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 20", "problem_latex": "$(2x+3)(x+3)-14=(2x+1)(x+1)$.", "markdown": "$(2x+3)(x+3)-14=(2x+1)(x+1)$.", "answer_latex": [ "$x = 1$." ], "answer_markdown": [ "$x = 1$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((2*x + 3)*(x + 3) - 14, (2*x + 1)*(x + 1))", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq((x + 3)*(2*x + 3) - 14, (x + 1)*(2*x + 1))" ], "shape": [ "solve: Eq(N + (N + x)*(N*x + N), (x + 1)*(N*x + 1))" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn" ], "expectation": "X=1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "3 ENTER 3 × 14 −", "1 ENTER 1 × x↔y −", "2 ENTER 3 × 3 +", "2 ENTER 1 × 1 + −", "÷" ], "calculator_value": "+1E+0", "printed_value": "1", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/21", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 21", "problem_latex": "$(x+1)^{2}+(x-5)^{2}=2(x+5)^{2}$.", "markdown": "$(x+1)^{2}+(x-5)^{2}=2(x+5)^{2}$.", "answer_latex": [ "$x = \\frac{6}{7}$." ], "answer_markdown": [ "$x = \\frac{6}{7}$." ], "checks": [ { "task": "solve", "verdict": "FLAG-MISMATCH", "judge_why": "Eq((x - 5)**2 + (x + 1)**2, 2*(x + 5)**2) fails at {x: 6/7}: leaves -48.0000000000", "problem_expr": "Eq((x + 1)**2 + (x - 5)**2, 2*(x + 5)**2)", "answer_expr": "6/7" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "solve: Eq((x - 5)**2 + (x + 1)**2, 2*(x + 5)**2)" ], "shape": [ "solve: Eq((N + x)**N + (x + 1)**N, N*(N + x)**N)" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/22", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 22", "problem_latex": "$7x - 15 + 4x - 6 = 4x - 9 - 9x$.", "markdown": "$7x - 15 + 4x - 6 = 4x - 9 - 9x$.", "answer_latex": [ "$x = \\frac{3}{4}$." ], "answer_markdown": [ "$x = \\frac{3}{4}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(7*x - 15 + 4*x - 6, 4*x - 9 - 9*x)", "answer_expr": "3/4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(11*x - 21, -5*x - 9)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=0.75", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "15 ENTER 6 + 9 −", "7 ENTER 4 + 9 ENTER 4 − +", "÷" ], "calculator_value": "+75E-2", "printed_value": "3/4", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/23", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 23", "problem_latex": "Divide the number 105 into three parts, such that the second\nshall be 5 more than the first, and the third three times the\nsecond.", "markdown": "Divide the number 105 into three parts, such that the second shall be 5 more than the first, and the third three times the second.", "answer_latex": [ "$17$; $22$; $66$." ], "answer_markdown": [ "$17$; $22$; $66$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 17, y: 22, z: 66}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 5), Eq(b, 3*a), Eq(a + b + x, 105))" ], "shape": [ "solve: (Eq(a, N + x), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/24", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 24", "problem_latex": "A man had a certain amount of money; he earned four times as\nmuch the next week, and found \\$30. If he then had seven times as\nmuch as at first, how much had he at first?", "markdown": "A man had a certain amount of money; he earned four times as much the next week, and found $30. If he then had seven times as much as at first, how much had he at first?", "answer_latex": [ "$\\$\\,15$." ], "answer_markdown": [ "$\\$ 15$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x + 4*x + 30, 7*x)", "answer_expr": "15" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(5*x + 30, 7*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": "X=15", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "30 ENTER 7 ENTER 1 ENTER 4 + − ÷" ], "constants": [ { "value": "7", "source": "the 'seven times' in 'he then had seven times as much as at first'" }, { "value": "1", "source": "the x alone in the equation x + 4x + 30 = 7x, i.e. one times the first amount" }, { "value": "4", "source": "the 'four times' in 'he earned four times as much the next week'" }, { "value": "30", "source": "the '$30' he found" } ], "calculator_value": "+15E+0", "printed_value": "15", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/25", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 25", "problem_latex": "How many fourths are there in $7x$?", "markdown": "How many fourths are there in $7x$?", "answer_latex": [ "$28x$ fourths." ], "answer_markdown": [ "$28x$ fourths." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "28*x" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/26", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 26", "problem_latex": "How long will it take a man to build $x$ yards of wall if he\nbuilds $z$ feet a day?", "markdown": "How long will it take a man to build $x$ yards of wall if he builds $z$ feet a day?", "answer_latex": [ "$\\displaystyle \\frac{3x}{z}$ days." ], "answer_markdown": [ "$\\displaystyle \\frac{3x}{z}$ days." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "3*x/z" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/27", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 27", "problem_latex": "$\\displaystyle 6x - \\frac{x + 4}{3} = \\frac{x}{3} + 28$.", "markdown": "$\\displaystyle 6x - \\frac{x + 4}{3} = \\frac{x}{3} + 28$.", "answer_latex": [ "$x = 5\\frac{1}{2}$." ], "answer_markdown": [ "$x = 5\\frac{1}{2}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(6*x - (x + 4)/3, x/3 + 28)", "answer_expr": "11/2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(17*x/3 - 4/3, x/3 + 28)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=5.5", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "3 ENTER 28 ×", "4 +", "6 ENTER 3 × 1 − 1 −", "÷" ], "constants": [ { "value": "1", "source": "the coefficient of x in 'x + 4' and in 'x/3' (the x terms that combine when the x's are moved to one side)" } ], "calculator_value": "+55E-1", "printed_value": "11/2", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/28", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 28", "problem_latex": "$\\displaystyle \\frac{2x - 1}{5} - \\frac{x + 12}{3} -\n4\\frac{4}{5} = \\frac{2x}{3}$.", "markdown": "$\\displaystyle \\frac{2x - 1}{5} - \\frac{x + 12}{3} - 4\\frac{4}{5} = \\frac{2x}{3}$.", "answer_latex": [ "$x = -15$." ], "answer_markdown": [ "$x = -15$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((2*x - 1)/5 - (x + 12)/3 - 24/5, 2*x/3)", "answer_expr": "-15" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x/15 - 9, 2*x/3)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=-15", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "1 ENTER 5 ÷ +/−", "12 ENTER 3 ÷ −", "4 ENTER 5 × 4 + 5 ÷ −", "2 ENTER 5 ÷ 1 ENTER 3 ÷ − 2 ENTER 3 ÷ −", "÷ +/−" ], "constants": [ { "value": "1", "source": "the 1 in '2x − 1' over 5" }, { "value": "5", "source": "the denominator 5 of (2x − 1)/5" }, { "value": "12", "source": "the 12 in '(x + 12)/3'" }, { "value": "3", "source": "the denominator 3 of (x + 12)/3, and of 2x/3" }, { "value": "4", "source": "the whole-number part of 4 4/5" }, { "value": "2", "source": "the 2 in '2x' (first term) and in '2x/3' (right side)" } ], "calculator_value": "-15E+0", "printed_value": "-15", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/29", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 29", "problem_latex": "$\\displaystyle x - \\frac{x}{4} + 25 = \\frac{x}{3} +\n\\frac{x}{2} + 21$.", "markdown": "$\\displaystyle x - \\frac{x}{4} + 25 = \\frac{x}{3} + \\frac{x}{2} + 21$.", "answer_latex": [ "$x = 48$." ], "answer_markdown": [ "$x = 48$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x - x/4 + 25, x/3 + x/2 + 21)", "answer_expr": "48" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(3*x/4 + 25, 5*x/6 + 21)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=48", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "21 ENTER 25 −", "1 ENTER 4 1/x −", "3 1/x −", "2 1/x −", "÷" ], "constants": [ { "value": "1", "source": "the coefficient of x in 'x - x/4' (the bare x), used to form 1 - 1/4 - 1/3 - 1/2" }, { "value": "4", "source": "the denominator in 'x/4'" }, { "value": "3", "source": "the denominator in 'x/3'" }, { "value": "2", "source": "the denominator in 'x/2'" } ], "calculator_value": "+4800000000000000000000000000000002E-32", "printed_value": "48", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/3", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 3", "problem_latex": "$23-8x=80-11x$.", "markdown": "$23-8x=80-11x$.", "answer_latex": [ "$x = 19$." ], "answer_markdown": [ "$x = 19$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(23 - 8*x, 80 - 11*x)", "answer_expr": "19" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-8*x + 23, -11*x + 80)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": "X=19", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "11 ENTER 8 −", "80 ENTER 23 −", "x↔y", "÷" ], "calculator_value": "+19E+0", "printed_value": "19", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/30", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 30", "problem_latex": "$\\displaystyle \\frac{x - 3}{3} + \\frac{5}{21} = -\\frac{x -\n8}{7}$.", "markdown": "$\\displaystyle \\frac{x - 3}{3} + \\frac{5}{21} = -\\frac{x - 8}{7}$.", "answer_latex": [ "$x = 4$." ], "answer_markdown": [ "$x = 4$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x - 3)/3 + 5/21, -(x - 8)/7)", "answer_expr": "4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x/3 - 16/21, -x/7 + 8/7)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=4", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "8 ENTER 3 ×", "21 ENTER 5 − +", "7 ENTER 3 + ÷" ], "constants": [ { "value": "8", "source": "the 8 in '(x − 8)' on the right-hand side" }, { "value": "3", "source": "the 3 in '× 3' (the denominator of '(x − 3)/3') and the 3 in '(x − 3)'; used as the coefficient 3 from moving '−(x − 8)/7' across and multiplying 3(x − 8)" }, { "value": "21", "source": "the denominator 21 of '5/21', used to clear fractions: multiply the equation by 21 and move terms so that 10x = 21 − 5 + 3·8" }, { "value": "5", "source": "the numerator 5 of '5/21'" }, { "value": "7", "source": "the denominator 7 of '−(x − 8)/7'; coefficient of x is 7 + 3 = 10 after clearing fractions" } ], "calculator_value": "+4E+0", "printed_value": "4", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/31", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 31, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 31", "problem_latex": "$\\displaystyle \\frac{8 - 5x}{12} + \\frac{5x - 6}{4} -\n\\frac{7x + 5}{6} = 0$.", "markdown": "$\\displaystyle \\frac{8 - 5x}{12} + \\frac{5x - 6}{4} - \\frac{7x + 5}{6} = 0$.", "answer_latex": [ "$x = -5$." ], "answer_markdown": [ "$x = -5$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((8 - 5*x)/12 + (5*x - 6)/4 - (7*x + 5)/6, 0)", "answer_expr": "-5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-x/3 - 5/3, 0)" ], "shape": [ "solve: Eq(N*x + N, 0)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=-5", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "8 ENTER 12 ÷ 6 ENTER 4 ÷ − 5 ENTER 6 ÷ −", "5 ENTER 4 ÷ 5 ENTER 12 ÷ +/− + 7 ENTER 6 ÷ −", "÷ +/−" ], "calculator_value": "-4999999999999999999999999999999996E-33", "printed_value": "-5", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/32", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 32, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 32", "problem_latex": "$\\displaystyle \\frac{3 + 5x}{4} + \\frac{x + 2}{2} =\n1\\frac{5}{9}$.", "markdown": "$\\displaystyle \\frac{3 + 5x}{4} + \\frac{x + 2}{2} = 1\\frac{5}{9}$.", "answer_latex": [ "$x = -\\frac{1}{9}$." ], "answer_markdown": [ "$x = -\\frac{1}{9}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((3 + 5*x)/4 + (x + 2)/2, 14/9)", "answer_expr": "-1/9" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(7*x/4 + 7/4, 14/9)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X#-0.1111111111111111111111111111111111,1E-30", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/33", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 33, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 33", "problem_latex": "$\\displaystyle \\frac{2x - 1}{3} - \\frac{13}{42} = \\frac{5x -\n4}{6}$.", "markdown": "$\\displaystyle \\frac{2x - 1}{3} - \\frac{13}{42} = \\frac{5x - 4}{6}$.", "answer_latex": [ "$x = \\frac{1}{7}$." ], "answer_markdown": [ "$x = \\frac{1}{7}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((2*x - 1)/3 - 13/42, (5*x - 4)/6)", "answer_expr": "1/7" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(2*x/3 - 9/14, 5*x/6 - 2/3)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X#0.1428571428571428571428571428571429,1E-30", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "1 ENTER 3 ÷ 13 ENTER 42 ÷ −", "2 ENTER 3 ÷ 5 ENTER 6 ÷ −", "÷ +/−" ], "calculator_value": "+1428571428571428571428571428571429E-34", "printed_value": "1/7", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/34", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 34, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 34", "problem_latex": "$\\displaystyle \\frac{1 - 11x}{7} - \\frac{7x}{13} =\n\\frac{2}{13} - \\frac{8x - 15}{3}$.", "markdown": "$\\displaystyle \\frac{1 - 11x}{7} - \\frac{7x}{13} = \\frac{2}{13} - \\frac{8x - 15}{3}$.", "answer_latex": [ "$x = 9$." ], "answer_markdown": [ "$x = 9$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((1 - 11*x)/7 - 7*x/13, 2/13 - (8*x - 15)/3)", "answer_expr": "9" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-192*x/91 + 1/7, -8*x/3 + 67/13)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=9", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "2 ENTER 13 ÷ 15 ENTER 3 ÷ + 1 ENTER 7 ÷ −", "8 ENTER 3 ÷ 11 ENTER 7 ÷ − 7 ENTER 13 ÷ −", "÷" ], "calculator_value": "+8999999999999999999999999999999988E-33", "printed_value": "9", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/35", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 35, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 35", "problem_latex": "$\\displaystyle \\frac{2}{x}-\\frac{3}{2x} =\n\\frac{7}{24}-\\frac{2}{3x}$.", "markdown": "$\\displaystyle \\frac{2}{x}-\\frac{3}{2x} = \\frac{7}{24}-\\frac{2}{3x}$.", "answer_latex": [ "$x = 4$." ], "answer_markdown": [ "$x = 4$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(2/x - 3/(2*x), 7/24 - 2/(3*x))", "answer_expr": "4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(1/(2*x), 7/24 - 2/(3*x))" ], "shape": [ "solve: Eq(N/x, N + N/x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=4", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "24 ENTER 2 ×", "24 ENTER 3 × 2 ÷ −", "24 ENTER 2 × 3 ÷ +", "7 ÷" ], "constants": [ { "value": "24", "source": "the 24 in the denominator of 7/24 (multiplying both sides by 24x clears the denominators)" }, { "value": "2", "source": "the 2 in 2/x, and the 2 in 3/(2x)" }, { "value": "3", "source": "the 3 in 3/(2x), and the 3 in 2/(3x)" }, { "value": "7", "source": "the 7 in the numerator of 7/24; after multiplying by 24x the equation reads 48 − 36 + 16 = 7x" } ], "calculator_value": "+4E+0", "printed_value": "4", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/36", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 36, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 36", "problem_latex": "$\\displaystyle \\frac{1}{4}+\\frac{1}{3x} =\n\\frac{11}{36}+\\frac{1}{6x}$.", "markdown": "$\\displaystyle \\frac{1}{4}+\\frac{1}{3x} = \\frac{11}{36}+\\frac{1}{6x}$.", "answer_latex": [ "$x = 3$." ], "answer_markdown": [ "$x = 3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(1/4 + 1/(3*x), 11/36 + 1/(6*x))", "answer_expr": "3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(1/4 + 1/(3*x), 11/36 + 1/(6*x))" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=3", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "11 ENTER 36 ÷ 1 ENTER 4 ÷ −", "1/x", "6 ÷" ], "calculator_value": "+2999999999999999999999999999999998E-33", "printed_value": "3", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/37", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 37, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 37", "problem_latex": "$\\displaystyle\n\\frac{3}{4x}-\\frac{2}{x}+\\frac{x-2}{2x}+7\\frac{5}{12} =\n5+\\frac{4}{6x}$.", "markdown": "$\\displaystyle \\frac{3}{4x}-\\frac{2}{x}+\\frac{x-2}{2x}+7\\frac{5}{12} = 5+\\frac{4}{6x}$.", "answer_latex": [ "$x = 1$." ], "answer_markdown": [ "$x = 1$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(3/(4*x) - 2/x + (x - 2)/(2*x) + 89/12, 5 + 4/(6*x))", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(89/12 + (x - 2)/(2*x) - 5/(4*x), 5 + 2/(3*x))" ], "shape": [ "solve: Eq(N + N*(N + x)/x + N/x, N + N/x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "4 ENTER 12 × 6 ÷", "2 ENTER 12 × +", "12 +", "3 ENTER 12 × 4 ÷ −", "7 ENTER 12 × 5 +", "12 ENTER 2 ÷ +", "12 ENTER 5 × −", "÷" ], "constants": [ { "value": "4", "source": "the 4 in 4/(6x) and the 4 in 3/(4x)" }, { "value": "6", "source": "the 6 in 4/(6x)" }, { "value": "12", "source": "the 12 in 5 5/12 (common denominator), used to multiply both sides by 12x" }, { "value": "2", "source": "the 2 in -2/x and the 2 in (x-2)/(2x)" }, { "value": "3", "source": "the 3 in 3/(4x)" }, { "value": "7", "source": "the 7 in the whole number part of 7 5/12" }, { "value": "5", "source": "the 5 in 7 5/12 (the numerator of the fraction part) and the 5 on the right side" } ], "calculator_value": "+1E+0", "printed_value": "1", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/38", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 38, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 38", "problem_latex": "$\\displaystyle \\frac{2x+3}{5x}-\\frac{3}{x}+4 =\n\\frac{1}{2x}+\\frac{3}{4x}+2\\frac{23}{40}$.", "markdown": "$\\displaystyle \\frac{2x+3}{5x}-\\frac{3}{x}+4 = \\frac{1}{2x}+\\frac{3}{4x}+2\\frac{23}{40}$.", "answer_latex": [ "$x = 2$." ], "answer_markdown": [ "$x = 2$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((2*x + 3)/(5*x) - 3/x + 4, 1/(2*x) + 3/(4*x) + 103/40)", "answer_expr": "2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(4 + (2*x + 3)/(5*x) - 3/x, 103/40 + 5/(4*x))" ], "shape": [ "solve: Eq(N + N*(N*x + N)/x + N/x, N + N/x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=2", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "1 ENTER 2 ÷ 3 ENTER 4 ÷ + 3 + 3 ENTER 5 ÷ −", "ENTER 2 ENTER 5 ÷ 4 + 103 ENTER 40 ÷ − ÷" ], "constants": [ { "value": "1", "source": "the 1 in '1/(2x)' on the right-hand side" }, { "value": "2", "source": "the 2 in '2x' and '1/(2x)' and '2 23/40' (also the 2 in the constant 2x-coefficient 2/5)" }, { "value": "3", "source": "the 3 in '3/(4x)' and the 3 in '(2x+3)' on the left-hand side" }, { "value": "4", "source": "the 4 in '3/(4x)' on the right-hand side, and the 4 in '+4' on the left-hand side" }, { "value": "5", "source": "the 5 in '5x' in the denominator on the left-hand side" }, { "value": "103", "source": "the working: 2 23/40 = 103/40 (2 x 40 + 23), as in the SymPy expression 103/40" }, { "value": "40", "source": "the 40 in '2 23/40' (the denominator of the mixed number), giving 103/40" } ], "calculator_value": "+2E+0", "printed_value": "2", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/39", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 39, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 39", "problem_latex": "$\\displaystyle \\frac{x+9}{11}-\\frac{2-x}{5} =\n\\frac{x+5}{7}$.", "markdown": "$\\displaystyle \\frac{x+9}{11}-\\frac{2-x}{5} = \\frac{x+5}{7}$.", "answer_latex": [ "$x = 2$." ], "answer_markdown": [ "$x = 2$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x + 9)/11 - (2 - x)/5, (x + 5)/7)", "answer_expr": "2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(16*x/55 + 23/55, x/7 + 5/7)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=2", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "1 ENTER 11 ÷ 1 ENTER 5 ÷ + 1 ENTER 7 ÷ −", "1/x", "5 ENTER 7 ÷ 2 ENTER 5 ÷ + 9 ENTER 11 ÷ −", "×" ], "constants": [ { "value": "1", "source": "the coefficient of x in 'x+9' and '2-x' (the x terms carry a 1 each), used as the numerator of each reciprocal" }, { "value": "11", "source": "the denominator of (x+9)/11 in the problem" }, { "value": "5", "source": "the denominator of (2-x)/5 in the problem" }, { "value": "7", "source": "the denominator of (x+5)/7 in the problem" }, { "value": "2", "source": "the 2 in '2-x' in the problem" }, { "value": "9", "source": "the 9 in 'x+9' in the problem" } ], "calculator_value": "+1999999999999999999999999999999999E-33", "printed_value": "2", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/4", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 4", "problem_latex": "$5x-21=7x + 5$.", "markdown": "$5x-21=7x + 5$.", "answer_latex": [ "$x = -13$." ], "answer_markdown": [ "$x = -13$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(5*x - 21, 7*x + 5)", "answer_expr": "-13" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(5*x - 21, 7*x + 5)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": "X=-13", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "5 ENTER 7 −", "5 ENTER 21 +/− −", "x↔y", "÷" ], "constants": [ { "value": "5", "source": "the 5 in 5x (coefficient of x on the left side)" }, { "value": "7", "source": "the 7 in 7x (coefficient of x on the right side)" }, { "value": "21", "source": "the 21 in 5x − 21 (constant term on the left, moved across as +21)" }, { "value": "5", "source": "the 5 in 7x + 5 (constant term on the right); used as 5 − (−21) = 26 for the numerator" } ], "calculator_value": "-13E+0", "printed_value": "-13", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/40", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 40, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 40", "problem_latex": "$\\displaystyle \\frac{x+4}{5}-\\frac{4-x}{7} = \\frac{x+1}{3}$.", "markdown": "$\\displaystyle \\frac{x+4}{5}-\\frac{4-x}{7} = \\frac{x+1}{3}$.", "answer_latex": [ "$x = 11$." ], "answer_markdown": [ "$x = 11$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x + 4)/5 - (4 - x)/7, (x + 1)/3)", "answer_expr": "11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(12*x/35 + 8/35, x/3 + 1/3)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=11", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "7 ENTER 3 × 4 ×", "5 ENTER 3 × 4 × −", "5 ENTER 7 × x↔y −" ], "constants": [ { "value": "7", "source": "the 7 in the denominator of (4 − x)/7" }, { "value": "3", "source": "the 3 in the denominator of (x + 1)/3" }, { "value": "4", "source": "the 4 in the numerator x + 4" }, { "value": "5", "source": "the 5 in the denominator of (x + 4)/5" } ], "calculator_value": "+11E+0", "printed_value": "11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/41", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 41, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 41", "problem_latex": "$\\displaystyle \\frac{2}{5}(x-6)-\\frac{3}{16}(x-1) =\n\\frac{5}{12}(4-x)-\\frac{5}{48}$.", "markdown": "$\\displaystyle \\frac{2}{5}(x-6)-\\frac{3}{16}(x-1) = \\frac{5}{12}(4-x)-\\frac{5}{48}$.", "answer_latex": [ "$x = 6$." ], "answer_markdown": [ "$x = 6$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(2/5*(x - 6) - 3/16*(x - 1), 5/12*(4 - x) - 5/48)", "answer_expr": "6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(17*x/80 - 177/80, -5*x/12 + 25/16)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=6", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "5 ENTER 12 ÷ 4 × 5 ENTER 48 ÷ − 2 ENTER 5 ÷ 6 × + 3 ENTER 16 ÷ −", "2 ENTER 5 ÷ 3 ENTER 16 ÷ − 5 ENTER 12 ÷ + ÷" ], "calculator_value": "+6000000000000000000000000000000000E-33", "printed_value": "6", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/42", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 42, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 42", "problem_latex": "$\\displaystyle \\frac{4+x}{4}-\\frac{1-x}{7}-\\frac{1}{5}(8-x)\n= \\frac{x-23}{5}+7$.", "markdown": "$\\displaystyle \\frac{4+x}{4}-\\frac{1-x}{7}-\\frac{1}{5}(8-x) = \\frac{x-23}{5}+7$.", "answer_latex": [ "$x = 8$." ], "answer_markdown": [ "$x = 8$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((4 + x)/4 - (1 - x)/7 - (8 - x)/5, (x - 23)/5 + 7)", "answer_expr": "8" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(83*x/140 - 26/35, x/5 + 12/5)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=8", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/43", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 43, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 43", "problem_latex": "How long will it take a man to walk $x$ miles if he walks 15\nmiles in $b$ hours?", "markdown": "How long will it take a man to walk $x$ miles if he walks 15 miles in $b$ hours?", "answer_latex": [ "$\\displaystyle \\frac{bx}{15}$ hrs." ], "answer_markdown": [ "$\\displaystyle \\frac{bx}{15}$ hrs." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "b*x/15" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/44", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 44, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 44", "problem_latex": "What is the interest on $m$ dollars for one year at 5 per\ncent?", "markdown": "What is the interest on $m$ dollars for one year at 5 per cent?", "answer_latex": [ "$\\displaystyle \\frac{5m}{100}$ dols." ], "answer_markdown": [ "$\\displaystyle \\frac{5m}{100}$ dols." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "5*m/100" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/45", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 45, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 45", "problem_latex": "What are the two numbers whose sum is 57, and whose\ndifference is 25?", "markdown": "What are the two numbers whose sum is 57, and whose difference is 25?", "answer_latex": [ "$16$; $41$." ], "answer_markdown": [ "$16$; $41$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 41, y: 16}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(-a + x, 25), Eq(a + x, 57))" ], "shape": [ "solve: (Eq(-a + x, N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/46", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 46, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 46", "problem_latex": "What is the interest on $b$ dollars for $y$ years at 4 per\ncent?", "markdown": "What is the interest on $b$ dollars for $y$ years at 4 per cent?", "answer_latex": [ "$\\displaystyle \\frac{4by}{100}$ dols." ], "answer_markdown": [ "$\\displaystyle \\frac{4by}{100}$ dols." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "4*b*y/100" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.frac", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/47", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 47, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 47", "problem_latex": "$(c+a)x+(c-b)x = c^2$.", "markdown": "$(c+a)x+(c-b)x = c^2$.", "answer_latex": [ "$\\displaystyle x = \\frac{c^2}{ a - b + 2c }$." ], "answer_markdown": [ "$\\displaystyle x = \\frac{c^2}{ a - b + 2c }$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((c + a)*x + (c - b)*x, c**2)", "answer_expr": "c**2/(a - b + 2*c)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x*(a + c) + x*(-b + c), c**2)" ], "shape": [ "solve: Eq(x*(a + c) + x*(-b + c), c**N)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/48", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 48, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 48", "problem_latex": "$(a-b)x+(a+b)x = a$.", "markdown": "$(a-b)x+(a+b)x = a$.", "answer_latex": [ "$x = \\frac{1}{2}$." ], "answer_markdown": [ "$x = \\frac{1}{2}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((a - b)*x + (a + b)*x, a)", "answer_expr": "1/2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x*(a - b) + x*(a + b), a)" ], "shape": [ "solve: Eq(x*(a - b) + x*(a + b), a)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.solve.poly" ], "expectation": "X=0.5", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/49", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 49, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 49", "problem_latex": "$2x+a(x-2) = a+6$.", "markdown": "$2x+a(x-2) = a+6$.", "answer_latex": [ "$x = 3$." ], "answer_markdown": [ "$x = 3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(2*x + a*(x - 2), a + 6)", "answer_expr": "3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(a*(x - 2) + 2*x, a + 6)" ], "shape": [ "solve: Eq(N*x + a*(N + x), N + a)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.solve.poly" ], "expectation": "X=3", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/5", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 5", "problem_latex": "$18x-43=17-6x$.", "markdown": "$18x-43=17-6x$.", "answer_latex": [ "$x = 2\\frac{1}{2}$." ], "answer_markdown": [ "$x = 2\\frac{1}{2}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(18*x - 43, 17 - 6*x)", "answer_expr": "5/2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(18*x - 43, -6*x + 17)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=2.5", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "17 ENTER 43 +", "18 ENTER 6 +", "÷" ], "calculator_value": "+25E-1", "printed_value": "5/2", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/50", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 50, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 50", "problem_latex": "$b(2x-a)-a^2 = 2x(a+b)-3ab$.", "markdown": "$b(2x-a)-a^2 = 2x(a+b)-3ab$.", "answer_latex": [ "$\\displaystyle x = \\frac{2b - 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1, 2*(19 + x)/(x + 12))", "answer_expr": "2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-1 + (6*x + 8)/(2*x + 1), (2*x + 38)/(x + 12))" ], "shape": [ "solve: Eq(-1 + (N*x + N)/(N*x + 1), (N*x + N)/(N + x))" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn", "core.frac" ], "expectation": "X=2", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/6", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 6", "problem_latex": "$18-8x=12x- 87$.", "markdown": "$18-8x=12x- 87$.", "answer_latex": [ "$x = 5\\frac{1}{4}$." ], "answer_markdown": [ "$x = 5\\frac{1}{4}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(18 - 8*x, 12*x - 87)", "answer_expr": "21/4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-8*x + 18, 12*x - 87)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=5.25", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "18 ENTER 87 +", "8 ENTER 12 +", "÷" ], "calculator_value": "+525E-2", "printed_value": "21/4", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/60", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 60, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 60", "problem_latex": "$\\displaystyle 1-\\frac{x}{x+2}=\\frac{4}{x+6}$.", "markdown": "$\\displaystyle 1-\\frac{x}{x+2}=\\frac{4}{x+6}$.", "answer_latex": [ "$x = 2$." ], "answer_markdown": [ "$x = 2$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(1 - x/(x + 2), 4/(x + 6))", "answer_expr": "2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-x/(x + 2) + 1, 4/(x + 6))" ], "shape": [ "solve: Eq(-x/(N + x) + 1, N/(N + x))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=2", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "4 ENTER 2 × 2 ENTER 6 × −", "2 ENTER 4 − ÷" ], "constants": [ { "value": "2", "source": "the 2 in 'x + 2' and the 2 in '4 × 2': after clearing denominators, 4(x + 2) = 4x + 8, so 4 × 2 gives the constant 8" }, { "value": "6", "source": "the 6 in 'x + 6': (x + 2)(x + 6) − x(x + 6) = 2(x + 6) = 2x + 12, so 2 × 6 gives the constant 12" }, { "value": "4", "source": "the 4 in '4/(x + 6)' and the 4 in '4(x + 2)': the right side becomes 4x + 8" } ], "calculator_value": "+2E+0", "printed_value": "2", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/61", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 61, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 61", "problem_latex": "$\\displaystyle\n\\frac{x^2}{1-x^2}+\\frac{x+1}{x-1}=\\frac{3}{x+1}$.", "markdown": "$\\displaystyle \\frac{x^2}{1-x^2}+\\frac{x+1}{x-1}=\\frac{3}{x+1}$.", "answer_latex": [ "$x = 4$." ], "answer_markdown": [ "$x = 4$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x**2/(1 - x**2) + (x + 1)/(x - 1), 3/(x + 1))", "answer_expr": "4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x**2/(-x**2 + 1) + (x + 1)/(x - 1), 3/(x + 1))" ], "shape": [ "solve: Eq(x**N/(-x**N + 1) + (x + 1)/(x - 1), N/(x + 1))" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn", "core.frac" ], "expectation": "X=4", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/62", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 62, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 62", "problem_latex": "$\\displaystyle \\frac{2+3x}{1-x}+5=\\frac{2x-4}{x+2}$.", "markdown": "$\\displaystyle \\frac{2+3x}{1-x}+5=\\frac{2x-4}{x+2}$.", "answer_latex": [ "$x = 6$." ], "answer_markdown": [ "$x = 6$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((2 + 3*x)/(1 - x) + 5, (2*x - 4)/(x + 2))", "answer_expr": "6" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(5 + (3*x + 2)/(-x + 1), (2*x - 4)/(x + 2))" ], "shape": [ "solve: Eq(N + (N*x + N)/(-x + 1), (N*x + N)/(N + x))" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn", "core.frac" ], "expectation": "X=6", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/63", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 63, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 63", "problem_latex": "$\\displaystyle\n\\frac{5}{6+2x}+\\frac{2}{x+1}=\\frac{2\\frac{1}{2}}{2+2x}+\\frac{4}{3+x}$.", "markdown": "$\\displaystyle \\frac{5}{6+2x}+\\frac{2}{x+1}=\\frac{2\\frac{1}{2}}{2+2x}+\\frac{4}{3+x}$.", "answer_latex": [ "$x = 1$." ], "answer_markdown": [ "$x = 1$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(5/(6 + 2*x) + 2/(x + 1), (5/2)/(2 + 2*x) + 4/(3 + x))", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(5/(2*x + 6) + 2/(x + 1), 5/(2*(2*x + 2)) + 4/(x + 3))" ], "shape": [ "solve: Eq(N/(N*x + N) + N/(x + 1), N/(N*x + N) + N/(N + x))" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn", "core.frac" ], "expectation": "X=1", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/64", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 64, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 64", "problem_latex": "$\\displaystyle\n\\frac{2(1-2x)}{1-3x}+\\frac{1}{6}=\\frac{1-3x}{1-2x}$.", "markdown": "$\\displaystyle \\frac{2(1-2x)}{1-3x}+\\frac{1}{6}=\\frac{1-3x}{1-2x}$.", "answer_latex": [ "$x = \\frac{7}{17}$." ], "answer_markdown": [ "$x = \\frac{7}{17}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(2*(1 - 2*x)/(1 - 3*x) + 1/6, (1 - 3*x)/(1 - 2*x))", "answer_expr": "7/17" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(1/6 + (-4*x + 2)/(-3*x + 1), (-3*x + 1)/(-2*x + 1))" ], "shape": [ "solve: Eq(N + (N*x + N)/(N*x + 1), 1)" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn", "core.frac" ], "expectation": "X#0.4117647058823529411764705882352941,1E-30", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/65", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 65, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 65", "problem_latex": "$\\displaystyle\n\\frac{x-8}{x-6}-\\frac{x}{x-2}=\\frac{x-9}{x-7}-\\frac{x+1}{x-1}$.", "markdown": "$\\displaystyle \\frac{x-8}{x-6}-\\frac{x}{x-2}=\\frac{x-9}{x-7}-\\frac{x+1}{x-1}$.", "answer_latex": [ "$x = 4$." ], "answer_markdown": [ "$x = 4$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x - 8)/(x - 6) - x/(x - 2), (x - 9)/(x - 7) - (x + 1)/(x - 1))", "answer_expr": "4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-x/(x - 2) + (x - 8)/(x - 6), (x - 9)/(x - 7) - (x + 1)/(x - 1))" ], "shape": [ "solve: Eq(-x/(N + x) + 1, 1 - (x + 1)/(x - 1))" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn", "core.frac" ], "expectation": "X=4", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/66", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 66, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 66", "problem_latex": "$\\displaystyle \\frac{x+5}{x+8} -\n\\frac{x+6}{x+9}=\\frac{x+2}{x+5}-\\frac{x+3}{x+6}$.", "markdown": "$\\displaystyle \\frac{x+5}{x+8} - \\frac{x+6}{x+9}=\\frac{x+2}{x+5}-\\frac{x+3}{x+6}$.", "answer_latex": [ "$x = -7$." ], "answer_markdown": [ "$x = -7$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x + 5)/(x + 8) - (x + 6)/(x + 9), (x + 2)/(x + 5) - (x + 3)/(x + 6))", "answer_expr": "-7" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq((x + 5)/(x + 8) - (x + 6)/(x + 9), (x + 2)/(x + 5) - (x + 3)/(x + 6))" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn", "core.frac" ], "expectation": "X=-7", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/67", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 67, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 67", "problem_latex": "Find three consecutive numbers whose sum is 81.", "markdown": "Find three consecutive numbers whose sum is 81.", "answer_latex": [ "$26$; $27$; $28$." ], "answer_markdown": [ "$26$; $27$; $28$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 26}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*x + 3, 81)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "81 ENTER 1 ENTER 2 + −", "3 ÷" ], "constants": [ { "value": "3", "source": "the 'three' in 'Find three consecutive numbers' (the coefficient of x in 3x + 3)" }, { "value": "1", "source": "the +1 in 'x + 1' in the expression Eq(x + (x + 1) + (x + 2), 81)" }, { "value": "2", "source": "the +2 in 'x + 2' in the expression Eq(x + (x + 1) + (x + 2), 81)" } ], "calculator_value": "+26E+0", "printed_value": "26", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/68", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 68, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 68", "problem_latex": "A's\nage is double B's, B's is three times C's, and C is $y$ years old.\nWhat is A's age?", "markdown": "A’s age is double B’s, B’s is three times C’s, and C is $y$ years old. What is A’s age?", "answer_latex": [ "$6y$ years." ], "answer_markdown": [ "$6y$ years." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "6*y" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/69", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 69, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 69", "problem_latex": "How many men will be required to do in $a$ hours what $x$\nmen do in 6 hours?", "markdown": "How many men will be required to do in $a$ hours what $x$ men do in 6 hours?", "answer_latex": [ "$\\displaystyle \\frac{6x}{a}$ men." ], "answer_markdown": [ "$\\displaystyle \\frac{6x}{a}$ men." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(n*a, 6*x)", "answer_expr": "6*x/a" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(a*x, 6*b)" ], "shape": [ "solve: Eq(a*x, N*b)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/7", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 7", "problem_latex": "$9x-(2x-5)=4x+(13 + x)$.", "markdown": "$9x-(2x-5)=4x+(13 + x)$.", "answer_latex": [ "$x = 4$." ], "answer_markdown": [ "$x = 4$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(9*x - (2*x - 5), 4*x + (13 + x))", "answer_expr": "4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(7*x + 5, 5*x + 13)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": "X=4", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "13 ENTER 5 −", "9 ENTER 2 − 4 − 1 −", "÷" ], "constants": [ { "value": "13", "source": "the 13 in '+ (13 + x)' on the right side" }, { "value": "5", "source": "the 5 in '− (2x − 5)' on the left side" }, { "value": "9", "source": "the coefficient 9 of x in '9x'" }, { "value": "2", "source": "the coefficient 2 of x in '(2x − 5)', subtracted from 9x" }, { "value": "4", "source": "the coefficient 4 of x in '4x' on the right side, moved to the left" }, { "value": "1", "source": "the bare x in '+ x' on the right side, which has coefficient 1, moved to the left" } ], "calculator_value": "+4E+0", "printed_value": "4", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/70", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 70, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 70", "problem_latex": "Find the sum of three consecutive odd numbers of which the\nmiddle one is $4x + 1$.", "markdown": "Find the sum of three consecutive odd numbers of which the middle one is $4x + 1$.", "answer_latex": [ "$12x + 3$." ], "answer_markdown": [ "$12x + 3$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": "12*x + 3" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/8", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 8", "problem_latex": "$15x-2(5x-4)-39 = 0$.", "markdown": "$15x-2(5x-4)-39 = 0$.", "answer_latex": [ "$x = 6\\frac{1}{5}$." ], "answer_markdown": [ "$x = 6\\frac{1}{5}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(15*x - 2*(5*x - 4) - 39, 0)", "answer_expr": "31/5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(5*x - 31, 0)" ], "shape": [ "solve: Eq(N*x + N, 0)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": "X=6.2", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "39 ENTER 2 ENTER 4 × −", "15 ENTER 2 ENTER 5 × − ÷" ], "constants": [ { "value": "39", "source": "the 39 in '15x-2(5x-4)-39 = 0'" }, { "value": "2", "source": "the 2 in '-2(5x-4)'; the working 2(5x-4) = 10x - 8 gives the 8 as 2 × 4" }, { "value": "4", "source": "the 4 in '(5x-4)' inside -2(...); the constant term -2 × (-4) = +8" }, { "value": "15", "source": "the 15 in '15x'" }, { "value": "5", "source": "the 5 in '(5x-4)'; the working 15x - 10x = 5x uses 2 × 5 = 10" } ], "calculator_value": "+62E-1", "printed_value": "31/5", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-53/9", "set": "boyden-first-book-in-algebra-1895/ex-53", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 53, problem 9", "problem_latex": "$12x-18x+17=8x+3$.", "markdown": "$12x-18x+17=8x+3$.", "answer_latex": [ "$x = 1$." ], "answer_markdown": [ "$x = 1$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(12*x - 18*x + 17, 8*x + 3)", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-6*x + 17, 8*x + 3)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": "X=1", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "3 ENTER 17 −", "12 ENTER 18 − 8 −", "÷" ], "calculator_value": "+1E+0", "printed_value": "1", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/1", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 1", "problem_latex": "In a school of 836 pupils there is one boy to every\nthree girls. How many are there of each?", "markdown": "In a school of 836 pupils there is one boy to every three girls. How many are there of each?", "answer_latex": [ "$209$ boys; $627$ girls." ], "answer_markdown": [ "$209$ boys; $627$ girls." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "b": "209", "g": "627" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 3*x), Eq(a + x, 836))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/10", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 10", "problem_latex": "If I add 18 to a certain number, five times this\nsecond number will equal eleven times the original number.\nWhat is the original number?", "markdown": "If I add 18 to a certain number, five times this second number will equal eleven times the original number. What is the original number?", "answer_latex": [ "$15$." ], "answer_markdown": [ "$15$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(5*(x+18),11*x)", "answer_expr": { "x": "15" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(5*x + 90, 11*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/11", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 11", "problem_latex": "In a mixture of 48 pounds of coffee there is one-third\nas much Mocha as Java. How much is there of\neach?", "markdown": "In a mixture of 48 pounds of coffee there is one-third as much Mocha as Java. How much is there of each?", "answer_latex": [ "$12$ M.; $36$ J." ], "answer_markdown": [ "$12$ M.; $36$ J." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "J": "36", "M": "12" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, a/3), Eq(a + x, 48))" ], "shape": [ "solve: (Eq(x, N*a), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/12", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 12", "problem_latex": "The half and fifth of a number are together equal to\n56. What is the number?", "markdown": "The half and fifth of a number are together equal to 56. What is the number?", "answer_latex": [ "$80$." ], "answer_markdown": [ "$80$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x/2+x/5,56)", "answer_expr": { "x": "80" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(7*x/10, 56)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/13", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 13", "problem_latex": "What number increased by one-third and one-fourth\nof itself, and 7 more, equals 45?", "markdown": "What number increased by one-third and one-fourth of itself, and 7 more, equals 45?", "answer_latex": [ "$24$." ], "answer_markdown": [ "$24$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x+x/3+x/4+7,45)", "answer_expr": { "x": "24" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(19*x/12 + 7, 45)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/14", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 14", "problem_latex": "What number is doubled by adding to it three-eighths\nof itself, one-third of itself, and 14?", "markdown": "What number is doubled by adding to it three-eighths of itself, one-third of itself, and 14?", "answer_latex": [ "$48$." ], "answer_markdown": [ "$48$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x+3*x/8+x/3+14,2*x)", "answer_expr": { "x": "48" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(41*x/24 + 14, 2*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/15", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 15", "problem_latex": "A grocer sold 27 pounds of sugar, tea, and meal.\nOf meal he sold 3 pounds more than of tea, and of sugar\n6 pounds more than of meal. How many pounds of each\ndid he sell?", "markdown": "A grocer sold 27 pounds of sugar, tea, and meal. Of meal he sold 3 pounds more than of tea, and of sugar 6 pounds more than of meal. How many pounds of each did he sell?", "answer_latex": [ "t., $5$ lbs.; m., $8$ lbs.; s., $14$ lbs." ], "answer_markdown": [ "t., $5$ lbs.; m., $8$ lbs.; s., $14$ lbs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "m": "8", "s": "14", "t": "5" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, x + 3), Eq(b, a + 6), Eq(a + b + x, 27))" ], "shape": [ "solve: (Eq(a, N + x), Eq(b, N + a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/16", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 16", "problem_latex": "A son is two-sevenths as old as his father. If the\nsum of their ages is 45 years, how old is each?", "markdown": "A son is two-sevenths as old as his father. If the sum of their ages is 45 years, how old is each?", "answer_latex": [ "$35$; $10$ yrs." ], "answer_markdown": [ "$35$; $10$ yrs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "f": "35", "s": "10" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, 2*x/7), Eq(a + x, 45))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/17", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 17", "problem_latex": "Two men invest \\$2990 in business, one putting in\nfour-ninths as much as the other. How much does each\ninvest?", "markdown": "Two men invest $2990 in business, one putting in four-ninths as much as the other. How much does each invest?", "answer_latex": [ "\\$2070, \\$920." ], "answer_markdown": [ "$2070, $920." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "a": "2070", "b": "920" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 4*x/9), Eq(a + x, 2990))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/18", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 18", "problem_latex": "In an election 47,519 votes were cast for three candidates.\nOne candidate received 2061 votes less, and the\nother 1546 votes less, than the winning candidate. How\nmany votes did each receive?", "markdown": "In an election 47,519 votes were cast for three candidates. One candidate received 2061 votes less, and the other 1546 votes less, than the winning candidate. How many votes did each receive?", "answer_latex": [ "$17,042$; $14,981$; $15,496$." ], "answer_markdown": [ "$17,042$; $14,981$; $15,496$." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "s": "14981", "t": "15496", "w": "17042" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, x - 2061), Eq(b, x - 1546), Eq(a + b + x, 47519))" ], "shape": [ "solve: (Eq(a, N + x), Eq(b, N + x), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/19", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 19", "problem_latex": "John had twice as many stamps as Ralph, but after\nhe had bought 65, and Ralph had lost 16, they found that\nthey had together 688. How many had each at first?", "markdown": "John had twice as many stamps as Ralph, but after he had bought 65, and Ralph had lost 16, they found that they had together 688. How many had each at first?", "answer_latex": [ "R., $213$; J., $426$." ], "answer_markdown": [ "R., $213$; J., $426$." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "J": "426", "R": "213" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(a + x + 49, 688))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N + a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/2", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 2", "problem_latex": "Divide 253 into three parts, so that the first part shall\nbe four times the second, and the second twice the third.", "markdown": "Divide 253 into three parts, so that the first part shall be four times the second, and the second twice the third.", "answer_latex": [ "$184$; $46$; $23$." ], "answer_markdown": [ "$184$; $46$; $23$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "x": "184", "y": "46", "z": "23" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 4*a), Eq(a, 2*b), Eq(a + b + x, 253))" ], "shape": [ "solve: (Eq(x, N*a), Eq(a, N*b), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/20", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 20", "problem_latex": "Find three consecutive numbers whose sum is 192.", "markdown": "Find three consecutive numbers whose sum is 192.", "answer_latex": [ "$63$; $64$; $65$." ], "answer_markdown": [ "$63$; $64$; $65$." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "a": "63", "b": "64", "c": "65" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, x + 1), Eq(b, a + 1), Eq(a + b + x, 192))" ], "shape": [ "solve: (Eq(a, x + 1), Eq(b, a + 1), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/21", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 21", "problem_latex": "If 17 be added to the sum of two numbers whose\ndifference is 12, the result will be 61. What are the\nnumbers?", "markdown": "If 17 be added to the sum of two numbers whose difference is 12, the result will be 61. What are the numbers?", "answer_latex": [ "$16$; $28$." ], "answer_markdown": [ "$16$; $28$." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "x": "28", "y": "16" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(-a + x, 12), Eq(a + x + 17, 61))" ], "shape": [ "solve: (Eq(-a + x, N), Eq(N + a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/22", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 22", "problem_latex": "Divide 120 into two parts such that five times one\npart may be equal to three times the other.", "markdown": "Divide 120 into two parts such that five times one part may be equal to three times the other.", "answer_latex": [ "$45$; $75$." ], "answer_markdown": [ "$45$; $75$." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "p": "45", "q": "75" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(5*x, 3*a), Eq(a + x, 120))" ], "shape": [ "solve: (Eq(N*x, N*a), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/23", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 23", "problem_latex": "Mr. Johnson is twice as old as his son; 12 years\nago he was three times as old. What is the age of each?", "markdown": "Mr. Johnson is twice as old as his son; 12 years ago he was three times as old. What is the age of each?", "answer_latex": [ "$24$; $48$ yrs." ], "answer_markdown": [ "$24$; $48$ yrs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "J": "48", "s": "24" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(a - 12, 3*x - 36))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N + a, N*x + N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/24", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 24", "problem_latex": "Henry is six times as old as his sister, but in 3 years\nfrom now he will be only three times as old. How old is\neach?", "markdown": "Henry is six times as old as his sister, but in 3 years from now he will be only three times as old. How old is each?", "answer_latex": [ "$2$; $12$ yrs." ], "answer_markdown": [ "$2$; $12$ yrs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "H": "12", "S": "2" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, 6*x), Eq(a + 3, 3*x + 9))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N + a, N*x + N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/25", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 25", "problem_latex": "Samuel is 16 years older than James; 4 years ago\nhe was three times as old. How old is each?", "markdown": "Samuel is 16 years older than James; 4 years ago he was three times as old. How old is each?", "answer_latex": [ "J., $12$ yrs.; S., $28$ yrs." ], "answer_markdown": [ "J., $12$ yrs.; S., $28$ yrs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "J": "12", "S": "28" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, x + 16), Eq(a - 4, 3*x - 12))" ], "shape": [ "solve: (Eq(a, N + x), Eq(N + a, N*x + N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/26", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 26", "problem_latex": "Martha is 5 years old and her father is 30. In\nhow many years will her father be twice as old as Martha?", "markdown": "Martha is 5 years old and her father is 30. In how many years will her father be twice as old as Martha?", "answer_latex": [ "$20$ yrs." ], "answer_markdown": [ "$20$ yrs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": "Eq(30+x,2*(5+x))", "answer_expr": { "x": "20" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: Eq(x + 30, 2*x + 10)" ], "shape": [ "solve: Eq(N + x, N*x + N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/27", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 27", "problem_latex": "George is three times as old as Amelia; in 6 years\nhis age will be twice hers. What is the age of each?", "markdown": "George is three times as old as Amelia; in 6 years his age will be twice hers. What is the age of each?", "answer_latex": [ "A., $6$ yrs.; G., $18$ yrs." ], "answer_markdown": [ "A., $6$ yrs.; G., $18$ yrs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "A": "6", "G": "18" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, 3*x), Eq(a + 6, 2*x + 12))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N + a, N*x + N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/28", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 28", "problem_latex": "Esther is three-fourths as old as Edward; 20 years\nago she was half as old. What is the age of each?", "markdown": "Esther is three-fourths as old as Edward; 20 years ago she was half as old. What is the age of each?", "answer_latex": [ "Ed., $40$ yrs.; Es., $30$ yrs." ], "answer_markdown": [ "Ed., $40$ yrs.; Es., $30$ yrs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "D": "40", "E": "30" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, 3*x/4), Eq(a - 20, x/2 - 10))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N + a, N*x + N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/29", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 29", "problem_latex": "Mary is 4 years old and Flora is 9. In how many\nwill Mary be two-thirds as old as Flora?", "markdown": "Mary is 4 years old and Flora is 9. In how many will Mary be two-thirds as old as Flora?", "answer_latex": [ "$6$ yrs." ], "answer_markdown": [ "$6$ yrs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": "Eq(4+x,2*(9+x)/3)", "answer_expr": { "x": "6" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: Eq(x + 4, 2*x/3 + 6)" ], "shape": [ "solve: Eq(N + x, N*x + N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/3", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 3", "problem_latex": "The sum of the ages of two brothers is 44 years, and\none of them is 12 years older than the other. Find their\nages.", "markdown": "The sum of the ages of two brothers is 44 years, and one of them is 12 years older than the other. Find their ages.", "answer_latex": [ "$16$; $28$ yrs" ], "answer_markdown": [ "$16$; $28$ yrs" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "o": "28", "y": "16" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 12), Eq(a + x, 44))" ], "shape": [ "solve: (Eq(a, N + x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/30", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 30", "problem_latex": "Harry is 9 years older than his little brother; in\n6 years he will be twice as old. How old is each?", "markdown": "Harry is 9 years older than his little brother; in 6 years he will be twice as old. How old is each?", "answer_latex": [ "$3$; $12$ yrs." ], "answer_markdown": [ "$3$; $12$ yrs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "H": "12", "b": "3" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a, x + 9), Eq(a + 6, 2*x + 12))" ], "shape": [ "solve: (Eq(a, N + x), Eq(N + a, N*x + N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/31", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 31, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 31", "problem_latex": "Divide $2x^4+27xy^3-81y^4$ by $x+3y$.", "markdown": "Divide $2x^4+27xy^3-81y^4$ by $x+3y$.", "answer_latex": [ "$2 x^3 -6 x^2y + 18xy^2 - 27 y^3$." ], "answer_markdown": [ "$2 x^3 -6 x^2y + 18xy^2 - 27 y^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(2*x**4 + 27*x*y**3 - 81*y**4)/(x + 3*y)", "answer_expr": "2*x**3 - 6*x**2*y + 18*x*y**2 - 27*y**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (-81*a**4 + 27*a**3*x + 2*x**4)/(3*a + x)" ], "shape": [ "identity: (N*a**N*x + N*a**N + N*x**N)/(N*a + x)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/32", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 32, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 32", "problem_latex": "Prove $\\left(a^2+ab+b^2\\right)^2-\\left(a^2-ab+b^2\\right)^2=4ab(a^2+b^2)$.", "markdown": "Prove $\\left(a^2+ab+b^2\\right)^2-\\left(a^2-ab+b^2\\right)^2=4ab(a^2+b^2)$.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/33", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 33, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 33", "problem_latex": "Find the value of $\\displaystyle\n\\frac{x-y}{y}+\\frac{2x}{x-y}-\\frac{x^3+x^2y}{x^2y-y^3}$.", "markdown": "Find the value of $\\displaystyle \\frac{x-y}{y}+\\frac{2x}{x-y}-\\frac{x^3+x^2y}{x^2y-y^3}$.", "answer_latex": [ "$\\displaystyle \\frac{y}{x - y}$." ], "answer_markdown": [ "$\\displaystyle \\frac{y}{x - y}$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x - y)/y + 2*x/(x - y) - (x**3 + x**2*y)/(x**2*y - y**3)", "answer_expr": "y/(x - y)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 2*x/(-a + x) - (a*x**2 + x**3)/(-a**3 + a*x**2) + (-a + x)/a" ], "shape": [ "identity: N*x/(-a + x) - (a*x**N + x**N)/(a*x**N - a**N) + (-a + x)/a" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/34", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 34, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 34", "problem_latex": "Solve $\\displaystyle \\frac{5x-7}{2}-3x=\\frac{2x+7}{3}-14$.", "markdown": "Solve $\\displaystyle \\frac{5x-7}{2}-3x=\\frac{2x+7}{3}-14$.", "answer_latex": [ "$x = 7$." ], "answer_markdown": [ "$x = 7$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((5*x-7)/2 - 3*x, (2*x+7)/3 - 14)", "answer_expr": "7" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-x/2 - 7/2, 2*x/3 - 35/3)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X=7", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "7 ENTER 3 ÷ 14 − 7 ENTER 2 ÷ +", "5 ENTER 2 ÷ 3 − 2 ENTER 3 ÷ − ÷" ], "calculator_value": "+7000000000000000000000000000000001E-33", "printed_value": "7", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/35", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 35, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 35", "problem_latex": "Mr. Ames has \\$132, and Mr. Jones \\$43. How\nmuch must Mr. A. give to Mr. J. so that Mr. J. may have\nthree-fourths as much as Mr. A.?", "markdown": "Mr. Ames has $132, and Mr. Jones $43. How much must Mr. A. give to Mr. J. so that Mr. J. may have three-fourths as much as Mr. A.?", "answer_latex": [ "\\$32." ], "answer_markdown": [ "$32." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(43+x,3*(132-x)/4)", "answer_expr": { "x": "32" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x + 43, -3*x/4 + 99)" ], "shape": [ "solve: Eq(N + x, N*x + N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/36", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 36, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 36", "problem_latex": "A has \\$101, and B has \\$35; each loses a certain\nsum, and then A has four times as much as B. What was\nthe sum lost by each?", "markdown": "A has $101, and B has $35; each loses a certain sum, and then A has four times as much as B. What was the sum lost by each?", "answer_latex": [ "\\$13." ], "answer_markdown": [ "$13." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(101-x,4*(35-x))", "answer_expr": { "x": "13" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(-x + 101, -4*x + 140)" ], "shape": [ "solve: Eq(N - x, N*x + N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/37", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 37, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 37", "problem_latex": "A certain sum of money was divided among A, B, and C; A and B\nreceived \\$75, A and C \\$108, and B and C \\$89. How much did each\nreceive?\n\n\\textit{ Suggestion}. Let $x$ equal what A received.", "markdown": "A certain sum of money was divided among A, B, and C; A and B received $75, A and C $108, and B and C $89. How much did each receive? *Suggestion*. Let $x$ equal what A received.", "answer_latex": [ "A, \\$47; B, \\$28; C, \\$61." ], "answer_markdown": [ "A, $47; B, $28; C, $61." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "A": "47", "B": "28", "C": "61" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a + x, 75), Eq(b + x, 108), Eq(a + b, 89))" ], "shape": [ "solve: (Eq(a + x, N), Eq(b + x, N), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/38", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 38, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 38", "problem_latex": "Mary and Jane have the same amount of money.\nIf Mary should give Jane 40 cents, she would have one-third\nas much as Jane. What amount of money has\neach?", "markdown": "Mary and Jane have the same amount of money. If Mary should give Jane 40 cents, she would have one-third as much as Jane. What amount of money has each?", "answer_latex": [ "80 cts." ], "answer_markdown": [ "80 cts." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(m-40,(m+40)/3)", "answer_expr": { "m": "80" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x - 40, x/3 + 40/3)" ], "shape": [ "solve: Eq(N + x, N*x + N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/39", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 39, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 39", "problem_latex": "An ulster and a suit of clothes cost \\$43; the ulster and a\nhat cost \\$27; the suit of clothes and the hat cost \\$34. How much\ndid each cost?", "markdown": "An ulster and a suit of clothes cost $43; the ulster and a hat cost $27; the suit of clothes and the hat cost $34. How much did each cost?", "answer_latex": [ "u., \\$18; cl., \\$25; h., \\$9." ], "answer_markdown": [ "u., $18; cl., $25; h., $9." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "h": "9", "s": "25", "u": "18" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a + b, 34), Eq(a + x, 27), Eq(b + x, 43))" ], "shape": [ "solve: (Eq(a + b, N), Eq(a + x, N), Eq(b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/4", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 4", "problem_latex": "Find two numbers whose sum is 158, and whose difference\nis 86.", "markdown": "Find two numbers whose sum is 158, and whose difference is 86.", "answer_latex": [ "$36$; $122$." ], "answer_markdown": [ "$36$; $122$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "x": "122", "y": "36" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(-a + x, 86), Eq(a + x, 158))" ], "shape": [ "solve: (Eq(-a + x, N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/40", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 40, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 40", "problem_latex": "John, Henry, and Arthur picked berries, and sold them; John\nand Henry received \\$4.22, John and Arthur \\$3.05, Henry and\nArthur \\$3.67. How much did each receive for his berries?", "markdown": "John, Henry, and Arthur picked berries, and sold them; John and Henry received $4.22, John and Arthur $3.05, Henry and Arthur $3.67. How much did each receive for his berries?", "answer_latex": [ "J., \\$ 1.80; H., \\$2.42; A., \\$1.25" ], "answer_markdown": [ "J., $ 1.80; H., $2.42; A., $1.25" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "A": "5/4", "H": "121/50", "J": "9/5" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a + b, 367/100), Eq(a + x, 61/20), Eq(b + x, 211/50))" ], "shape": [ "solve: (Eq(a + b, N), Eq(a + x, N), Eq(b + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/41", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 41, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 41", "problem_latex": "A can do a piece of work in 4 days, and B can do it\nin 6 days. In what time can they do it working together?\n\n\\textit{ Suggestion}. Let $x$ equal the required time. Then find\nwhat part of the work each can do in one day.", "markdown": "A can do a piece of work in 4 days, and B can do it in 6 days. In what time can they do it working together? *Suggestion*. Let $x$ equal the required time. Then find what part of the work each can do in one day.", "answer_latex": [ "$2\\frac{2}{5}$ days." ], "answer_markdown": [ "$2\\frac{2}{5}$ days." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x*(1/4+1/6),1)", "answer_expr": { "x": "12/5" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(5*x/12, 1)" ], "shape": [ "solve: Eq(N*x, 1)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/42", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 42, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 42", "problem_latex": "Mr. Brown can build a stone wall in 10 days, and Mr.\nMansfield in 12 days. How long would it take them to do\nit working together?", "markdown": "Mr. Brown can build a stone wall in 10 days, and Mr. Mansfield in 12 days. How long would it take them to do it working together?", "answer_latex": [ "$5\\frac{5}{11}$ days." ], "answer_markdown": [ "$5\\frac{5}{11}$ days." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x*(1/10+1/12),1)", "answer_expr": { "x": "60/11" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(11*x/60, 1)" ], "shape": [ "solve: Eq(N*x, 1)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/43", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 43, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 43", "problem_latex": "Mr. Richards and his son can hoe a field of corn in\n9 hours, but it takes Mr. Richards alone 15 hours. How\nlong would it take the son to hoe the field?", "markdown": "Mr. Richards and his son can hoe a field of corn in 9 hours, but it takes Mr. Richards alone 15 hours. How long would it take the son to hoe the field?", "answer_latex": [ "$22\\frac{1}{2}$ hrs." ], "answer_markdown": [ "$22\\frac{1}{2}$ hrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(1/15+1/s,1/9)", "answer_expr": { "s": "45/2" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(1/15 + 1/x, 1/9)" ], "shape": [ "solve: Eq(N + 1/x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/44", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 44, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 44", "problem_latex": "A can do a piece of work in 4 hours, B can do it in\n6 hours, and C in 3 hours. How long would it take them\nworking together?", "markdown": "A can do a piece of work in 4 hours, B can do it in 6 hours, and C in 3 hours. How long would it take them working together?", "answer_latex": [ "$1\\frac{1}{3}$ hrs." ], "answer_markdown": [ "$1\\frac{1}{3}$ hrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x*(1/4+1/6+1/3),1)", "answer_expr": { "x": "4/3" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*x/4, 1)" ], "shape": [ "solve: Eq(N*x, 1)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/45", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 45, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 45", "problem_latex": "A can mow a field in 6 hours, B in 8 hours, and with\nthe help of C they can do it in 2 hours. How long would\nit take C working alone?", "markdown": "A can mow a field in 6 hours, B in 8 hours, and with the help of C they can do it in 2 hours. How long would it take C working alone?", "answer_latex": [ "$4\\frac{4}{5}$ hrs." ], "answer_markdown": [ "$4\\frac{4}{5}$ hrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(1/6+1/8+1/c,1/2)", "answer_expr": { "c": "24/5" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(7/24 + 1/x, 1/2)" ], "shape": [ "solve: Eq(N + 1/x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/46", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 46, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 46", "problem_latex": "A tank can be emptied by two pipes in 5 hours and\n7 hours respectively. In what time can it be emptied\nby the two pipes together?", "markdown": "A tank can be emptied by two pipes in 5 hours and 7 hours respectively. In what time can it be emptied by the two pipes together?", "answer_latex": [ "$2\\frac{11}{12}$ hrs." ], "answer_markdown": [ "$2\\frac{11}{12}$ hrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x*(1/5+1/7),1)", "answer_expr": { "x": "35/12" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(12*x/35, 1)" ], "shape": [ "solve: Eq(N*x, 1)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/47", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 47, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 47", "problem_latex": "A cistern can be filled by two pipes in 4 hours and\n6 hours respectively, and can be emptied by a third in 15\nhours. In what time could the cistern be filled if all three\npipes were running?", "markdown": "A cistern can be filled by two pipes in 4 hours and 6 hours respectively, and can be emptied by a third in 15 hours. In what time could the cistern be filled if all three pipes were running?", "answer_latex": [ "$2\\frac{6}{7}$ hrs." ], "answer_markdown": [ "$2\\frac{6}{7}$ hrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x*(1/4+1/6-1/15),1)", "answer_expr": { "x": "20/7" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(7*x/20, 1)" ], "shape": [ "solve: Eq(N*x, 1)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/48", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 48, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 48", "problem_latex": "A and B together can do a piece of work in 8 days,\nA and C together in 10 days, and A by himself in 12 days.\nIn what time can B and C do it? In what time can A, B,\nand C together do it?", "markdown": "A and B together can do a piece of work in 8 days, A and C together in 10 days, and A by himself in 12 days. In what time can B and C do it? In what time can A, B, and C together do it?", "answer_latex": [ "$17\\frac{1}{7}$; $7\\frac{1}{17}$ days." ], "answer_markdown": [ "$17\\frac{1}{7}$; $7\\frac{1}{17}$ days." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": [ "120/7", "120/17" ] } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/49", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 49, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 49", "problem_latex": "John and Henry can together paint a fence in 2\nhours, John and Lewis together in 4 hours, and John by\nhimself in 6 hours. In what time can the three together\ndo the painting?", "markdown": "John and Henry can together paint a fence in 2 hours, John and Lewis together in 4 hours, and John by himself in 6 hours. In what time can the three together do the painting?", "answer_latex": [ "$1\\frac{5}{7}$ hrs." ], "answer_markdown": [ "$1\\frac{5}{7}$ hrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x*(1/6+1/3+1/12),1)", "answer_expr": { "x": "12/7" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(7*x/12, 1)" ], "shape": [ "solve: Eq(N*x, 1)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/5", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 5", "problem_latex": "Henry and Susan picked 16 quarts of berries.\nHenry picked 4 quarts less than three times as many as\nSusan. How many quarts did each pick?", "markdown": "Henry and Susan picked 16 quarts of berries. Henry picked 4 quarts less than three times as many as Susan. How many quarts did each pick?", "answer_latex": [ "S., $5$; H., $11$ qts." ], "answer_markdown": [ "S., $5$; H., $11$ qts." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "H": "11", "S": "5" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 3*x - 4), Eq(a + x, 16))" ], "shape": [ "solve: (Eq(a, N*x + N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/50", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 50, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 50", "problem_latex": "C can do a piece of work in $a$ days, and D can do the\nsame work in $b$ days. In how many days can they do it\nworking together?", "markdown": "C can do a piece of work in $a$ days, and D can do the same work in $b$ days. In how many days can they do it working together?", "answer_latex": [ "$\\displaystyle \\frac{ab}{a + b}$ days." ], "answer_markdown": [ "$\\displaystyle \\frac{ab}{a + b}$ days." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x*(1/a+1/b),1)", "answer_expr": "a*b/(a + b)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x*(1/b + 1/a), 1)" ], "shape": [ "solve: Eq(x*(1/b + 1/a), 1)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/51", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 51, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 51", "problem_latex": "James and Thomas can do a piece of work in $d$ days\nand James alone can do it in $c$ days. How long would it\ntake Thomas alone?", "markdown": "James and Thomas can do a piece of work in $d$ days and James alone can do it in $c$ days. How long would it take Thomas alone?", "answer_latex": [ "$\\displaystyle \\frac{cd}{c - d}$ days." ], "answer_markdown": [ "$\\displaystyle \\frac{cd}{c - d}$ days." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(1/t,1/d-1/c)", "answer_expr": "c*d/(c - d)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(1/x, 1/b - 1/a)" ], "shape": [ "solve: Eq(1/x, 1/b - 1/a)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/52", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 52, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 52", "problem_latex": "Solve $\\displaystyle\n\\frac{3+x}{3-x}-\\frac{1+x}{1-x}-\\frac{2+x}{2-x}=1$.", "markdown": "Solve $\\displaystyle \\frac{3+x}{3-x}-\\frac{1+x}{1-x}-\\frac{2+x}{2-x}=1$.", "answer_latex": [ "$x = 1\\frac{1}{2}$." ], "answer_markdown": [ "$x = 1\\frac{1}{2}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((3+x)/(3-x) - (1+x)/(1-x) - (2+x)/(2-x), 1)", "answer_expr": "3/2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq((x + 3)/(-x + 3) - (x + 2)/(-x + 2) - (x + 1)/(-x + 1), 1)" ], "shape": [ "solve: False" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn", "core.frac" ], "expectation": "X=1.5", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/53", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 53, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 53", "problem_latex": "Find the value of $\\displaystyle\n\\frac{x^2}{(x-y)(x-z)}+\\frac{y^2}{(y-x)(y-z)}+\\frac{z^2}{(z-x)(z-y)}$.", "markdown": "Find the value of $\\displaystyle \\frac{x^2}{(x-y)(x-z)}+\\frac{y^2}{(y-x)(y-z)}+\\frac{z^2}{(z-x)(z-y)}$.", "answer_latex": [ "$1$." ], "answer_markdown": [ "$1$." ], "checks": [ { "task": "identity", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": "x**2/((x - y)*(x - z)) + y**2/((y - x)*(y - z)) + z**2/((z - x)*(z - y))", "answer_expr": "1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "identity: a**2/((a - b)*(a - x)) + b**2/((-a + b)*(b - x)) + x**2/((-a + x)*(-b + x))" ], "shape": [ "identity: a**N/((a - b)*(a - x)) + b**N/((-a + b)*(b - x)) + x**N/((-a + x)*(-b + x))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/54", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 54, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 54", "problem_latex": "Expand $(x^2-2)(x^2+2)(x^2+3)(x^2-3)$.", "markdown": "Expand $(x^2-2)(x^2+2)(x^2+3)(x^2-3)$.", "answer_latex": [ "$x^8 - 13x^4 + 36$." ], "answer_markdown": [ "$x^8 - 13x^4 + 36$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x**2-2)*(x**2+2)*(x**2+3)*(x**2-3)", "answer_expr": "x**8 - 13*x**4 + 36" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x**2 - 3)*(x**2 - 2)*(x**2 + 2)*(x**2 + 3)" ], "shape": [ "identity: (N + x**N)**4" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/55a", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 55, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 55a", "problem_latex": "Factor $9a^2+12ab+4b^2$, $12+7x+x^2$, $ac-2bc-3ad+6bd$.", "markdown": "Factor $9a^2+12ab+4b^2$, $12+7x+x^2$, $ac-2bc-3ad+6bd$.", "answer_latex": [ "$(3a + 2b)^2$; $(3 + x)(4 + x)$; $(a - 2b)(c - 3d)$." ], "answer_markdown": [ "$(3a + 2b)^2$; $(3 + x)(4 + x)$; $(a - 2b)(c - 3d)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "9*a**2 + 12*a*b + 4*b**2", "answer_expr": "(3*a + 2*b)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 4*a**2 + 12*a*x + 9*x**2" ], "shape": [ "factor: N*a*x + N*a**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/55b", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 55, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 55b", "problem_latex": "Factor $9a^2+12ab+4b^2$, $12+7x+x^2$, $ac-2bc-3ad+6bd$.", "markdown": "Factor $9a^2+12ab+4b^2$, $12+7x+x^2$, $ac-2bc-3ad+6bd$.", "answer_latex": [ "$(3a + 2b)^2$; $(3 + x)(4 + x)$; $(a - 2b)(c - 3d)$." ], "answer_markdown": [ "$(3a + 2b)^2$; $(3 + x)(4 + x)$; $(a - 2b)(c - 3d)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "12 + 7*x + x**2", "answer_expr": "(3 + x)*(4 + x)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2 + 7*x + 12" ], "shape": [ "factor: N*x + N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/55c", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 55, "part": "c", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 55c", "problem_latex": "Factor $9a^2+12ab+4b^2$, $12+7x+x^2$, $ac-2bc-3ad+6bd$.", "markdown": "Factor $9a^2+12ab+4b^2$, $12+7x+x^2$, $ac-2bc-3ad+6bd$.", "answer_latex": [ "$(3a + 2b)^2$; $(3 + x)(4 + x)$; $(a - 2b)(c - 3d)$." ], "answer_markdown": [ "$(3a + 2b)^2$; $(3 + x)(4 + x)$; $(a - 2b)(c - 3d)$." ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "a*c - 2*b*c - 3*a*d + 6*b*d", "answer_expr": "(a - 2*b)*(c - 3*d)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -2*a*b + 6*a*c + b*x - 3*c*x" ], "shape": [ "factor: N*a*b + N*a*c + N*c*x + b*x" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/56a", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 56, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 56a", "problem_latex": "At what time are the hands of a clock together\nbetween 2 and 3? Between 5 and 6? Between 9 and 10?", "markdown": "At what time are the hands of a clock together between 2 and 3? Between 5 and 6? Between 9 and 10?", "answer_latex": [ "\\begin{tabular}{ll}(1)& $10\\frac{10}{11}$ m. \\\\\n (2)& $27\\frac{3}{11}$ m. \\\\\n (3) &$49\\frac{1}{11}$ m.\n \\end{tabular}" ], "answer_markdown": [ "tabularll(1)& $10\\frac{10}{11}$ m. (2)& $27\\frac{3}{11}$ m. (3) &$49\\frac{1}{11}$ m. tabular" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(Abs(11*x/2 - 30*2), 0)", "answer_expr": "120/11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 60), 0)" ], "shape": [ "solve: Eq(Abs(N*x + N), 0)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X#10.9090909090909090909090909090909091,1E-30", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "30 ENTER 2 ×", "2 ×", "11 ÷" ], "constants": [ { "value": "30", "source": "the 30 in '30*2' of the mathematics Eq(Abs(11*x/2 - 30*2), 0), the 30 minute-marks per hour on the dial" }, { "value": "2", "source": "the 2 in 'between 2 and 3' in the problem text (second multiplier 2 is the 2 in 'between 2 and 3'); the 2 in '11*x/2' of the mathematics clears the denominator" } ], "calculator_value": "+1090909090909090909090909090909091E-32", "printed_value": "120/11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/56b", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 56, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 56b", "problem_latex": "At what time are the hands of a clock together\nbetween 2 and 3? Between 5 and 6? Between 9 and 10?", "markdown": "At what time are the hands of a clock together between 2 and 3? Between 5 and 6? Between 9 and 10?", "answer_latex": [ "\\begin{tabular}{ll}(1)& $10\\frac{10}{11}$ m. \\\\\n (2)& $27\\frac{3}{11}$ m. \\\\\n (3) &$49\\frac{1}{11}$ m.\n \\end{tabular}" ], "answer_markdown": [ "tabularll(1)& $10\\frac{10}{11}$ m. (2)& $27\\frac{3}{11}$ m. (3) &$49\\frac{1}{11}$ m. tabular" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(Abs(11*x/2 - 30*5), 0)", "answer_expr": "300/11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 150), 0)" ], "shape": [ "solve: Eq(Abs(N*x + N), 0)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X#27.2727272727272727272727272727272727,1E-30", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "5 ENTER 30 ×", "2 ×", "11 ÷" ], "constants": [ { "value": "5", "source": "the 5 in 'Between 5 and 6'" }, { "value": "30", "source": "degrees per hour mark on the dial (360 ÷ 12); clock geometry, not printed in the problem, and the 30 in SymPy's 30*5" }, { "value": "2", "source": "the 2 in SymPy's 11*x/2: multiplying by 2 clears the ½ left by the minute hand's rate (6) minus the hour hand's rate (½)" }, { "value": "11", "source": "the 11 in SymPy's 11*x/2, from 6 − ½ = 11/2 degrees per minute, the rate at which the minute hand gains on the hour hand; clock geometry, not printed in the problem" } ], "calculator_value": "+2727272727272727272727272727272727E-32", "printed_value": "300/11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/56c", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 56, "part": "c", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 56c", "problem_latex": "At what time are the hands of a clock together\nbetween 2 and 3? Between 5 and 6? Between 9 and 10?", "markdown": "At what time are the hands of a clock together between 2 and 3? Between 5 and 6? Between 9 and 10?", "answer_latex": [ "\\begin{tabular}{ll}(1)& $10\\frac{10}{11}$ m. \\\\\n (2)& $27\\frac{3}{11}$ m. \\\\\n (3) &$49\\frac{1}{11}$ m.\n \\end{tabular}" ], "answer_markdown": [ "tabularll(1)& $10\\frac{10}{11}$ m. (2)& $27\\frac{3}{11}$ m. (3) &$49\\frac{1}{11}$ m. tabular" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(Abs(11*x/2 - 30*9), 0)", "answer_expr": "540/11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 270), 0)" ], "shape": [ "solve: Eq(Abs(N*x + N), 0)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X#49.0909090909090909090909090909090909,1E-30", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "9 ENTER 30 ×", "2 ×", "11 ÷" ], "constants": [ { "value": "30", "source": "the 30 in '30*9' of the SymPy expression Eq(Abs(11*x/2 - 30*9), 0)" }, { "value": "2", "source": "the 2 in '11*x/2' of the SymPy expression" }, { "value": "11", "source": "the 11 in '11*x/2' of the SymPy expression" } ], "calculator_value": "+4909090909090909090909090909090909E-32", "printed_value": "540/11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/57a", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 57, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 57a", "problem_latex": "At what time are the hands of a clock at right\nangles between 2 and 3? Between 4 and 5? Between 7\nand 8?", "markdown": "At what time are the hands of a clock at right angles between 2 and 3? Between 4 and 5? Between 7 and 8?", "answer_latex": [ "\\begin{tabular}{rrcl}(1)& $27\\frac{3}{11}$ m. \\\\\n (2)& $5\\frac{5}{11}$ m.; &$38\\frac{2}{11}$ m. \\\\\n (3)& $21\\frac{9}{11}$ m.; &$54\\frac{6}{11}$ m.\n \\end{tabular}" ], "answer_markdown": [ "tabularrrcl(1)& $27\\frac{3}{11}$ m. (2)& $5\\frac{5}{11}$ m.; &$38\\frac{2}{11}$ m. (3)& $21\\frac{9}{11}$ m.; &$54\\frac{6}{11}$ m. tabular" ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": "Eq(Abs(11*x/2 - 60), 90) fails at {x: 150/11}: leaves -75.0000000000", "problem_expr": "Eq(Abs(11*x/2 - 30*2), 90)", "answer_expr": [ "150/11" ] } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 60), 90)" ], "shape": [ "solve: Eq(Abs(N*x + N), N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/57b", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 57, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 57b", "problem_latex": "At what time are the hands of a clock at right\nangles between 2 and 3? Between 4 and 5? Between 7\nand 8?", "markdown": "At what time are the hands of a clock at right angles between 2 and 3? Between 4 and 5? Between 7 and 8?", "answer_latex": [ "\\begin{tabular}{rrcl}(1)& $27\\frac{3}{11}$ m. \\\\\n (2)& $5\\frac{5}{11}$ m.; &$38\\frac{2}{11}$ m. \\\\\n (3)& $21\\frac{9}{11}$ m.; &$54\\frac{6}{11}$ m.\n \\end{tabular}" ], "answer_markdown": [ "tabularrrcl(1)& $27\\frac{3}{11}$ m. (2)& $5\\frac{5}{11}$ m.; &$38\\frac{2}{11}$ m. (3)& $21\\frac{9}{11}$ m.; &$54\\frac{6}{11}$ m. tabular" ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": "Eq(Abs(11*x/2 - 30*4), 90)", "answer_expr": [ "60/11", "420/11" ] } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 120), 90)" ], "shape": [ "solve: Eq(Abs(N*x + N), N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/57c", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 57, "part": "c", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 57c", "problem_latex": "At what time are the hands of a clock at right\nangles between 2 and 3? Between 4 and 5? Between 7\nand 8?", "markdown": "At what time are the hands of a clock at right angles between 2 and 3? Between 4 and 5? Between 7 and 8?", "answer_latex": [ "\\begin{tabular}{rrcl}(1)& $27\\frac{3}{11}$ m. \\\\\n (2)& $5\\frac{5}{11}$ m.; &$38\\frac{2}{11}$ m. \\\\\n (3)& $21\\frac{9}{11}$ m.; &$54\\frac{6}{11}$ m.\n \\end{tabular}" ], "answer_markdown": [ "tabularrrcl(1)& $27\\frac{3}{11}$ m. (2)& $5\\frac{5}{11}$ m.; &$38\\frac{2}{11}$ m. (3)& $21\\frac{9}{11}$ m.; &$54\\frac{6}{11}$ m. tabular" ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": "Eq(Abs(11*x/2 - 210), 90) fails at {x: 120/11}: leaves 60.0000000000", "problem_expr": "Eq(Abs(11*x/2 - 30*7), 90)", "answer_expr": [ "120/11", "600/11" ] } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 210), 90)" ], "shape": [ "solve: Eq(Abs(N*x + N), N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/58a", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 58, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 58a", "problem_latex": "At what time are the hands of a clock opposite each\nother between 3 and 4? Between 8 and 9? Between 12\nand 1?", "markdown": "At what time are the hands of a clock opposite each other between 3 and 4? Between 8 and 9? Between 12 and 1?", "answer_latex": [ "\\begin{tabular}{ll}(1)& $49\\frac{1}{11}$ m. \\\\\n (2) & $10\\frac{10}{11}$ m. \\\\\n (3) & $32\\frac{8}{11}$ m.\n \\end{tabular}" ], "answer_markdown": [ "tabularll(1)& $49\\frac{1}{11}$ m. (2) & $10\\frac{10}{11}$ m. (3) & $32\\frac{8}{11}$ m. tabular" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(Abs(11*x/2 - 30*3), 180)", "answer_expr": "540/11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 90), 180)" ], "shape": [ "solve: Eq(Abs(N*x + N), N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X#49.0909090909090909090909090909090909,1E-30", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "30 ENTER 3 × 180 + 2 × 11 ÷" ], "constants": [ { "value": "30", "source": "the 30 in the SymPy expression 11*x/2 - 30*3 (30 degrees per hour mark); not printed in the problem text" }, { "value": "3", "source": "the 3 in 'between 3 and 4' (the 30*3 term in SymPy)" }, { "value": "180", "source": "the 180 in SymPy Eq(..., 180); the problem's 'opposite each other' means the hands are 180 degrees apart; not printed as a number in the problem text" }, { "value": "2", "source": "the 2 in 11*x/2 in the SymPy expression" }, { "value": "11", "source": "the 11 in 11*x/2 in the SymPy expression" } ], "calculator_value": "+4909090909090909090909090909090909E-32", "printed_value": "540/11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/58b", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 58, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 58b", "problem_latex": "At what time are the hands of a clock opposite each\nother between 3 and 4? Between 8 and 9? Between 12\nand 1?", "markdown": "At what time are the hands of a clock opposite each other between 3 and 4? Between 8 and 9? Between 12 and 1?", "answer_latex": [ "\\begin{tabular}{ll}(1)& $49\\frac{1}{11}$ m. \\\\\n (2) & $10\\frac{10}{11}$ m. \\\\\n (3) & $32\\frac{8}{11}$ m.\n \\end{tabular}" ], "answer_markdown": [ "tabularll(1)& $49\\frac{1}{11}$ m. (2) & $10\\frac{10}{11}$ m. (3) & $32\\frac{8}{11}$ m. tabular" ], "checks": [ { "task": "solve", "verdict": "FLAG-MISMATCH", "judge_why": "Eq(Abs(11*x/2 - 240), 180) fails at {x: 780/11}: leaves -30.0000000000", "problem_expr": "Eq(Abs(11*x/2 - 30*8), 180)", "answer_expr": [ "120/11", "780/11" ] } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 240), 180)" ], "shape": [ "solve: Eq(Abs(N*x + N), N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/58c", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 58, "part": "c", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 58c", "problem_latex": "At what time are the hands of a clock opposite each\nother between 3 and 4? Between 8 and 9? Between 12\nand 1?", "markdown": "At what time are the hands of a clock opposite each other between 3 and 4? Between 8 and 9? Between 12 and 1?", "answer_latex": [ "\\begin{tabular}{ll}(1)& $49\\frac{1}{11}$ m. \\\\\n (2) & $10\\frac{10}{11}$ m. \\\\\n (3) & $32\\frac{8}{11}$ m.\n \\end{tabular}" ], "answer_markdown": [ "tabularll(1)& $49\\frac{1}{11}$ m. (2) & $10\\frac{10}{11}$ m. (3) & $32\\frac{8}{11}$ m. tabular" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(Abs(11*x/2 - 30*12), 180)", "answer_expr": "360/11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 360), 180)" ], "shape": [ "solve: Eq(Abs(N*x + N), N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X#32.7272727272727272727272727272727273,1E-30", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/59", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 59, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 59", "problem_latex": "At what times between 4 and 5 o'clock are the hands\nof a watch ten minutes apart?", "markdown": "At what times between 4 and 5 o’clock are the hands of a watch ten minutes apart?", "answer_latex": [ "$10\\frac{10}{11}$ m., $32\\frac{8}{11}$ m." ], "answer_markdown": [ "$10\\frac{10}{11}$ m., $32\\frac{8}{11}$ m." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(Abs(11*x/2 - 30*4), 60)", "answer_expr": [ "120/11", "360/11" ] } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 120), 60)" ], "shape": [ "solve: Eq(Abs(N*x + N), N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/6", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 6", "problem_latex": "Divide 127 into three parts, such that the second\nshall be 5 more than the first, and the third four times\nthe second.", "markdown": "Divide 127 into three parts, such that the second shall be 5 more than the first, and the third four times the second.", "answer_latex": [ "$17$; $22$; $88$." ], "answer_markdown": [ "$17$; $22$; $88$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "a": "17", "b": "22", "c": "88" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 5), Eq(b, 4*a), Eq(a + b + x, 127))" ], "shape": [ "solve: (Eq(a, N + x), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/60", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 60, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 60", "problem_latex": "At what time between 8 and 9 o'clock are the\nhands of a watch 25 minutes apart?", "markdown": "At what time between 8 and 9 o’clock are the hands of a watch 25 minutes apart?", "answer_latex": [ "$16\\frac{4}{11}$ m." ], "answer_markdown": [ "$16\\frac{4}{11}$ m." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(Abs(11*x/2 - 30*8), 150)", "answer_expr": "180/11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 240), 150)" ], "shape": [ "solve: Eq(Abs(N*x + N), N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X#16.3636363636363636363636363636363636,1E-30", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "30 ENTER 8 × 150 − 2 × 11 ÷" ], "constants": [ { "value": "30", "source": "the 30 in the expression '30*8' (degrees per hour mark)" }, { "value": "8", "source": "the 8 in the expression '30*8' (the 8 o'clock start)" }, { "value": "150", "source": "the 150 on the right of the expression 'Abs(11*x/2 - 30*8) = 150' (25 minutes × 6 degrees)" }, { "value": "2", "source": "the 2 in '11*x/2': isolating x gives x = (240 − 150)·2/11" }, { "value": "11", "source": "the 11 in '11*x/2' (the 11/2 coefficient)" } ], "calculator_value": "+1636363636363636363636363636363636E-32", "printed_value": "180/11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/61", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 61, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 61", "problem_latex": "At what time between 5 and 6 o'clock is the minute\nhand three minutes ahead of the hour hand?", "markdown": "At what time between 5 and 6 o’clock is the minute hand three minutes ahead of the hour hand?", "answer_latex": [ "$30\\frac{6}{11}$ m." ], "answer_markdown": [ "$30\\frac{6}{11}$ m." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(11*x/2 - 30*5, 18)", "answer_expr": "336/11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(11*x/2 - 150, 18)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X#30.5454545454545454545454545454545455,1E-30", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "18 ENTER 30 ENTER 5 × +", "2 × 11 ÷" ], "constants": [ { "value": "18", "source": "the 18 in the problem's mathematics, Eq(11*x/2 - 30*5, 18)" }, { "value": "30", "source": "the 30 in the problem's mathematics, 30*5" }, { "value": "5", "source": "the 5 in 'between 5 and 6 o'clock' and the 5 in 30*5" }, { "value": "2", "source": "the 2 in the denominator of 11*x/2 in the problem's mathematics" }, { "value": "11", "source": "the 11 in the coefficient 11*x/2 in the problem's mathematics" } ], "calculator_value": "+3054545454545454545454545454545455E-32", "printed_value": "336/11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/62", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 62, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 62", "problem_latex": "It was between 12 and 1 o'clock; but a man, mistaking\nthe hour hand for the minute hand, thought that\nit was 55 minutes later than it really was. What time\nwas it?", "markdown": "It was between 12 and 1 o’clock; but a man, mistaking the hour hand for the minute hand, thought that it was 55 minutes later than it really was. What time was it?", "answer_latex": [ "$5\\frac{5}{11}$ m. past 12M." ], "answer_markdown": [ "$5\\frac{5}{11}$ m. past 12M." ], "checks": [ { "task": "solve", "verdict": "FLAG-MISMATCH", "judge_why": "Eq(133*x/12, 55) fails at {x: 60/11}: leaves 5.45454545455", "problem_expr": "Eq(12*x + x/12 - x, 55)", "answer_expr": "60/11" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "solve: Eq(133*x/12, 55)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/63", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 63, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 63", "problem_latex": "At what time between 11 and 12 o'clock are the\nhands two minutes apart?", "markdown": "At what time between 11 and 12 o’clock are the hands two minutes apart?", "answer_latex": [ "$57\\frac{9}{11}$ m." ], "answer_markdown": [ "$57\\frac{9}{11}$ m." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(Abs(11*x/2 - 30*11), 12)", "answer_expr": "636/11" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(Abs(11*x/2 - 330), 12)" ], "shape": [ "solve: Eq(Abs(N*x + N), N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X#57.8181818181818181818181818181818182,1E-30", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "30 ENTER 11 × 12 −", "2 × 11 ÷" ], "constants": [ { "value": "30", "source": "the 30 in 30*11 in the SymPy expression Eq(Abs(11*x/2 - 30*11), 12)" }, { "value": "11", "source": "the 11 in 30*11 and in 11*x/2 in the SymPy expression; also the 11 o'clock in the problem text" }, { "value": "12", "source": "the 12 on the right-hand side of the SymPy expression (2 minutes at 6 degrees per minute of the minute hand)" }, { "value": "2", "source": "the 2 in 11*x/2 in the SymPy expression (the hour hand moves half a degree per minute, so 11x/2 is 5.5x)" } ], "calculator_value": "+5781818181818181818181818181818182E-32", "printed_value": "636/11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/64", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 64, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 64", "problem_latex": "A messenger who travels at the rate of 10 miles an\nhour is followed, 4 hours later, by another who travels at\nthe rate of 12 miles an hour. How long will it take the\nsecond to overtake the first?", "markdown": "A messenger who travels at the rate of 10 miles an hour is followed, 4 hours later, by another who travels at the rate of 12 miles an hour. How long will it take the second to overtake the first?", "answer_latex": [ "20 hrs." ], "answer_markdown": [ "20 hrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(12*t,10*(t+4))", "answer_expr": { "t": "20" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(12*x, 10*x + 40)" ], "shape": [ "solve: Eq(N*x, N*x + N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/65", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 65, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 65", "problem_latex": "A courier who travels at the rate of 19 miles in 4 hours\nis followed, 8 hours later, by another who travels at the rate\nof 19 miles in 3 hours. In what time will the second\novertake the first? How far will the first have gone\nbefore he is overtaken?", "markdown": "A courier who travels at the rate of 19 miles in 4 hours is followed, 8 hours later, by another who travels at the rate of 19 miles in 3 hours. In what time will the second overtake the first? How far will the first have gone before he is overtaken?", "answer_latex": [ "24 hrs.; 152 hrs" ], "answer_markdown": [ "24 hrs.; 152 hrs" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "d": "152", "t": "24" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 19*x/4 + 38), Eq(19*x/3, 19*x/4 + 38))" ], "shape": [ "solve: (Eq(a, N*x + N), Eq(N*x, N*x + N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/66", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 66, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 66", "problem_latex": "A train going at the rate of 20 miles an hour is\nfollowed, on a parallel track, 4 hours later, by an express\ntrain. The express overtakes the first train in $5\\frac{1}{3}$ hours.\nWhat is the rate of the express train?", "markdown": "A train going at the rate of 20 miles an hour is followed, on a parallel track, 4 hours later, by an express train. The express overtakes the first train in $5\\frac{1}{3}$ hours. What is the rate of the express train?", "answer_latex": [ "35 miles." ], "answer_markdown": [ "35 miles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(r*16/3,20*(4+16/3))", "answer_expr": { "r": "35" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(16*x/3, 560/3)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/67", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 67, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 67", "problem_latex": "A messenger started for Washington at the rate of\n$6\\frac{1}{2}$ miles an hour. Six hours later a second messenger\nfollowed and in $4\\frac{7}{8}$ hours overtook the first just as he was\nentering the city. At what rate did the second messenger\ngo? How far was it to Washington?", "markdown": "A messenger started for Washington at the rate of $6\\frac{1}{2}$ miles an hour. Six hours later a second messenger followed and in $4\\frac{7}{8}$ hours overtook the first just as he was entering the city. At what rate did the second messenger go? How far was it to Washington?", "answer_latex": [ "$14\\frac{1}{2}$ miles; $70\\frac{11}{16}$ miles." ], "answer_markdown": [ "$14\\frac{1}{2}$ miles; $70\\frac{11}{16}$ miles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "d": "1131/16", "r": "29/2" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 39*x/8), Eq(39*x/8, 1131/16))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N*x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/68", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 68, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 68", "problem_latex": "How far could a man ride at the rate of 8 miles an\nhour so as to walk back at the rate of 4 miles an hour and\nbe gone only 9 hours?", "markdown": "How far could a man ride at the rate of 8 miles an hour so as to walk back at the rate of 4 miles an hour and be gone only 9 hours?", "answer_latex": [ "24 miles." ], "answer_markdown": [ "24 miles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(d/8+d/4,9)", "answer_expr": { "d": "24" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*x/8, 9)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/69", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 69, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 69", "problem_latex": "Two persons start at 10 A.M. from towns A and B,\n$55\\frac{1}{2}$ miles apart. The one starting from A walks at the\nrate of $4\\frac{1}{4}$ miles an hour, but stops 2 hours on the way;\nthe other walks at the rate of $3\\frac{3}{4}$ miles an hour without\nstopping. When will they meet? How far will each\nhave traveled?\n\n\\textit{ Suggestion}. Let x equal the number of hours.", "markdown": "Two persons start at 10 A.M. from towns A and B, $55\\frac{1}{2}$ miles apart. The one starting from A walks at the rate of $4\\frac{1}{4}$ miles an hour, but stops 2 hours on the way; the other walks at the rate of $3\\frac{3}{4}$ miles an hour without stopping. When will they meet? How far will each have traveled? *Suggestion*. Let x equal the number of hours.", "answer_latex": [ "6 P.M.; 30 miles from B; $25\\frac{1}{2}$ miles from A." ], "answer_markdown": [ "6 P.M.; 30 miles from B; $25\\frac{1}{2}$ miles from A." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "t": "8", "dA": "51/2", "dB": "30" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(8*x - 17/2, 111/2)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/7", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 7", "problem_latex": "Twice a certain number added to four times the double of that number is 90. What is the number?", "markdown": "Twice a certain number added to four times the double of that number is 90. What is the number?", "answer_latex": [ "$9$." ], "answer_markdown": [ "$9$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(2*x+4*(2*x),90)", "answer_expr": { "x": "9" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(10*x, 90)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/70", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 70, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 70", "problem_latex": "A boy who runs at the rate of $12\\frac{1}{2}$ yards per second,\nstarts 16 yards behind another whose rate is 11 yards per\nsecond. How soon will the first boy be 8 yards ahead of\nthe second?", "markdown": "A boy who runs at the rate of $12\\frac{1}{2}$ yards per second, starts 16 yards behind another whose rate is 11 yards per second. How soon will the first boy be 8 yards ahead of the second?", "answer_latex": [ "16 sec." ], "answer_markdown": [ "16 sec." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(25*t/2 - 16 - 11*t, 8)", "answer_expr": { "t": "16" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(3*x/2 - 16, 8)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/71", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 71, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 71", "problem_latex": "A rectangle whose length is 4 ft. more than its\nwidth would have its area increased 56 sq. ft. if its length\nand width were each made 2 ft. more. What are its\ndimensions?", "markdown": "A rectangle whose length is 4 ft. more than its width would have its area increased 56 sq. ft. if its length and width were each made 2 ft. more. What are its dimensions?", "answer_latex": [ "11 ft. by 15 ft." ], "answer_markdown": [ "11 ft. by 15 ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "L": "15", "W": "11" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 4), Eq((a + 2)*(x + 2), a*x + 56))" ], "shape": [ "solve: (Eq(a, N + x), Eq((N + a)*(N + x), N + a*x))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/72", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 72, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 72", "problem_latex": "The length of a room is double its width. If the\nlength were 3 ft. less and the width 3 ft. more, the area\nwould be increased 27 sq. ft. Find the dimensions of the\nroom.", "markdown": "The length of a room is double its width. If the length were 3 ft. less and the width 3 ft. more, the area would be increased 27 sq. ft. Find the dimensions of the room.", "answer_latex": [ "12 ft. by 24 ft." ], "answer_markdown": [ "12 ft. by 24 ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "L": "24", "W": "12" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x), Eq((a - 3)*(x + 3), a*x + 27))" ], "shape": [ "solve: (Eq(a, N*x), Eq((N + a)*(N + x), N + a*x))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/73", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 73, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 73", "problem_latex": "A floor is two-thirds as wide as it is long. If the\nwidth were 2 ft. more and the length 4 ft. less, the area\nwould be diminished 22 sq. ft. What are its dimensions?", "markdown": "A floor is two-thirds as wide as it is long. If the width were 2 ft. more and the length 4 ft. less, the area would be diminished 22 sq. ft. What are its dimensions?", "answer_latex": [ "14 ft. by 21 ft." ], "answer_markdown": [ "14 ft. by 21 ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "L": "21", "W": "14" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 2*a/3), Eq((a - 4)*(x + 2), a*x - 22))" ], "shape": [ "solve: (Eq(x, N*a), Eq((N + a)*(N + x), N + a*x))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/74", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 74, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 74", "problem_latex": "A rectangle has its length and width respectively\n4 ft. longer and 2 ft. shorter than the side of an equivalent\nsquare. Find its area.", "markdown": "A rectangle has its length and width respectively 4 ft. longer and 2 ft. shorter than the side of an equivalent square. Find its area.", "answer_latex": [ "16 sq. ft." ], "answer_markdown": [ "16 sq. ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq((s+4)*(s-2),s**2)", "answer_expr": { "area": "16" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq((x - 2)*(x + 4), x**2)" ], "shape": [ "solve: Eq((N + x)**2, x**N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/75", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 75, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 75", "problem_latex": "An enclosed garden is 24 ft. greater in length than in\nwidth. 684 sq. ft. is used for a walk 3 ft. wide extending\naround the garden inside the fence. How long is the\ngarden?", "markdown": "An enclosed garden is 24 ft. greater in length than in width. 684 sq. ft. is used for a walk 3 ft. wide extending around the garden inside the fence. How long is the garden?", "answer_latex": [ "48 ft. by 72 ft." ], "answer_markdown": [ "48 ft. by 72 ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "L": "72", "W": "48" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x + 24), Eq(a*x - (a - 6)*(x - 6), 684))" ], "shape": [ "solve: (Eq(a, N + x), Eq(a*x - (N + a)*(N + x), N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/76a", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 76, "part": "a", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 76a", "problem_latex": "Factor $\\displaystyle \\frac{x^2}{4}-\\frac{y^2z^4}{9m^6}$,\n$x^6-27y^3$, $a^{16}-b^{16}$, $2c-4c^3+2c^5$.", "markdown": "Factor $\\displaystyle \\frac{x^2}{4}-\\frac{y^2z^4}{9m^6}$, $x^6-27y^3$, $a^{16}-b^{16}$, $2c-4c^3+2c^5$.", "answer_latex": [ "\\begin{tabular}{l}\n $\\displaystyle \\left( \\frac{x}{2} + \\frac{yz^2}{3m^3} \\right)\n \\left( \\frac{x}{2} - \\frac{yz^2}{3m^3} \\right) $; \\\\\n $(x^2 - 3y)(x^4 + 3x^2y + 9 y^2) $; \\\\\n $(a^8 + b^8)(a^4 + b^4) $ etc.; \\\\\n $2c(c^2 - 1)^2$.\n\\end{tabular}" ], "answer_markdown": [ "tabularl $\\displaystyle \\left( \\frac{x}{2} + \\frac{yz^2}{3m^3} \\right) \\left( \\frac{x}{2} - \\frac{yz^2}{3m^3} \\right) $; $(x^2 - 3y)(x^4 + 3x^2y + 9 y^2) $; $(a^8 + b^8)(a^4 + b^4) $ etc.; $2c(c^2 - 1)^2$. tabular" ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**2/4 - y**2*z**4/(9*m**6)", "answer_expr": "(x/2 + y*z**2/(3*m**3))*(x/2 - y*z**2/(3*m**3))" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: x**2/4 - b**2*c**4/(9*a**6)" ], "shape": [ "factor: N*a**N*b**N*c**N + N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/76b", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 76, "part": "b", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 76b", "problem_latex": "Factor $\\displaystyle \\frac{x^2}{4}-\\frac{y^2z^4}{9m^6}$,\n$x^6-27y^3$, $a^{16}-b^{16}$, $2c-4c^3+2c^5$.", "markdown": "Factor $\\displaystyle \\frac{x^2}{4}-\\frac{y^2z^4}{9m^6}$, $x^6-27y^3$, $a^{16}-b^{16}$, $2c-4c^3+2c^5$.", "answer_latex": [ "\\begin{tabular}{l}\n $\\displaystyle \\left( \\frac{x}{2} + \\frac{yz^2}{3m^3} \\right)\n \\left( \\frac{x}{2} - \\frac{yz^2}{3m^3} \\right) $; \\\\\n $(x^2 - 3y)(x^4 + 3x^2y + 9 y^2) $; \\\\\n $(a^8 + b^8)(a^4 + b^4) $ etc.; \\\\\n $2c(c^2 - 1)^2$.\n\\end{tabular}" ], "answer_markdown": [ "tabularl $\\displaystyle \\left( \\frac{x}{2} + \\frac{yz^2}{3m^3} \\right) \\left( \\frac{x}{2} - \\frac{yz^2}{3m^3} \\right) $; $(x^2 - 3y)(x^4 + 3x^2y + 9 y^2) $; $(a^8 + b^8)(a^4 + b^4) $ etc.; $2c(c^2 - 1)^2$. tabular" ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "x**6 - 27*y**3", "answer_expr": "(x**2 - 3*y)*(x**4 + 3*x**2*y + 9*y**2)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: -27*a**3 + x**6" ], "shape": [ "factor: N*a**N + x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/76c", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 76, "part": "c", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 76c", "problem_latex": "Factor $\\displaystyle \\frac{x^2}{4}-\\frac{y^2z^4}{9m^6}$,\n$x^6-27y^3$, $a^{16}-b^{16}$, $2c-4c^3+2c^5$.", "markdown": "Factor $\\displaystyle \\frac{x^2}{4}-\\frac{y^2z^4}{9m^6}$, $x^6-27y^3$, $a^{16}-b^{16}$, $2c-4c^3+2c^5$.", "answer_latex": [ "\\begin{tabular}{l}\n $\\displaystyle \\left( \\frac{x}{2} + \\frac{yz^2}{3m^3} \\right)\n \\left( \\frac{x}{2} - \\frac{yz^2}{3m^3} \\right) $; \\\\\n $(x^2 - 3y)(x^4 + 3x^2y + 9 y^2) $; \\\\\n $(a^8 + b^8)(a^4 + b^4) $ etc.; \\\\\n $2c(c^2 - 1)^2$.\n\\end{tabular}" ], "answer_markdown": [ "tabularl $\\displaystyle \\left( \\frac{x}{2} + \\frac{yz^2}{3m^3} \\right) \\left( \\frac{x}{2} - \\frac{yz^2}{3m^3} \\right) $; $(x^2 - 3y)(x^4 + 3x^2y + 9 y^2) $; $(a^8 + b^8)(a^4 + b^4) $ etc.; $2c(c^2 - 1)^2$. tabular" ], "checks": [ { "task": "factor", "verdict": "FLAG-MISMATCH", "judge_why": [ "320700.99506608275119", "16259.143681520819824" ], "problem_expr": "a**16 - b**16", "answer_expr": "(a**8 + b**8)*(a**4 + b**4)" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "factor: -a**16 + x**16" ], "shape": [ "factor: -a**N + x**N" ], "same_problem_in": [ "boyden-first-book-in-algebra-1895/ex-33/17" ], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/76d", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 76, "part": "d", "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 76d", "problem_latex": "Factor $\\displaystyle \\frac{x^2}{4}-\\frac{y^2z^4}{9m^6}$,\n$x^6-27y^3$, $a^{16}-b^{16}$, $2c-4c^3+2c^5$.", "markdown": "Factor $\\displaystyle \\frac{x^2}{4}-\\frac{y^2z^4}{9m^6}$, $x^6-27y^3$, $a^{16}-b^{16}$, $2c-4c^3+2c^5$.", "answer_latex": [ "\\begin{tabular}{l}\n $\\displaystyle \\left( \\frac{x}{2} + \\frac{yz^2}{3m^3} \\right)\n \\left( \\frac{x}{2} - \\frac{yz^2}{3m^3} \\right) $; \\\\\n $(x^2 - 3y)(x^4 + 3x^2y + 9 y^2) $; \\\\\n $(a^8 + b^8)(a^4 + b^4) $ etc.; \\\\\n $2c(c^2 - 1)^2$.\n\\end{tabular}" ], "answer_markdown": [ "tabularl $\\displaystyle \\left( \\frac{x}{2} + \\frac{yz^2}{3m^3} \\right) \\left( \\frac{x}{2} - \\frac{yz^2}{3m^3} \\right) $; $(x^2 - 3y)(x^4 + 3x^2y + 9 y^2) $; $(a^8 + b^8)(a^4 + b^4) $ etc.; $2c(c^2 - 1)^2$. tabular" ], "checks": [ { "task": "factor", "verdict": "PASS", "judge_why": null, "problem_expr": "2*c - 4*c**3 + 2*c**5", "answer_expr": "2*c*(c**2 - 1)**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "factor: 2*x**5 - 4*x**3 + 2*x" ], "shape": [ "factor: N*x + 2*N*x**N" ], "same_problem_in": [], "needs": [ "cas.factor" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/77", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 77, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 77", "problem_latex": "Extract the square root of $12x^4-24x+9+x^6-22x^3-4x^5+28x^2$.", "markdown": "Extract the square root of $12x^4-24x+9+x^6-22x^3-4x^5+28x^2$.", "answer_latex": [ "$x^3 -2x^2 + 4x -3$." ], "answer_markdown": [ "$x^3 -2x^2 + 4x -3$." ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "12*x**4 - 24*x + 9 + x**6 - 22*x**3 - 4*x**5 + 28*x**2", "answer_expr": "x**3 - 2*x**2 + 4*x - 3" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.root.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/78", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 78, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 78", "problem_latex": "What must be subtracted from the sum of\n$4x^3+3x^2y-y^3$, $4x^2y-3x^3$, $7x^2y+9y^3-2x^2y$, to leave the remainder\n$2x^3-3x^2y+y^3$?", "markdown": "What must be subtracted from the sum of $4x^3+3x^2y-y^3$, $4x^2y-3x^3$, $7x^2y+9y^3-2x^2y$, to leave the remainder $2x^3-3x^2y+y^3$?", "answer_latex": [ "$7y^3 + 15x^2y - x^3$." ], "answer_markdown": [ "$7y^3 + 15x^2y - x^3$." ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(4*x**3 + 3*x**2*y - y**3) + (4*x**2*y - 3*x**3) + (7*x**2*y + 9*y**3 - 2*x**2*y) - (2*x**3 - 3*x**2*y + y**3)", "answer_expr": "7*y**3 + 15*x**2*y - x**3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: 7*a**3 + 15*a*x**2 - x**3" ], "shape": [ "identity: N*a*x**N + N*a**N - x**N" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/79", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 79, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 79", "problem_latex": "Find the G.C.F. of $x\\left(x+1\\right)^2$, $x^2(x^2-1)$, and\n$2x^3-2x^2-4x$.", "markdown": "Find the G.C.F. of $x\\left(x+1\\right)^2$, $x^2(x^2-1)$, and $2x^3-2x^2-4x$.", "answer_latex": [ "$x(x + 1)$." ], "answer_markdown": [ "$x(x + 1)$." ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "x*(x + 1)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (x*(x + 1)**2, x**2*(x**2 - 1), 2*x**3 - 2*x**2 - 4*x)" ], "shape": [ "hcf: (x*(x + 1)**N, x**N*(x**N - 1), N*x + 2*N*x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/8", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 8", "problem_latex": "I bought some five-cent stamps, and twice as many\ntwo-cent stamps, paying for the whole 81 cents. How\nmany stamps of each kind did I buy?", "markdown": "I bought some five-cent stamps, and twice as many two-cent stamps, paying for the whole 81 cents. How many stamps of each kind did I buy?", "answer_latex": [ "$9$ fives; $18$ twos." ], "answer_markdown": [ "$9$ fives; $18$ twos." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "f": "9", "t": "18" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(2*a + 5*x, 81))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/80", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 80, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 80", "problem_latex": "From one end of a line I cut off 5 feet less than one-fifth\nof it, and from the other end 4 feet more than one-fourth of it,\nand then there remained 34 feet. How long was the line?", "markdown": "From one end of a line I cut off 5 feet less than one-fifth of it, and from the other end 4 feet more than one-fourth of it, and then there remained 34 feet. How long was the line?", "answer_latex": [ "60 ft." ], "answer_markdown": [ "60 ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(L-(L/5-5)-(L/4+4),34)", "answer_expr": { "L": "60" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(11*x/20 + 1, 34)" ], "shape": [ "solve: Eq(N*x + 1, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/81", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 81, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 81", "problem_latex": "A can do twice as much work as B, B can do twice\nas much as C, and together they can complete a piece of\nwork in 4 days. In what time can each alone complete the\nwork.", "markdown": "A can do twice as much work as B, B can do twice as much as C, and together they can complete a piece of work in 4 days. In what time can each alone complete the work.", "answer_latex": [ "A, 7 days; B, 14 days; C, 28 days." ], "answer_markdown": [ "A, 7 days; B, 14 days; C, 28 days." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "A": "7", "B": "14", "C": "28" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(b, 2*a), Eq(1/x + 1/b + 1/a, 1/4))" ], "shape": [ "solve: (Eq(a, N*x), Eq(b, N*a), Eq(1/x + 1/b + 1/a, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/82", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 82, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 82", "problem_latex": "Separate 57 into two parts, such that one divided by\nthe other may give 5 as a quotient, with 3 as a remainder.", "markdown": "Separate 57 into two parts, such that one divided by the other may give 5 as a quotient, with 3 as a remainder.", "answer_latex": [ "$9$; $48$." ], "answer_markdown": [ "$9$; $48$." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "x": "48", "y": "9" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(x, 5*a + 3), Eq(a + x, 57))" ], "shape": [ "solve: (Eq(x, N*a + N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/83", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 83, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 83", "problem_latex": "Divide 92 into two parts, such that one divided by\nthe other may give 4 as a quotient, with 2 as a remainder.", "markdown": "Divide 92 into two parts, such that one divided by the other may give 4 as a quotient, with 2 as a remainder.", "answer_latex": [ "$18$; $74$." ], "answer_markdown": [ "$18$; $74$." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "x": "74", "y": "18" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(x, 4*a + 2), Eq(a + x, 92))" ], "shape": [ "solve: (Eq(x, N*a + N), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/84", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 84, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 84", "problem_latex": "Fourteen persons engaged a yacht, but before sailing,\nfour of the company withdrew, by which the expense\nof each was increased \\$4. What was paid for the yacht?", "markdown": "Fourteen persons engaged a yacht, but before sailing, four of the company withdrew, by which the expense of each was increased $4. What was paid for the yacht?", "answer_latex": [ "\\$140." ], "answer_markdown": [ "$140." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(T/14+4,T/10)", "answer_expr": { "T": "140" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x/14 + 4, x/10)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/85", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 85, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 85", "problem_latex": "Find two consecutive numbers such that a fifth of\nthe larger shall equal the difference between a third and an\neighth of the smaller.", "markdown": "Find two consecutive numbers such that a fifth of the larger shall equal the difference between a third and an eighth of the smaller.", "answer_latex": [ "$24$; $25$." ], "answer_markdown": [ "$24$; $25$." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "L": "25", "s": "24" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(a/5, 5*x/24), Eq(a, x + 1))" ], "shape": [ "solve: (Eq(N*a, N*x), Eq(a, x + 1))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/86", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 86, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 86", "problem_latex": "A is 24 years older than B, and A's age is as much\nabove 50 as B's is below 40. What is the age of each?", "markdown": "A is 24 years older than B, and A’s age is as much above 50 as B’s is below 40. What is the age of each?", "answer_latex": [ "A, $57$ yrs.; B $33$ yrs." ], "answer_markdown": [ "A, $57$ yrs.; B $33$ yrs." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": null, "answer_expr": { "A": "57", "B": "33" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(x, a + 24), Eq(x - 50, -a + 40))" ], "shape": [ "solve: (Eq(x, N + a), Eq(N + x, N - a))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/87", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 87, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 87", "problem_latex": "Find the number, whose double added to 16 will\nbe as much above 70 as the number itself is below 60.", "markdown": "Find the number, whose double added to 16 will be as much above 70 as the number itself is below 60.", "answer_latex": [ "$38$." ], "answer_markdown": [ "$38$." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": null, "problem_expr": "Eq(2*x+16-70,60-x)", "answer_expr": { "x": "38" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: Eq(2*x - 54, -x + 60)" ], "shape": [ "solve: Eq(N*x + N, N - x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.solve.num" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/88", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 88, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 88", "problem_latex": "A hare takes 5 leaps to a dog's 4, but 3 of the dog's\nleaps are equal to 4 of the hare's; the hare has a start of\n20 leaps. How many leaps will the hare take before he is\ncaught?\n\n\\textit{ Suggestion}. Let $5x$ equal the number of leaps the hare\nwill take, and let $m$ equal the length of one leap.", "markdown": "A hare takes 5 leaps to a dog’s 4, but 3 of the dog’s leaps are equal to 4 of the hare’s; the hare has a start of 20 leaps. How many leaps will the hare take before he is caught? *Suggestion*. Let $5x$ equal the number of leaps the hare will take, and let $m$ equal the length of one leap.", "answer_latex": [ "$300$ leaps." ], "answer_markdown": [ "$300$ leaps." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": "the equations leave [{d: 4*h/3}]", "problem_expr": null, "answer_expr": { "n": "300" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(3*a, 4*b), Eq(b*x + 20*b, 4*a*x/5))" ], "shape": [ "solve: (Eq(N*a, N*b), Eq(N*b + b*x, N*a*x))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/89", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 89, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 89", "problem_latex": "A greyhound takes 3 leaps to a hare's 5, but 2 of\nthe greyhound's leaps are equal to 4 of the hare's. If the\nhare has a start of 48 leaps, how soon will the greyhound\novertake him?", "markdown": "A greyhound takes 3 leaps to a hare’s 5, but 2 of the greyhound’s leaps are equal to 4 of the hare’s. If the hare has a start of 48 leaps, how soon will the greyhound overtake him?", "answer_latex": [ "With $144$ leaps." ], "answer_markdown": [ "With $144$ leaps." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": "the equations leave [{g: 2*h}]", "problem_expr": null, "answer_expr": { "n": "144" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(2*a, 4*b), Eq(a*x, 5*b*x/3 + 48*b))" ], "shape": [ "solve: (Eq(N*a, N*b), Eq(a*x, N*b*x + N*b))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/9", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 9", "problem_latex": "Three barns contain 58 tons of hay. In the first\nbarn there are 3 tons more than in the second, and 7 less\nthan in the third. How many tons in each barn?", "markdown": "Three barns contain 58 tons of hay. In the first barn there are 3 tons more than in the second, and 7 less than in the third. How many tons in each barn?", "answer_latex": [ "$18$; $15$; $25$ tons." ], "answer_markdown": [ "$18$; $15$; $25$ tons." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "a": "18", "b": "15", "c": "25" } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, a + 3), Eq(x, b - 7), Eq(a + b + x, 58))" ], "shape": [ "solve: (Eq(x, N + a), Eq(x, N + b), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-54/90", "set": "boyden-first-book-in-algebra-1895/ex-54", "number": 90, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 54, problem 90", "problem_latex": "A hare has 40 leaps the start of a dog. When will\nhe be caught if 5 of his leaps are equal to 4 of the dog's,\nand if he takes 7 leaps while the dog takes 6?", "markdown": "A hare has 40 leaps the start of a dog. When will he be caught if 5 of his leaps are equal to 4 of the dog’s, and if he takes 7 leaps while the dog takes 6?", "answer_latex": [ "After $560$ leaps." ], "answer_markdown": [ "After $560$ leaps." ], "checks": [ { "task": "solve", "verdict": "FLAG-EXTRACTION", "judge_why": "the equations leave [{d: 5*h/4}]", "problem_expr": null, "answer_expr": { "n": "560" } } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-EXTRACTION" ] }, "form": [ "solve: (Eq(5*b, 4*a), Eq(6*a*x/7, b*x + 40*b))" ], "shape": [ "solve: (Eq(N*b, N*a), Eq(N*a*x, N*b + b*x))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/1", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 1", "problem_latex": "$\n \\left\\{ \\begin{array}{rcrcl}\n x &+& y &=& 4, \\\\\n3x &-& 2y &=& 7 .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} x &+& y &=& 4, \\\\ 3x &-& 2y &=& 7 . \\end{array} \\right. $", "answer_latex": [ "$x=3$, $y=1$." ], "answer_markdown": [ "$x=3$, $y=1$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 3, y: 1}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a + x, 4), Eq(-2*a + 3*x, 7))" ], "shape": [ "solve: (Eq(a + x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/10", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 10", "problem_latex": "$\n \\left\\{ \\begin{array}{rcrcl}\n3x &-& 5y &=& 15, \\\\\n5x &+& 3y &=& 8 .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 3x &-& 5y &=& 15, \\\\ 5x &+& 3y &=& 8 . \\end{array} \\right. $", "answer_latex": [ "$x=2\\frac{1}{2}$, $y=-1\\frac{1}{2}$." ], "answer_markdown": [ "$x=2\\frac{1}{2}$, $y=-1\\frac{1}{2}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: Rational(5, 2), y: -Rational(3, 2)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(-5*a + 3*x, 15), Eq(3*a + 5*x, 8))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/11", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 11", "problem_latex": "$\n\\left\\{ \\begin{array}{rcrcl}\n3y &-& 2x &=& 3, \\\\\n4y &-& 6x &=& 2\\frac{1}{3} .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 3y &-& 2x &=& 3, \\\\ 4y &-& 6x &=& 2\\frac{1}{3} . \\end{array} \\right. $", "answer_latex": [ "$x=\\frac{1}{2}$, $y=1\\frac{1}{3}$." ], "answer_markdown": [ "$x=\\frac{1}{2}$, $y=1\\frac{1}{3}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: Rational(1, 2), y: Rational(4, 3)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(4*a - 6*x, 7/3), Eq(3*a - 2*x, 3))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/12", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 12", "problem_latex": "$\n\\left\\{ \\begin{array}{rcrcl}\n3x &+ & 2y &=& 11,\\\\\n 7x &-& 5y &=& 190.\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 3x &+ & 2y &=& 11,\\\\ 7x &-& 5y &=& 190. \\end{array} \\right. $", "answer_latex": [ "$x=15$, $y=-17$." ], "answer_markdown": [ "$x=15$, $y=-17$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 15, y: -17}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(2*a + 3*x, 11), Eq(-5*a + 7*x, 190))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/13", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 13", "problem_latex": "$\n\\left\\{ \\begin{array}{rcrcl}\n\\frac{1}{2}x &+& \\frac{1}{3}y &=& 11,\\\\\n 8x &+& \\frac{2}{5}y &=& 102.\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} \\frac{1}{2}x &+& \\frac{1}{3}y &=& 11,\\\\ 8x &+& \\frac{2}{5}y &=& 102. \\end{array} \\right. $", "answer_latex": [ "$x=12$, $y=15$." ], "answer_markdown": [ "$x=12$, $y=15$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 12, y: 15}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a/3 + x/2, 11), Eq(2*a/5 + 8*x, 102))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/14", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 14", "problem_latex": "$\n\\left\\{ \\begin{array}{rcrcl}\n 5x &+& 2y &=& 66,\\\\\n\\frac{x}{3} &+& \\frac{3y}{4} &=& 15\\frac{1}{2}.\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 5x &+& 2y &=& 66,\\\\ \\frac{x}{3} &+& \\frac{3y}{4} &=& 15\\frac{1}{2}. \\end{array} \\right. $", "answer_latex": [ "$x=6$, $y=18$." ], "answer_markdown": [ "$x=6$, $y=18$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 6, y: 18}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(3*a/4 + x/3, 31/2), Eq(2*a + 5*x, 66))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/15", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 15", "problem_latex": "$\\left\\{ \\begin{matrix}\\frac{3x}{5} - \\frac{2y}{7} = 35, \\\\ x + 2y = -63.\\end{matrix}\\right.$", "markdown": "$\\left\\{ \\begin{matrix}\\frac{3x}{5} - \\frac{2y}{7} = 35, \\\\ x + 2y = -63.\\end{matrix}\\right.$", "answer_latex": [ "$x=35$, $y=-49$." ], "answer_markdown": [ "$x=35$, $y=-49$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 35, y: -49}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(-2*a/7 + 3*x/5, 35), Eq(2*a + x, -63))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/16", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 16", "problem_latex": "$\\left\\{ \\begin{matrix}x - \\frac{3y}{5} = 6,\n\\\\ \\frac{2x}{3} + 7y = 189.\\end{matrix}\\right.$", "markdown": "$\\left\\{ \\begin{matrix}x - \\frac{3y}{5} = 6, \\\\ \\frac{2x}{3} + 7y = 189.\\end{matrix}\\right.$", "answer_latex": [ "$x=21$, $y=25$." ], "answer_markdown": [ "$x=21$, $y=25$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 21, y: 25}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(7*a + 2*x/3, 189), Eq(-3*a/5 + x, 6))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/17", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 17", "problem_latex": "$\\left\\{ \\begin{matrix}\\frac{x + 2y}{3x - y} = 1, \\\\\n\\frac{4y - x}{3 + x - 2y} = 2\\frac{1}{2}.\\end{matrix}\\right.$", "markdown": "$\\left\\{ \\begin{matrix}\\frac{x + 2y}{3x - y} = 1, \\\\ \\frac{4y - x}{3 + x - 2y} = 2\\frac{1}{2}.\\end{matrix}\\right.$", "answer_latex": [ "$x=3$, $y=2$." ], "answer_markdown": [ "$x=3$, $y=2$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 3, y: 2}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq((4*a - x)/(-2*a + x + 3), 5/2), Eq((2*a + x)/(-a + 3*x), 1))" ], "shape": [ "solve: (Eq((N*a - x)/(N*a + N + x), N), Eq((N*a + x)/(N*x - a), 1))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/18", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 18", "problem_latex": "$\\left\\{ \\begin{matrix}\\frac{x + 2y}{x - 2} = -5\\frac{2}{3},\n\\\\ \\frac{2y - 4x}{3 - y} = -6.\\end{matrix}\\right.$", "markdown": "$\\left\\{ \\begin{matrix}\\frac{x + 2y}{x - 2} = -5\\frac{2}{3}, \\\\ \\frac{2y - 4x}{3 - y} = -6.\\end{matrix}\\right.$", "answer_latex": [ "$x=\\frac{1}{2}$, $y=4$." ], "answer_markdown": [ "$x=\\frac{1}{2}$, $y=4$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: Rational(1, 2), y: 4}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq((2*a - 4*x)/(-a + 3), -6), Eq((2*a + x)/(x - 2), -17/3))" ], "shape": [ "solve: (Eq((N*a + N*x)/(N - a), N), Eq((N*a + x)/(N + x), N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/19", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 19", "problem_latex": "$\\left\\{ \\begin{matrix}y - \\frac{2y + x}{3} = \\frac{2x + y}{4} - 8\\frac{3}{4}, \\\\ \\frac{3x + y}{2} - \\frac{y}{3} = \\frac{109}{10} + \\frac{4y - x}{5}.\\end{matrix}\\right.$", "markdown": "$\\left\\{ \\begin{matrix}y - \\frac{2y + x}{3} = \\frac{2x + y}{4} - 8\\frac{3}{4}, \\\\ \\frac{3x + y}{2} - \\frac{y}{3} = \\frac{109}{10} + \\frac{4y - x}{5}.\\end{matrix}\\right.$", "answer_latex": [ "$x=12$, $y=15$." ], "answer_markdown": [ "$x=12$, $y=15$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 12, y: 15}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a/3 - x/3, a/4 + x/2 - 35/4), Eq(a/6 + 3*x/2, 4*a/5 - x/5 + 109/10))" ], "shape": [ "solve: (Eq(N*a + N*x, N*a + N*x + N), Eq(N*a + N*x, N*a + N*x + N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/2", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 2", "problem_latex": "$\n\\left\\{ \\begin{array}{rcrcl}\n x &-& y &=& 2, \\\\\n2x &+& 5y &=& 18 .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} x &-& y &=& 2, \\\\ 2x &+& 5y &=& 18 . \\end{array} \\right. $", "answer_latex": [ "$x=4$, $y=2$." ], "answer_markdown": [ "$x=4$, $y=2$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 4, y: 2}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(-a + x, 2), Eq(5*a + 2*x, 18))" ], "shape": [ "solve: (Eq(-a + x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/20", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 20", "problem_latex": "$\\left\\{ \\begin{matrix}x + y = a, \\\\ x - y = b.\\end{matrix}\\right.$", "markdown": "$\\left\\{ \\begin{matrix}x + y = a, \\\\ x - y = b.\\end{matrix}\\right.$", "answer_latex": [ "$x=\\frac{a+b}{2}$, $y=\\frac{a-b}{2}$." ], "answer_markdown": [ "$x=\\frac{a+b}{2}$, $y=\\frac{a-b}{2}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: (a + b)/2, y: (a - b)/2}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(-c + x, b), Eq(c + x, a))" ], "shape": [ "solve: (Eq(-c + x, b), Eq(c + x, a))" ], "same_problem_in": [], "needs": [ "cas.simplify", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/21", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 21", "problem_latex": "$\\left\\{ \\begin{matrix}\\frac{3x - 19}{2} + 4 = \\frac{3y + x}{3} + \\frac{5x - 3}{2}, \\\\ \\frac{4x + 5y}{16} + \\frac{2x + y}{2} = \\frac{9x - 7}{8} + \\frac{3y + 9}{4}.\\end{matrix}\\right.$", "markdown": "$\\left\\{ \\begin{matrix}\\frac{3x - 19}{2} + 4 = \\frac{3y + x}{3} + \\frac{5x - 3}{2}, \\\\ \\frac{4x + 5y}{16} + \\frac{2x + y}{2} = \\frac{9x - 7}{8} + \\frac{3y + 9}{4}.\\end{matrix}\\right.$", "answer_latex": [ "$x=39$, $y=-56$." ], "answer_markdown": [ "$x=39$, $y=-56$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 39, y: -56}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(13*a/16 + 5*x/4, 3*a/4 + 9*x/8 + 11/8), Eq(3*x/2 - 11/2, a + 17*x/6 - 3/2))" ], "shape": [ "solve: (Eq(N*a + N*x, N*a + N*x + N), Eq(N*x + N, N*x + N + a))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/22", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 22", "problem_latex": "$\\left\\{ \\begin{matrix}\\frac{1}{5}(3x - 2y) + \\frac{1}{3}(5x - 3y) = x, \\\\ \\frac{4x - 3y}{2} + \\frac{2}{3}x - y = 1 + y.\\end{matrix}\\right.$", "markdown": "$\\left\\{ \\begin{matrix}\\frac{1}{5}(3x - 2y) + \\frac{1}{3}(5x - 3y) = x, \\\\ \\frac{4x - 3y}{2} + \\frac{2}{3}x - y = 1 + y.\\end{matrix}\\right.$", "answer_latex": [ "$x=-2$, $y=-1\\frac{17}{21}$." ], "answer_markdown": [ "$x=-2$, $y=-1\\frac{17}{21}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: -2, y: -Rational(38, 21)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(-7*a/5 + 34*x/15, x), Eq(-5*a/2 + 8*x/3, a + 1))" ], "shape": [ "solve: (Eq(N*a + N*x, x), Eq(N*a + N*x, a + 1))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/23", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 23", "problem_latex": "If 1 is added to the numerator of a fraction, its\nvalue is $\\frac{1}{8}$; but if 4 is added to its denominator, its value\nis $\\frac{1}{4}$. What is the fraction?", "markdown": "If 1 is added to the numerator of a fraction, its value is $\\frac{1}{8}$; but if 4 is added to its denominator, its value is $\\frac{1}{4}$. What is the fraction?", "answer_latex": [ "$ \\frac{7}{24}$." ], "answer_markdown": [ "$ \\frac{7}{24}$." ], "checks": [ { "task": "solve", "verdict": "FLAG-MISMATCH", "judge_why": "Eq((x + 1)/y, 1/8) fails at {x: 7, y: 24}: leaves 0.208333333333", "problem_expr": null, "answer_expr": "{x: 7, y: 24}" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "solve: (Eq(x/(a + 4), 1/4), Eq((x + 1)/a, 1/8))" ], "shape": [ "solve: (Eq(x/(N + a), N), Eq((x + 1)/a, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/24", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 24", "problem_latex": "If 2 is subtracted from both numerator and denominator\nof a certain fraction, its value is $\\frac{3}{5}$; and if 1 is\nadded to both numerator and denominator, its value is $\\frac{2}{3}$.\nWhat is the fraction?", "markdown": "If 2 is subtracted from both numerator and denominator of a certain fraction, its value is $\\frac{3}{5}$; and if 1 is added to both numerator and denominator, its value is $\\frac{2}{3}$. What is the fraction?", "answer_latex": [ "$ \\frac{11}{17}$." ], "answer_markdown": [ "$ \\frac{11}{17}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 11, y: 17}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq((x - 2)/(a - 2), 3/5), Eq((x + 1)/(a + 1), 2/3))" ], "shape": [ "solve: (Eq((N + x)/(N + a), N), Eq((x + 1)/(a + 1), N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/25", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 25, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 25", "problem_latex": "If 2 is added to both numerator and denominator of\na certain fraction, its value is $\\frac{2}{3}$; but if 3 is subtracted\nfrom both numerator and denominator, its value is $\\frac{1}{2}$.\nWhat is the fraction?", "markdown": "If 2 is added to both numerator and denominator of a certain fraction, its value is $\\frac{2}{3}$; but if 3 is subtracted from both numerator and denominator, its value is $\\frac{1}{2}$. What is the fraction?", "answer_latex": [ "$\\frac{8}{13}$." ], "answer_markdown": [ "$\\frac{8}{13}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 8, y: 13}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq((x - 3)/(a - 3), 1/2), Eq((x + 2)/(a + 2), 2/3))" ], "shape": [ "solve: (Eq((N + x)/(N + a), N), Eq((N + x)/(N + a), N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/26", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 26, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 26", "problem_latex": "If 3 be subtracted from the numerator of a certain\nfraction, and 3 be added to the denominator, its value will\nbe $\\frac{1}{2}$; but if 5 be added to the numerator, and 5 be subtracted\nfrom its denominator, its value will be 2. What is\nthe fraction?", "markdown": "If 3 be subtracted from the numerator of a certain fraction, and 3 be added to the denominator, its value will be $\\frac{1}{2}$; but if 5 be added to the numerator, and 5 be subtracted from its denominator, its value will be 2. What is the fraction?", "answer_latex": [ "$\\frac{11}{13}$." ], "answer_markdown": [ "$\\frac{11}{13}$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 11, y: 13}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq((x - 3)/(a + 3), 1/2), Eq((x + 5)/(a - 5), 2))" ], "shape": [ "solve: (Eq((N + x)/(N + a), N), Eq((N + x)/(N + a), N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/27", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 27, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 27", "problem_latex": "The sum of two numbers divided by 2 is 43, and\ntheir difference divided by 2 is 19. What are the numbers?", "markdown": "The sum of two numbers divided by 2 is 43, and their difference divided by 2 is 19. What are the numbers?", "answer_latex": [ "$24$; $62$." ], "answer_markdown": [ "$24$; $62$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 62, y: 24}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(-a/2 + x/2, 19), Eq(a/2 + x/2, 43))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/28", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 28, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 28", "problem_latex": "The sum of two numbers divided by 3 gives as a\nquotient 30, and their difference divided by 9 gives 4.\nWhat are the numbers?", "markdown": "The sum of two numbers divided by 3 gives as a quotient 30, and their difference divided by 9 gives 4. What are the numbers?", "answer_latex": [ "$27$; $63$." ], "answer_markdown": [ "$27$; $63$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 63, y: 27}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(-a/9 + x/9, 4), Eq(a/3 + x/3, 30))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/29", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 29, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 29", "problem_latex": "Five years ago the age of a father was four times\nthat of his son; five years hence the age of the father will\nbe $2\\frac{1}{3}$ times that of the son. What are their ages?", "markdown": "Five years ago the age of a father was four times that of his son; five years hence the age of the father will be $2\\frac{1}{3}$ times that of the son. What are their ages?", "answer_latex": [ "$13$; $37$." ], "answer_markdown": [ "$13$; $37$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{f: 37, s: 13}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x - 5, 4*a - 20), Eq(x + 5, 7*a/3 + 35/3))" ], "shape": [ "solve: (Eq(N + x, N*a + N), Eq(N + x, N*a + N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/3", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 3", "problem_latex": "$\n\\left\\{ \\begin{array}{rcrcl}\n5x &+& 2y &=& 47, \\\\\n2x &-& y &=& 8 .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 5x &+& 2y &=& 47, \\\\ 2x &-& y &=& 8 . \\end{array} \\right. $", "answer_latex": [ "$x=7$, $y=6$." ], "answer_markdown": [ "$x=7$, $y=6$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 7, y: 6}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(-a + 2*x, 8), Eq(2*a + 5*x, 47))" ], "shape": [ "solve: (Eq(N*x - a, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/30", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 30, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 30", "problem_latex": "Seven years ago John was one-half as old as Henry,\nbut five years hence he will be three-quarters as old.\nHow old is each?", "markdown": "Seven years ago John was one-half as old as Henry, but five years hence he will be three-quarters as old. How old is each?", "answer_latex": [ "J., $13$ yrs.; H., $19$ yrs." ], "answer_markdown": [ "J., $13$ yrs.; H., $19$ yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{J: 13, H: 19}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x - 7, a/2 - 7/2), Eq(x + 5, 3*a/4 + 15/4))" ], "shape": [ "solve: (Eq(N + x, N*a + N), Eq(N + x, N*a + N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/31", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 31, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 31", "problem_latex": "$A$ and $B$ own herds of cows. If $A$ should sell 6\ncows, and $B$ should buy 6, they would have the same number;\nif $B$ should sell 4 cows to $A$, he would have only\nhalf as many as A. How many cows are there in each\nherd?", "markdown": "$A$ and $B$ own herds of cows. If $A$ should sell 6 cows, and $B$ should buy 6, they would have the same number; if $B$ should sell 4 cows to $A$, he would have only half as many as A. How many cows are there in each herd?", "answer_latex": [ "A, $36$ cows; B, $24$ cows." ], "answer_markdown": [ "A, $36$ cows; B, $24$ cows." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{A: 36, B: 24}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x - 6, a + 6), Eq(2*a - 8, x + 4))" ], "shape": [ "solve: (Eq(N + x, N + a), Eq(N*a + N, N + x))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/32", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 32, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 32", "problem_latex": "The cost of 5 pounds of tea and 7 pounds of coffee is\n\\$4.94; the cost of 3 pounds of tea and 6 pounds of coffee is\n\\$3.54. What is the cost of the tea and coffee per pound?", "markdown": "The cost of 5 pounds of tea and 7 pounds of coffee is $4.94; the cost of 3 pounds of tea and 6 pounds of coffee is $3.54. What is the cost of the tea and coffee per pound?", "answer_latex": [ "tea, $54$; coffee, $32$." ], "answer_markdown": [ "tea, $54$; coffee, $32$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{t: 54, c: 32}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(6*a + 3*x, 354), Eq(7*a + 5*x, 494))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/33", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 33, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 33", "problem_latex": "What is the price of corn and oats when 4 bushels of corn\nwith 6 bushels of oats cost \\$4.66, and 5 bushels of corn with 9\nbushels of oats cost \\$6.38?", "markdown": "What is the price of corn and oats when 4 bushels of corn with 6 bushels of oats cost $4.66, and 5 bushels of corn with 9 bushels of oats cost $6.38?", "answer_latex": [ "corn, $61$; oats, $37$." ], "answer_markdown": [ "corn, $61$; oats, $37$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{c: 61, o: 37}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(6*a + 4*x, 466), Eq(9*a + 5*x, 638))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/34", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 34, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 34", "problem_latex": "A merchant mixes tea which cost him 87 cents a pound with\ntea which cost him 29 cents a pound. The cost of the mixture is\n\\$17.98. He sells the mixture at 55 cents a pound and gains\n\\$2.92. How many pounds of each did he put into the mixture?", "markdown": "A merchant mixes tea which cost him 87 cents a pound with tea which cost him 29 cents a pound. The cost of the mixture is $17.98. He sells the mixture at 55 cents a pound and gains $2.92. How many pounds of each did he put into the mixture?", "answer_latex": [ "$12$ lbs of $87$ kind; $26$ lbs of $29$ kind." ], "answer_markdown": [ "$12$ lbs of $87$ kind; $26$ lbs of $29$ kind." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 12, y: 26}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(55*a + 55*x, 2090), Eq(29*a + 87*x, 1798))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/4", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 4", "problem_latex": "$\n \\left\\{ \\begin{array}{rcrcl}\n4x &-& 3y &=& 10, \\\\\n6x &+& 4y &=& 49 .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 4x &-& 3y &=& 10, \\\\ 6x &+& 4y &=& 49 . \\end{array} \\right. $", "answer_latex": [ "$x=5\\frac{1}{2}$, $y=4$." ], "answer_markdown": [ "$x=5\\frac{1}{2}$, $y=4$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: Rational(11, 2), y: 4}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(-3*a + 4*x, 10), Eq(4*a + 6*x, 49))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/5", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 5", "problem_latex": "$\n \\left\\{ \\begin{array}{rcrcl}\n 8x &-& 2y &=& 6, \\\\\n 10x &+& 7y &=& 36 .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 8x &-& 2y &=& 6, \\\\ 10x &+& 7y &=& 36 . \\end{array} \\right. $", "answer_latex": [ "$x=1\\frac{1}{2}$, $y=3$." ], "answer_markdown": [ "$x=1\\frac{1}{2}$, $y=3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: Rational(3, 2), y: 3}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(-2*a + 8*x, 6), Eq(7*a + 10*x, 36))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/6", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 6", "problem_latex": "$\n \\left\\{ \\begin{array}{rcrcl}\n 2x &-& 5y &=& -11, \\\\\n 3x &+& y &=& 9 .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 2x &-& 5y &=& -11, \\\\ 3x &+& y &=& 9 . \\end{array} \\right. $", "answer_latex": [ "$x=2$, $y=3$." ], "answer_markdown": [ "$x=2$, $y=3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 2, y: 3}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(-5*a + 2*x, -11), Eq(a + 3*x, 9))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*x + a, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/7", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 7", "problem_latex": "$\n\\left\\{ \\begin{array}{rcrcl}\n 7x &-& 3y &=& 41, \\\\\n 2x &+& y &=& 12 .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 7x &-& 3y &=& 41, \\\\ 2x &+& y &=& 12 . \\end{array} \\right. $", "answer_latex": [ "$x=5$, $y=-2$." ], "answer_markdown": [ "$x=5$, $y=-2$." ], "checks": [ { "task": "solve", "verdict": "FLAG-MISMATCH", "judge_why": "Eq(2*x + y, 12) fails at {x: 5, y: -2}: leaves -4.00000000000", "problem_expr": null, "answer_expr": "{x: 5, y: -2}" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-MISMATCH" ] }, "form": [ "solve: (Eq(a + 2*x, 12), Eq(-3*a + 7*x, 41))" ], "shape": [ "solve: (Eq(N*x + a, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/8", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 8", "problem_latex": "$\n \\left\\{ \\begin{array}{rcrcl}\n 2x &+& 9y &=& -5, \\\\\n11x &+& 15y &=& 7 .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 2x &+& 9y &=& -5, \\\\ 11x &+& 15y &=& 7 . \\end{array} \\right. $", "answer_latex": [ "$x=2$, $y=-1$." ], "answer_markdown": [ "$x=2$, $y=-1$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 2, y: -1}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(9*a + 2*x, -5), Eq(15*a + 11*x, 7))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-55/9", "set": "boyden-first-book-in-algebra-1895/ex-55", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 55, problem 9", "problem_latex": "$\n\\left\\{ \\begin{array}{rcrcl}\n 4y &-& 2x &=& 4, \\\\\n10y &+& 3x &=& -8 .\n\\end{array} \\right.\n$", "markdown": "$ \\left\\{ \\begin{array}{rcrcl} 4y &-& 2x &=& 4, \\\\ 10y &+& 3x &=& -8 . \\end{array} \\right. $", "answer_latex": [ "$x=-2\\frac{1}{4}$, $y=-\\frac{1}{8}$." ], "answer_markdown": [ "$x=-2\\frac{1}{4}$, $y=-\\frac{1}{8}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{x: -Rational(9, 4), y: -Rational(1, 8)}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(4*a - 2*x, 4), Eq(10*a + 3*x, -8))" ], "shape": [ "solve: (Eq(N*a + N*x, N), Eq(N*a + N*x, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/1", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 1", "problem_latex": "$5x^2-12 = 33$.", "markdown": "$5x^2-12 = 33$.", "answer_latex": [ "$x=\\pm 3$." ], "answer_markdown": [ "$x=\\pm 3$." ], "checks": [ { "task": "solve", "verdict": "FLAG-INTERPRETED", "judge_why": "only the model reading is judged for algebra tasks", "problem_expr": "Eq(5*x**2 - 12, 33)", "answer_expr": "[-3, 3]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "solve: Eq(5*x**2 - 12, 33)" ], "shape": [ "solve: Eq(N*x**N + N, N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/10", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 10", "problem_latex": "$\\displaystyle \\frac{x+1}{x-1}+\\frac{2(x-3)}{x-2} =\n\\frac{16-9x}{x^2-3x+2}$.", "markdown": "$\\displaystyle \\frac{x+1}{x-1}+\\frac{2(x-3)}{x-2} = \\frac{16-9x}{x^2-3x+2}$.", "answer_latex": [ "$x=\\pm 2$." ], "answer_markdown": [ "$x=\\pm 2$." ], "checks": [ { "task": "solve", "verdict": "FLAG-PARSE", "judge_why": "TypeError: Invalid NaN comparison", "problem_expr": "Eq((x + 1)/(x - 1) + 2*(x - 3)/(x - 2), (16 - 9*x)/(x**2 - 3*x + 2))", "answer_expr": "[-2, 2]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-PARSE" ] }, "form": [ "solve: Eq((x + 1)/(x - 1) + (2*x - 6)/(x - 2), (-9*x + 16)/(x**2 - 3*x + 2))" ], "shape": [ "solve: Eq((x + 1)/(x - 1) + (N*x + N)/(N + x), (N*x + N)/(N*x + N + x**N))" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/11", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 11", "problem_latex": "$\\displaystyle\n\\frac{1}{(2-x)(3-x)}-\\frac{2}{(1-x)(x-3)}+\\frac{1}{(x-1)(x-2)} =\n\\frac{1}{2-x}+\\frac{1}{(x-1)(2-x)(x-3)}$.", "markdown": "$\\displaystyle \\frac{1}{(2-x)(3-x)}-\\frac{2}{(1-x)(x-3)}+\\frac{1}{(x-1)(x-2)} = \\frac{1}{2-x}+\\frac{1}{(x-1)(2-x)(x-3)}$.", "answer_latex": [ "$x=\\pm 2$." ], "answer_markdown": [ "$x=\\pm 2$." ], "checks": [ { "task": "solve", "verdict": "FLAG-PARSE", "judge_why": "TypeError: Invalid NaN comparison", "problem_expr": "Eq(1/((2-x)*(3-x)) - 2/((1-x)*(x-3)) + 1/((x-1)*(x-2)), 1/(2-x) + 1/((x-1)*(2-x)*(x-3)))", "answer_expr": "[-2, 2]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-PARSE" ] }, "form": [ "solve: Eq(1/((x - 2)*(x - 1)) + 1/((-x + 2)*(-x + 3)) - 2/((-x + 1)*(x - 3)), 1/(-x + 2) + 1/((-x + 2)*(x - 3)*(x - 1)))" ], "shape": [ "solve: Eq(N/((-x + 1)*(N + x)) + 1/((N + x)*(x - 1)) + (N - x)**(-2), 1/(N - x) + 1/((N - x)*(N + x)*(x - 1)))" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/12", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 12", "problem_latex": "$\\displaystyle\n\\frac{1}{6x+6}-\\frac{1}{2x+2}+\\frac{10}{3-3x^2} =\n\\frac{x}{3(1-x)}$.", "markdown": "$\\displaystyle \\frac{1}{6x+6}-\\frac{1}{2x+2}+\\frac{10}{3-3x^2} = \\frac{x}{3(1-x)}$.", "answer_latex": [ "$x=\\pm 3$." ], "answer_markdown": [ "$x=\\pm 3$." ], "checks": [ { "task": "solve", "verdict": "FLAG-INTERPRETED", "judge_why": "only the model reading is judged for algebra tasks", "problem_expr": "Eq(1/(6*x + 6) - 1/(2*x + 2) + 10/(3 - 3*x**2), x/(3*(1 - x)))", "answer_expr": "[-3, 3]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "solve: Eq(1/(6*x + 6) - 1/(2*x + 2) + 10/(-3*x**2 + 3), x/(-3*x + 3))" ], "shape": [ "solve: Eq(N/(N*x**N + N), x/(N*x + N))" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/13", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 13", "problem_latex": "A father is 30 years old, and his son is two years\nold. In how many years will the father be three times as\nold as his son?", "markdown": "A father is 30 years old, and his son is two years old. In how many years will the father be three times as old as his son?", "answer_latex": [ "$12$ yrs." ], "answer_markdown": [ "$12$ yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 12}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x + 30, 3*x + 6)" ], "shape": [ "solve: Eq(N + x, N*x + N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.eqn" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "3 ENTER 2 × 30 −", "1 ENTER 3 −", "÷" ], "constants": [ { "value": "1", "source": "the coefficient of x in 30 + x (the father's age plus x years, so 1·x)" } ], "calculator_value": "+12E+0", "printed_value": "12", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/14", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 14", "problem_latex": "Divide the number 112 into two parts such that the\nsmaller divided by their difference will give as a quotient\n3.", "markdown": "Divide the number 112 into two parts such that the smaller divided by their difference will give as a quotient 3.", "answer_latex": [ "$48$; $64$." ], "answer_markdown": [ "$48$; $64$." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 48, y: 64}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 3*a - 3*x), Eq(a + x, 112))" ], "shape": [ "solve: (Eq(x, N*a + N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/15", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 15", "problem_latex": "The numerator of a fraction is 4 less than the denominator;\nif 30 be added to the denominator, or if 10 be subtracted\nfrom the numerator, the resulting fractions will\nbe equal. What is the original fraction?", "markdown": "The numerator of a fraction is 4 less than the denominator; if 30 be added to the denominator, or if 10 be subtracted from the numerator, the resulting fractions will be equal. What is the original fraction?", "answer_latex": [ "$\\frac{17}{21}$" ], "answer_markdown": [ "$\\frac{17}{21}$" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{n: 17, d: 21}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, a + 4), Eq(a/(x + 30), (a - 10)/x))" ], "shape": [ "solve: (Eq(x, N + a), Eq(a/(N + x), (N + a)/x))" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/2", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 2", "problem_latex": "$3x^2+4 = 16$.", "markdown": "$3x^2+4 = 16$.", "answer_latex": [ "$x=\\pm 2$." ], "answer_markdown": [ "$x=\\pm 2$." ], "checks": [ { "task": "solve", "verdict": "FLAG-INTERPRETED", "judge_why": "only the model reading is judged for algebra tasks", "problem_expr": "Eq(3*x**2 + 4, 16)", "answer_expr": "[-2, 2]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "solve: Eq(3*x**2 + 4, 16)" ], "shape": [ "solve: Eq(N*x**N + N, N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/3", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 3", "problem_latex": "$4x^2+ll = 136-x^2$.", "markdown": "$4x^2+ll = 136-x^2$.", "answer_latex": [ "$x=\\pm 5$." ], "answer_markdown": [ "$x=\\pm 5$." ], "checks": [ { "task": "solve", "verdict": "FLAG-INTERPRETED", "judge_why": "only the model reading is judged for algebra tasks", "problem_expr": "Eq(4*x**2 + ll, 136 - x**2)", "answer_expr": "[-5, 5]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "solve: Eq(a + 4*x**2, -x**2 + 136)" ], "shape": [ "solve: Eq(N*x**N + a, N - x**N)" ], "same_problem_in": [], "needs": [ "cas.collect", "cas.solve.poly", "core.arith" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/4", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 4", "problem_latex": "$5(3x^2-1) = 11(x^2+1)$.", "markdown": "$5(3x^2-1) = 11(x^2+1)$.", "answer_latex": [ "$x=\\pm 2$." ], "answer_markdown": [ "$x=\\pm 2$." ], "checks": [ { "task": "solve", "verdict": "FLAG-INTERPRETED", "judge_why": "only the model reading is judged for algebra tasks", "problem_expr": "Eq(5*(3*x**2 - 1), 11*(x**2 + 1))", "answer_expr": "[-2, 2]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "solve: Eq(15*x**2 - 5, 11*x**2 + 11)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/5", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 5", "problem_latex": "$\\displaystyle \\frac{2}{5x^2}-\\frac{1}{3x^2} =\n\\frac{4}{15}$.", "markdown": "$\\displaystyle \\frac{2}{5x^2}-\\frac{1}{3x^2} = \\frac{4}{15}$.", "answer_latex": [ "$x=\\pm \\frac{1}{2}$." ], "answer_markdown": [ "$x=\\pm \\frac{1}{2}$." ], "checks": [ { "task": "solve", "verdict": "FLAG-INTERPRETED", "judge_why": "only the model reading is judged for algebra tasks", "problem_expr": "Eq(2/(5*x**2) - 1/(3*x**2), Rational(4, 15))", "answer_expr": "[-Rational(1, 2), Rational(1, 2)]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "solve: Eq(1/(15*x**2), 4/15)" ], "shape": [ "solve: Eq(N*x**N, N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/6", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 6", "problem_latex": "$\\displaystyle \\frac{x^2-1}{6}+\\frac{1}{4} =\n\\frac{x^2+1}{8}$.", "markdown": "$\\displaystyle \\frac{x^2-1}{6}+\\frac{1}{4} = \\frac{x^2+1}{8}$.", "answer_latex": [ "$x=\\pm 1$." ], "answer_markdown": [ "$x=\\pm 1$." ], "checks": [ { "task": "solve", "verdict": "FLAG-INTERPRETED", "judge_why": "only the model reading is judged for algebra tasks", "problem_expr": "Eq((x**2 - 1)/6 + Rational(1, 4), (x**2 + 1)/8)", "answer_expr": "[-1, 1]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "solve: Eq(x**2/6 + 1/12, x**2/8 + 1/8)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/7", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 7", "problem_latex": "$(x+3)^2 = 6x+58$.", "markdown": "$(x+3)^2 = 6x+58$.", "answer_latex": [ "$x=\\pm 7$." ], "answer_markdown": [ "$x=\\pm 7$." ], "checks": [ { "task": "solve", "verdict": "FLAG-INTERPRETED", "judge_why": "only the model reading is judged for algebra tasks", "problem_expr": "Eq((x + 3)**2, 6*x + 58)", "answer_expr": "[-7, 7]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "solve: Eq((x + 3)**2, 6*x + 58)" ], "shape": [ "solve: Eq((N + x)**N, N*x + N)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/8", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 8", "problem_latex": "$\\displaystyle 6x+2+\\frac{16}{x} =\n\\frac{15+40x}{4}-1\\frac{3}{4}$.", "markdown": "$\\displaystyle 6x+2+\\frac{16}{x} = \\frac{15+40x}{4}-1\\frac{3}{4}$.", "answer_latex": [ "$x=\\pm 2$." ], "answer_markdown": [ "$x=\\pm 2$." ], "checks": [ { "task": "solve", "verdict": "FLAG-INTERPRETED", "judge_why": "only the model reading is judged for algebra tasks", "problem_expr": "Eq(6*x + 2 + 16/x, (15 + 40*x)/4 - (1 + Rational(3, 4)))", "answer_expr": "[-2, 2]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-INTERPRETED" ] }, "form": [ "solve: Eq(6*x + 2 + 16/x, 10*x + 2)" ], "shape": [ "solve: Eq(N*x + N + N/x, N*x + N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-56/9", "set": "boyden-first-book-in-algebra-1895/ex-56", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 56, problem 9", "problem_latex": "$\\displaystyle\n\\frac{x-3}{x-1}+\\frac{x+1}{x+3}+\\frac{8}{x^2+2x-3} = 0$.", "markdown": "$\\displaystyle \\frac{x-3}{x-1}+\\frac{x+1}{x+3}+\\frac{8}{x^2+2x-3} = 0$.", "answer_latex": [ "$x=\\pm 1$." ], "answer_markdown": [ "$x=\\pm 1$." ], "checks": [ { "task": "solve", "verdict": "FLAG-PARSE", "judge_why": "TypeError: Invalid NaN comparison", "problem_expr": "Eq((x - 3)/(x - 1) + (x + 1)/(x + 3) + 8/(x**2 + 2*x - 3), 0)", "answer_expr": "[-1, 1]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-PARSE" ] }, "form": [ "solve: Eq((x - 3)/(x - 1) + (x + 1)/(x + 3) + 8/(x**2 + 2*x - 3), 0)" ], "shape": [ "solve: Eq(N/(N*x + N + x**N) + (N + x)/(x - 1) + (x + 1)/(N + x), 0)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/1", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 1", "problem_latex": "$x^{2}+3x=18$.", "markdown": "$x^{2}+3x=18$.", "answer_latex": [ "$x = 3 \\text{ or } -6$." ], "answer_markdown": [ "$x = 3 \\text{ or } -6$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x**2 + 3*x, 18)", "answer_expr": "[3, -6]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x**2 + 3*x, 18)" ], "shape": [ "solve: Eq(N*x + x**N, N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/10", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 10", "problem_latex": "$adx-acx^{2}=bcx-bd$.", "markdown": "$adx-acx^{2}=bcx-bd$.", "answer_latex": [ "$x = \\frac{d}{c} \\text{ or } -\\frac{b}{a}$." ], "answer_markdown": [ "$x = \\frac{d}{c} \\text{ or } -\\frac{b}{a}$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(a*d*x - a*c*x**2, b*c*x - b*d)", "answer_expr": "[d/c, -b/a]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-a*c*x**2 + a*d*x, b*c*x - b*d)" ], "shape": [ "solve: Eq(-a*c*x**N + a*d*x, b*c*x - b*d)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/11", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 11", "problem_latex": "$(x+3)(x-3)=8(x+3)$.", "markdown": "$(x+3)(x-3)=8(x+3)$.", "answer_latex": [ "$x = 11 \\text{ or } -3$." ], "answer_markdown": [ "$x = 11 \\text{ or } -3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x + 3)*(x - 3), 8*(x + 3))", "answer_expr": "[11, -3]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq((x - 3)*(x + 3), 8*x + 24)" ], "shape": [ "solve: Eq((N + x)**2, N*x + N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/12", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 12", "problem_latex": "$(x+2)(x-5)=4(x-4)$.", "markdown": "$(x+2)(x-5)=4(x-4)$.", "answer_latex": [ "$x = 6 \\text{ or } 1$." ], "answer_markdown": [ "$x = 6 \\text{ or } 1$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x + 2)*(x - 5), 4*(x - 4))", "answer_expr": "[6, 1]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq((x - 5)*(x + 2), 4*x - 16)" ], "shape": [ "solve: Eq((N + x)**2, N*x + N)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/13", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 13", "problem_latex": "$\\displaystyle \\frac{x}{5}+\\frac{2}{x}=1\\frac{2}{5}$.", "markdown": "$\\displaystyle \\frac{x}{5}+\\frac{2}{x}=1\\frac{2}{5}$.", "answer_latex": [ "$x = 5 \\text{ or } 2$." ], "answer_markdown": [ "$x = 5 \\text{ or } 2$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/5 + 2/x, 7/5)", "answer_expr": "[5, 2]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x/5 + 2/x, 7/5)" ], "shape": [ "solve: Eq(N*x + N/x, N)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/14", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 14", "problem_latex": "$\\displaystyle \\frac{x}{3}-2=\\frac{x^{2}}{12}-\\frac{x}{2}$.", "markdown": "$\\displaystyle \\frac{x}{3}-2=\\frac{x^{2}}{12}-\\frac{x}{2}$.", "answer_latex": [ "$x = 6 \\text{ or } 4$." ], "answer_markdown": [ "$x = 6 \\text{ or } 4$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/3 - 2, x**2/12 - x/2)", "answer_expr": "[6, 4]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x/3 - 2, x**2/12 - x/2)" ], "shape": [ "solve: Eq(N*x + N, N*x + N*x**N)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/15", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 15", "problem_latex": "$\\displaystyle \\frac{8}{x-2}-3+\\frac{x+1}{7}=0$.", "markdown": "$\\displaystyle \\frac{8}{x-2}-3+\\frac{x+1}{7}=0$.", "answer_latex": [ "$x = 6 \\text{ or } 16$." ], "answer_markdown": [ "$x = 6 \\text{ or } 16$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(8/(x - 2) - 3 + (x + 1)/7, 0)", "answer_expr": "[6, 16]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x/7 - 20/7 + 8/(x - 2), 0)" ], "shape": [ "solve: Eq(N*x + N + N/(N + x), 0)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/16", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 16", "problem_latex": "$\\displaystyle \\frac{x}{x+1}-2\\frac{1}{6}+\\frac{x+1}{x}=0$.", "markdown": "$\\displaystyle \\frac{x}{x+1}-2\\frac{1}{6}+\\frac{x+1}{x}=0$.", "answer_latex": [ "$x = 2 \\text{ or } -3$." ], "answer_markdown": [ "$x = 2 \\text{ or } -3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/(x + 1) - 13/6 + (x + 1)/x, 0)", "answer_expr": "[2, -3]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x/(x + 1) - 13/6 + (x + 1)/x, 0)" ], "shape": [ "solve: Eq(N + x/(x + 1) + (x + 1)/x, 0)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/17", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 17", "problem_latex": "$\\displaystyle x+4=3x-\\frac{24}{x-1}$.", "markdown": "$\\displaystyle x+4=3x-\\frac{24}{x-1}$.", "answer_latex": [ "$x = 5 \\text{ or } -2$." ], "answer_markdown": [ "$x = 5 \\text{ or } -2$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x + 4, 3*x - 24/(x - 1))", "answer_expr": "[5, -2]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x + 4, 3*x - 24/(x - 1))" ], "shape": [ "solve: Eq(N + x, N*x + N/(x - 1))" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/18", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 18", "problem_latex": "$\\displaystyle\n\\frac{x-1}{x+1}+\\frac{x+3}{x-3}=\\frac{2(x+2)}{x-2}$.", "markdown": "$\\displaystyle \\frac{x-1}{x+1}+\\frac{x+3}{x-3}=\\frac{2(x+2)}{x-2}$.", "answer_latex": [ "$x = 0 \\text{ or } 5$." ], "answer_markdown": [ "$x = 0 \\text{ or } 5$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x - 1)/(x + 1) + (x + 3)/(x - 3), 2*(x + 2)/(x - 2))", "answer_expr": "[0, 5]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq((x - 1)/(x + 1) + (x + 3)/(x - 3), (2*x + 4)/(x - 2))" ], "shape": [ "solve: Eq((x - 1)/(x + 1) + 1, (N*x + N)/(N + x))" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/19", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 19, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 19", "problem_latex": "$\\displaystyle\n\\frac{x-1}{x+2}-\\frac{3x^{2}+2}{x^{2}-4}=\\frac{3x}{2-x}$.", "markdown": "$\\displaystyle \\frac{x-1}{x+2}-\\frac{3x^{2}+2}{x^{2}-4}=\\frac{3x}{2-x}$.", "answer_latex": [ "$x = 0 \\text{ or } -3$." ], "answer_markdown": [ "$x = 0 \\text{ or } -3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x - 1)/(x + 2) - (3*x**2 + 2)/(x**2 - 4), 3*x/(2 - x))", "answer_expr": "[0, -3]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq((x - 1)/(x + 2) - (3*x**2 + 2)/(x**2 - 4), 3*x/(-x + 2))" ], "shape": [ "solve: Eq(-(N*x**N + N)/(N + x**N) + (x - 1)/(N + x), N*x/(N - x))" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/2", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 2", "problem_latex": "$x^{2}+5x=14$.", "markdown": "$x^{2}+5x=14$.", "answer_latex": [ "$x = 2 \\text{ or } -7$." ], "answer_markdown": [ "$x = 2 \\text{ or } -7$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x**2 + 5*x, 14)", "answer_expr": "[2, -7]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x**2 + 5*x, 14)" ], "shape": [ "solve: Eq(N*x + x**N, N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/20", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 20, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 20", "problem_latex": "$\\displaystyle\n\\frac{2x}{3-x}+\\frac{2x(x-3)}{x^2-9}=\\frac{x-3}{x+3}$.", "markdown": "$\\displaystyle \\frac{2x}{3-x}+\\frac{2x(x-3)}{x^2-9}=\\frac{x-3}{x+3}$.", "answer_latex": [ "$x = 3 \\text{ or } 3$." ], "answer_markdown": [ "$x = 3 \\text{ or } 3$." ], "checks": [ { "task": "solve", "verdict": "FLAG-PARSE", "judge_why": "TypeError: Invalid NaN comparison", "problem_expr": "Eq(2*x/(3 - x) + 2*x*(x - 3)/(x**2 - 9), (x - 3)/(x + 3))", "answer_expr": "[3, 3]" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "FLAG-PARSE" ] }, "form": [ "solve: Eq(2*x*(x - 3)/(x**2 - 9) + 2*x/(-x + 3), (x - 3)/(x + 3))" ], "shape": [ "solve: Eq(N*x*(N + x)/(N + x**N) + N*x/(N - x), 1)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/21", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 21, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 21", "problem_latex": "At what time between 4 and 5 o'clock are the hands of a\nclock opposite each other?", "markdown": "At what time between 4 and 5 o’clock are the hands of a clock opposite each other?", "answer_latex": [ "$54\\frac{6}{11}$ m." ], "answer_markdown": [ "$54\\frac{6}{11}$ m." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{t: 600/11}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(6*x, x/2 + 300)" ], "shape": [ "solve: Eq(N*x, N*x + N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "120 ENTER 180 +", "ENTER 6 ENTER 1 ENTER 2 ÷ − ÷" ], "constants": [ { "value": "6", "source": "the 6 in '6*t' in the mathematics (the minute hand moves 6 degrees per minute)" }, { "value": "1", "source": "the implicit coefficient of t in 't/2' in the mathematics (1·t/2), used to form 6 − 1/2 = 5.5" }, { "value": "2", "source": "the 2 in 't/2' in the mathematics" }, { "value": "120", "source": "the 120 in 'Eq(6*t, 120 + t/2 + 180)' (the hour hand's head start at 4 o'clock)" }, { "value": "180", "source": "the 180 in 'Eq(6*t, 120 + t/2 + 180)' (the 180-degree offset for hands opposite)" } ], "calculator_value": "+5454545454545454545454545454545455E-32", "printed_value": "600/11", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/22", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 22, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 22", "problem_latex": "John, having three times as much money as Lewis, gave Lewis\n\\$2, and then had twice as much as Lewis. How much had each at\nfirst?", "markdown": "John, having three times as much money as Lewis, gave Lewis $2, and then had twice as much as Lewis. How much had each at first?", "answer_latex": [ "J., \\$18; L., \\$6." ], "answer_markdown": [ "J., $18; L., $6." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{J: 18, L: 6}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 3*x), Eq(a - 2, 2*x + 4))" ], "shape": [ "solve: (Eq(a, N*x), Eq(N + a, N*x + N))" ], "same_problem_in": [], "needs": [ "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/23", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 23, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 23", "problem_latex": "A fish is 3 feet long; its head is equal in length to the\ntail, and its body is five times the length of the head and tail\ntogether. What is the length of the head?", "markdown": "A fish is 3 feet long; its head is equal in length to the tail, and its body is five times the length of the head and tail together. What is the length of the head?", "answer_latex": [ "$3$ in." ], "answer_markdown": [ "$3$ in." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{h: 3}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 5*b + 5*x), Eq(x, b), Eq(a + b + x, 36))" ], "shape": [ "solve: (Eq(a, N*b + N*x), Eq(x, b), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.linsys", "core.units" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "3 ENTER 12 ×", "12 ÷" ], "constants": [ { "value": "12", "source": "The 12 inches in a foot, to convert the 3 feet given in the problem to 36 inches, which is the answer's unit. Also the coefficient of h in the working: h + b + t = h + 10h + h = 12h, since t = h and b = 5(h + t) = 10h." } ], "calculator_value": "+3E+0", "printed_value": "3", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/24", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 24, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 24", "problem_latex": "In how many days can A, B, and C build a boat\nif they work together, provided A alone can build it in\n24 days, B in 18 days, and C in 30 days?", "markdown": "In how many days can A, B, and C build a boat if they work together, provided A alone can build it in 24 days, B in 18 days, and C in 30 days?", "answer_latex": [ "$7\\frac{31}{47}$ days." ], "answer_markdown": [ "$7\\frac{31}{47}$ days." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(d/24 + d/18 + d/30, 1)", "answer_expr": "{d: 360/47}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(47*x/360, 1)" ], "shape": [ "solve: Eq(N*x, 1)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/3", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 3", "problem_latex": "$x(x-1)=72$.", "markdown": "$x(x-1)=72$.", "answer_latex": [ "$x = 9 \\text{ or } -8$." ], "answer_markdown": [ "$x = 9 \\text{ or } -8$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x*(x - 1), 72)", "answer_expr": "[9, -8]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x*(x - 1), 72)" ], "shape": [ "solve: Eq(x*(x - 1), N)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/4", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 4", "problem_latex": "$x^{2}=10x-21$.", "markdown": "$x^{2}=10x-21$.", "answer_latex": [ "$x = 7 \\text{ or } 3$." ], "answer_markdown": [ "$x = 7 \\text{ or } 3$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x**2, 10*x - 21)", "answer_expr": "[7, 3]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x**2, 10*x - 21)" ], "shape": [ "solve: Eq(x**N, N*x + N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/5", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 5", "problem_latex": "$23x=120+x^{2}$.", "markdown": "$23x=120+x^{2}$.", "answer_latex": [ "$x = 8 \\text{ or } 15$." ], "answer_markdown": [ "$x = 8 \\text{ or } 15$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(23*x, 120 + x**2)", "answer_expr": "[8, 15]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(23*x, x**2 + 120)" ], "shape": [ "solve: Eq(N*x, N + x**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/6", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 6", "problem_latex": "$187=x^{2}+6x$.", "markdown": "$187=x^{2}+6x$.", "answer_latex": [ "$x = 11 \\text{ or } -17$." ], "answer_markdown": [ "$x = 11 \\text{ or } -17$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(187, x**2 + 6*x)", "answer_expr": "[11, -17]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(187, x**2 + 6*x)" ], "shape": [ "solve: Eq(N, N*x + x**N)" ], "same_problem_in": [], "needs": [ "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/7", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 7", "problem_latex": "$x^{2}-2bx=-b^{2}$.", "markdown": "$x^{2}-2bx=-b^{2}$.", "answer_latex": [ "$x = b \\text{ or } b$." ], "answer_markdown": [ "$x = b \\text{ or } b$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x**2 - 2*b*x, -b**2)", "answer_expr": "[b, b]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-2*a*x + x**2, -a**2)" ], "shape": [ "solve: Eq(N*a*x + x**N, -a**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/8", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 8", "problem_latex": "$x^{2}=4ax-3a^{2}$.", "markdown": "$x^{2}=4ax-3a^{2}$.", "answer_latex": [ "$x = a \\text{ or } 3a$." ], "answer_markdown": [ "$x = a \\text{ or } 3a$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x**2, 4*a*x - 3*a**2)", "answer_expr": "[a, 3*a]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x**2, -3*a**2 + 4*a*x)" ], "shape": [ "solve: Eq(x**N, N*a*x + N*a**N)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-57/9", "set": "boyden-first-book-in-algebra-1895/ex-57", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 57, problem 9", "problem_latex": "$x^{2}+(a-1)x=a$.", "markdown": "$x^{2}+(a-1)x=a$.", "answer_latex": [ "$x = 1 \\text{ or } -a$." ], "answer_markdown": [ "$x = 1 \\text{ or } -a$." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x**2 + (a - 1)*x, a)", "answer_expr": "[1, -a]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(x**2 + x*(a - 1), a)" ], "shape": [ "solve: Eq(x*(a - 1) + x**N, a)" ], "same_problem_in": [], "needs": [ "cas.expand", "cas.factor", "cas.solve.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-58/1", "set": "boyden-first-book-in-algebra-1895/ex-58", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 58, problem 1", "problem_latex": "When $a=l$, $b = 3$, $c = 5$, and $d = O$, what is the\nvalue of\n\n$\\displaystyle\n\\frac{4a+b^2+b^2c^2+ad}{b^2+c^2+d^2}-\\frac{1+a^2c^2}{a^2+c^2+d^2}\n+\\frac{a^2+b^2+d^2}{1+a^2b^2+bd}-\\frac{a^2+2ab+b^2}{b^2-2bc+c^2}$?", "markdown": "When $a=l$, $b = 3$, $c = 5$, and $d = O$, what is the value of $\\displaystyle \\frac{4a+b^2+b^2c^2+ad}{b^2+c^2+d^2}-\\frac{1+a^2c^2}{a^2+c^2+d^2} +\\frac{a^2+b^2+d^2}{1+a^2b^2+bd}-\\frac{a^2+2ab+b^2}{b^2-2bc+c^2}$?", "answer_latex": [ "$3$" ], "answer_markdown": [ "$3$" ], "checks": [ { "task": "evaluate", "verdict": "PASS", "judge_why": "computed 3.0, printed 3 (half-unit 0.5; correctly rounded at the printed digits: 3.0)", "problem_expr": "(4*a+b**2+b**2*c**2+a*d)/(b**2+c**2+d**2) - (1+a**2*c**2)/(a**2+c**2+d**2) + (a**2+b**2+d**2)/(1+a**2*b**2+b*d) - (a**2+2*a*b+b**2)/(b**2-2*b*c+c**2)", "answer_expr": "3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "evaluate: -(a**2*c**2 + 1)/(a**2 + c**2 + d**2) + (a**2 + b**2 + d**2)/(a**2*b**2 + b*d + 1) - (a**2 + 2*a*b + b**2)/(b**2 - 2*b*c + c**2) + (a*d + 4*a + b**2*c**2 + b**2)/(b**2 + c**2 + d**2) at a=1, b=3, c=5, d=0" ], "shape": [ "evaluate: -(a**N*c**N + 1)/(a**N + c**N + d**N) + (a**N + b**N + d**N)/(a**N*b**N + b*d + 1) - (N*a*b + a**N + b**N)/(N*b*c + b**N + c**N) + (N*a + a*d + b**N*c**N + b**N)/(b**N + c**N + d**N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.frac" ], "expectation": "X=3", "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-58/10", "set": "boyden-first-book-in-algebra-1895/ex-58", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 58, problem 10", "problem_latex": "Simplify\n\n\\[\n\\left(\\frac{1}{x-1}-\\frac{3}{(x+3)(x-1)}\\right)\\div\\left(\\frac{1}{x+3}+\\frac{1}{(x-1)(x+3)}\\right).\n\\]", "markdown": "Simplify (1x-1-3(x+3)(x-1))÷(1x+3+1(x-1)(x+3)).", "answer_latex": [ "$1$" ], "answer_markdown": [ "$1$" ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "((1/(x-1)) - 3/((x+3)*(x-1))) / (1/(x+3) + 1/((x-1)*(x+3)))", "answer_expr": "1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (1/(x - 1) - 3/((x - 1)*(x + 3)))/(1/(x + 3) + 1/((x - 1)*(x + 3)))" ], "shape": [ "identity: (N/((N + x)*(x - 1)) + 1/(x - 1))/(1/(N + x) + 1/((N + x)*(x - 1)))" ], "same_problem_in": [], "needs": [ "cas.cancel", "cas.simplify", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-58/2", "set": "boyden-first-book-in-algebra-1895/ex-58", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 58, problem 2", "problem_latex": "Prove that $\\displaystyle\n(x^{2}+xy+y^{2})(x^{2}-xy+y^2)=\\frac{x^{6}-y^{6}}{x^{2}-y^{2}}$", "markdown": "Prove that $\\displaystyle (x^{2}+xy+y^{2})(x^{2}-xy+y^2)=\\frac{x^{6}-y^{6}}{x^{2}-y^{2}}$", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": null, "answer_expr": null } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.simplify" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-58/3", "set": "boyden-first-book-in-algebra-1895/ex-58", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 58, problem 3", "problem_latex": "Solve $(x+5)^{2}-(x+1)^{2}-16x=(x-1)^{2}-(x-5)^{2}$.", "markdown": "Solve $(x+5)^{2}-(x+1)^{2}-16x=(x-1)^{2}-(x-5)^{2}$.", "answer_latex": [ "$x=3$" ], "answer_markdown": [ "$x=3$" ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x+5)**2-(x+1)**2-16*x, (x-1)**2-(x-5)**2)", "answer_expr": "3" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(-16*x - (x + 1)**2 + (x + 5)**2, -(x - 5)**2 + (x - 1)**2)" ], "shape": [ "solve: Eq(N*x + (N + x)**N - (x + 1)**N, -(N + x)**N + (x - 1)**N)" ], "same_problem_in": [], "needs": [ "cas.expand", "core.eqn" ], "expectation": "X=3", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "5 ENTER 2 × 1 ENTER 2 × − 16 −", "1 ENTER 2 × +/− 5 ENTER 2 × + −", "1 ENTER 5 GOLD x² − 5 GOLD x² − 1 GOLD x² +", "x↔y ÷" ], "constants": [ { "value": "5", "source": "the 5 in (x+5)² and (x−5)²" }, { "value": "1", "source": "the 1 in (x+1)² and (x−1)²" }, { "value": "2", "source": "the 2 of the binomial term 2·a·x in each squared bracket (the exponent 2 in the problem, so each expansion's linear term is 2 times the constant)" }, { "value": "16", "source": "the 16 in '−16x' on the left-hand side" } ], "calculator_value": "+3E+0", "printed_value": "3", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-58/4", "set": "boyden-first-book-in-algebra-1895/ex-58", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 58, problem 4", "problem_latex": "A tank is filled by two pipes, $A$ and $B$, running\ntogether, in 12 hours, and by the pipe $B$ alone in 20 hours.\nIn what time will the pipe $A$ alone fill it?", "markdown": "A tank is filled by two pipes, $A$ and $B$, running together, in 12 hours, and by the pipe $B$ alone in 20 hours. In what time will the pipe $A$ alone fill it?", "answer_latex": [ "$30$ hrs" ], "answer_markdown": [ "$30$ hrs" ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{\"x\": 30}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(1/20 + 1/x, 1/12)" ], "shape": [ "solve: Eq(N + 1/x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "12 1/x 20 1/x −", "1/x" ], "calculator_value": "+3000000000000000000000000000000000E-32", "printed_value": "30", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-58/5", "set": "boyden-first-book-in-algebra-1895/ex-58", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 58, problem 5", "problem_latex": "Find the G.C.F. of $x^{3}+1-x-x^{2}$, $x^{3}+x-1-x^{2}$,\n$x^{4}-1$, and $x^{2}-4x+3$.", "markdown": "Find the G.C.F. of $x^{3}+1-x-x^{2}$, $x^{3}+x-1-x^{2}$, $x^{4}-1$, and $x^{2}-4x+3$.", "answer_latex": [ "$x-1$" ], "answer_markdown": [ "$x-1$" ], "checks": [ { "task": "hcf", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "x-1" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "hcf: (x**4 - 1, x**2 - 4*x + 3, x**3 - x**2 - x + 1, x**3 - x**2 + x - 1)" ], "shape": [ "hcf: (x**N - 1, N*x + N + x**N, -x + 1, x - 1)" ], "same_problem_in": [], "needs": [ "cas.factor", "cas.pgcd" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-58/6", "set": "boyden-first-book-in-algebra-1895/ex-58", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 58, problem 6", "problem_latex": "Divide $a^{5}+a^{4}b-a^{3}b^{2}+a^{3}-2ab^{2}+b^{3}$ by $a^{3}-b+a$.", "markdown": "Divide $a^{5}+a^{4}b-a^{3}b^{2}+a^{3}-2ab^{2}+b^{3}$ by $a^{3}-b+a$.", "answer_latex": [ "$a^2+ab-b^2$" ], "answer_markdown": [ "$a^2+ab-b^2$" ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(a**5+a**4*b-a**3*b**2+a**3-2*a*b**2+b**3)/(a**3-b+a)", "answer_expr": "a**2+a*b-b**2" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (a**3 - a**2*x**3 - 2*a**2*x + a*x**4 + x**5 + x**3)/(-a + x**3 + x)" ], "shape": [ "identity: (N*a**N*x + a*x**N - a**N*x**N + a**N + 2*x**N)/(-a + x + x**N)" ], "same_problem_in": [], "needs": [ "cas.pdiv" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-58/7", "set": "boyden-first-book-in-algebra-1895/ex-58", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 58, problem 7", "problem_latex": "Find the square root of $5y^{4}+1+12y^{5}-2y-2y^{3}+4y^{6}+7y^{2}$.", "markdown": "Find the square root of $5y^{4}+1+12y^{5}-2y-2y^{3}+4y^{6}+7y^{2}$.", "answer_latex": [ "$1-y+3y^2+2y^3$" ], "answer_markdown": [ "$1-y+3y^2+2y^3$" ], "checks": [ { "task": "other", "verdict": "UNJUDGED-OTHER", "judge_why": "task other: verbatim only", "problem_expr": "5*y**4+1+12*y**5-2*y-2*y**3+4*y**6+7*y**2", "answer_expr": "2*y**3+3*y**2-y+1" } ], "verdict": "unverified", "judge": { "commit": "4a88328", "verdicts": [ "UNJUDGED-OTHER" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "cas.root.poly" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-58/8", "set": "boyden-first-book-in-algebra-1895/ex-58", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 58, problem 8", "problem_latex": "Expand\n\\[\n(x+1)(x+2)-(2x+1)(2x+3)+(x-4)(x-9)+(x-5)^{2}.\n\\]", "markdown": "Expand (x+1)(x+2)-(2x+1)(2x+3)+(x-4)(x-9)+(x-5)^2.", "answer_latex": [ "$60-x^2-28x$" ], "answer_markdown": [ "$60-x^2-28x$" ], "checks": [ { "task": "identity", "verdict": "PASS", "judge_why": null, "problem_expr": "(x+1)*(x+2)-(2*x+1)*(2*x+3)+(x-4)*(x-9)+(x-5)**2", "answer_expr": "60-x**2-28*x" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "identity: (x - 9)*(x - 4) + (x - 5)**2 + (x + 1)*(x + 2) - (2*x + 1)*(2*x + 3)" ], "shape": [ "identity: (N + x)**2 + (N + x)*(x + 1) + (N + x)**N - (N*x + 1)*(N*x + N)" ], "same_problem_in": [], "needs": [ "cas.expand" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-58/9", "set": "boyden-first-book-in-algebra-1895/ex-58", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 58, problem 9", "problem_latex": "Solve $\\displaystyle\n\\frac{x+2}{x-2}+\\frac{x-2}{x+2}=\\frac{5}{2}$.", "markdown": "Solve $\\displaystyle \\frac{x+2}{x-2}+\\frac{x-2}{x+2}=\\frac{5}{2}$.", "answer_latex": [ "$x=\\pm 6$" ], "answer_markdown": [ "$x=\\pm 6$" ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq((x+2)/(x-2)+(x-2)/(x+2), 5/2)", "answer_expr": "[6, -6]" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq((x - 2)/(x + 2) + (x + 2)/(x - 2), 5/2)" ], "shape": [ "solve: True" ], "same_problem_in": [], "needs": [ "cas.solve.poly", "core.frac" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/1", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 1", "problem_latex": "What number, being increased by 36, will be equal to ten\ntimes itself?", "markdown": "What number, being increased by 36, will be equal to ten times itself?", "answer_latex": [ "4." ], "answer_markdown": [ "4." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x + 36, 10*x)", "answer_expr": "4" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x + 36, 10*x)" ], "shape": [ "solve: Eq(N + x, N*x)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.solve.num" ], "expectation": "X=4", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "36 ENTER 10 ENTER 1 − ÷" ], "constants": [ { "value": "1", "source": "the working: subtract x from both sides, 10x − x = 9x, so x + 36 = 10x becomes 36 = (10 − 1)x; the 1 is the coefficient of x that moves across" } ], "calculator_value": "+4E+0", "printed_value": "4", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/10", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 10", "problem_latex": "James is 3 years older than William, and twice James's age\nis equal to three times William's age. What is the age of each?", "markdown": "James is 3 years older than William, and twice James’s age is equal to three times William’s age. What is the age of each?", "answer_latex": [ "W, 6 yrs.; J, 9 yrs." ], "answer_markdown": [ "W, 6 yrs.; J, 9 yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{W: 6, J: 9}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b + 3), Eq(2*a, 3*b))" ], "shape": [ "solve: (Eq(a, N + b), Eq(N*a, N*b))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/11", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 11", "problem_latex": "One boy has 10 more marbles than another boy. Three times\nthe first boy's marbles equals five times the second boy's\nmarbles. How many has each?", "markdown": "One boy has 10 more marbles than another boy. Three times the first boy’s marbles equals five times the second boy’s marbles. How many has each?", "answer_latex": [ "25; 15 marbles." ], "answer_markdown": [ "25; 15 marbles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 25, b: 15}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b + 10), Eq(3*a, 5*b))" ], "shape": [ "solve: (Eq(a, N + b), Eq(N*a, N*b))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/12", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 12", "problem_latex": "If I add 12 to a certain number, four times this second\nnumber will equal seven times the original number. What is the\noriginal number?", "markdown": "If I add 12 to a certain number, four times this second number will equal seven times the original number. What is the original number?", "answer_latex": [ "16." ], "answer_markdown": [ "16." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(4*(x + 12), 7*x)", "answer_expr": "16" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(4*x + 48, 7*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.solve.num" ], "expectation": "X=16", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "12 ENTER 4 ×", "7 ENTER 4 − ÷" ], "calculator_value": "+16E+0", "printed_value": "16", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/13", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 13", "problem_latex": "Four dozen oranges cost as much as 7 dozen apples, and a\ndozen oranges cost 15 cents more than a dozen apples. What is the\nprice of each?", "markdown": "Four dozen oranges cost as much as 7 dozen apples, and a dozen oranges cost 15 cents more than a dozen apples. What is the price of each?", "answer_latex": [ "Oranges, 35 cents; apples, 20 cents." ], "answer_markdown": [ "Oranges, 35 cents; apples, 20 cents." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{o: 35, a: 20}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, a + 15), Eq(4*b, 7*a))" ], "shape": [ "solve: (Eq(b, N + a), Eq(N*b, N*a))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/14", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 14", "problem_latex": "Two numbers differ by 6, and three times one number equals\nfive times the other number. What are the numbers?", "markdown": "Two numbers differ by 6, and three times one number equals five times the other number. What are the numbers?", "answer_latex": [ "9; 15." ], "answer_markdown": [ "9; 15." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 15, y: 9}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(3*a, 5*b), Eq(a - b, 6))" ], "shape": [ "solve: (Eq(N*a, N*b), Eq(a - b, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/15", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 15", "problem_latex": "A man is 2 years older than his wife, and 15 times his age\nequals 16 times her age. What is the age of each?", "markdown": "A man is 2 years older than his wife, and 15 times his age equals 16 times her age. What is the age of each?", "answer_latex": [ "30 yrs.; 32 yrs." ], "answer_markdown": [ "30 yrs.; 32 yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{M: 32, W: 30}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b + 2), Eq(15*a, 16*b))" ], "shape": [ "solve: (Eq(a, N + b), Eq(N*a, N*b))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/16", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 16", "problem_latex": "A farmer pays just as much for 4 horses as he does for 6\ncows. If a cow costs 15 dollars less than a horse, what is the\ncost of each?", "markdown": "A farmer pays just as much for 4 horses as he does for 6 cows. If a cow costs 15 dollars less than a horse, what is the cost of each?", "answer_latex": [ "Cow, \\$30; horse,\\$45." ], "answer_markdown": [ "Cow, $30; horse,$45." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{h: 45, c: 30}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b - 15), Eq(4*b, 6*a))" ], "shape": [ "solve: (Eq(a, N + b), Eq(N*b, N*a))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/17", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 17", "problem_latex": "What number is that which is 15 less than four times the\nnumber itself?", "markdown": "What number is that which is 15 less than four times the number itself?", "answer_latex": [ "5." ], "answer_markdown": [ "5." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x, 4*x - 15)", "answer_expr": "5" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(x, 4*x - 15)" ], "shape": [ "solve: Eq(x, N*x + N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.solve.num" ], "expectation": "X=5", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "15 ENTER 4 ENTER 1 − ÷" ], "constants": [ { "value": "15", "source": "the 15 in '15 less than'" }, { "value": "4", "source": "the 4 in 'four times the number itself'" }, { "value": "1", "source": "the coefficient of the x on the left side (x = 1·x), which is subtracted from both sides to give 4x − x = 3x, so 3x = 15 and x = 15 ÷ 3" } ], "calculator_value": "+5E+0", "printed_value": "5", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/18", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 18", "problem_latex": "A man bought 12 pairs of boots and 6 suits of clothes for\n\\$168. If a suit of clothes cost \\$2 less than four times as much\nas a pair of boots, what was the price of each?", "markdown": "A man bought 12 pairs of boots and 6 suits of clothes for $168. If a suit of clothes cost $2 less than four times as much as a pair of boots, what was the price of each?", "answer_latex": [ "Boots, \\$5; clothes, \\$18." ], "answer_markdown": [ "Boots, $5; clothes, $18." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{b: 5, s: 18}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, 4*a - 2), Eq(12*a + 6*b, 168))" ], "shape": [ "solve: (Eq(b, N*a + N), Eq(N*a + N*b, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/2", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 2", "problem_latex": "Find the number whose double increased by 28 will equal six\ntimes the number itself.", "markdown": "Find the number whose double increased by 28 will equal six times the number itself.", "answer_latex": [ "7." ], "answer_markdown": [ "7." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(2*x + 28, 6*x)", "answer_expr": "7" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(2*x + 28, 6*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.solve.num" ], "expectation": "X=7", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "28 ENTER 6 ENTER 2 −", "÷" ], "constants": [ { "value": "28", "source": "the 28 in 'increased by 28' (2*x + 28)" }, { "value": "6", "source": "the 6 in 'six times the number' (6*x)" }, { "value": "2", "source": "the 2 in 'double' (2*x)" } ], "calculator_value": "+7E+0", "printed_value": "7", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/3", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 3", "problem_latex": "If John's age be multiplied by 5, and if 24 be added to the\nproduct, the sum will be seven times his age. What is his age?", "markdown": "If John’s age be multiplied by 5, and if 24 be added to the product, the sum will be seven times his age. What is his age?", "answer_latex": [ "12 yrs." ], "answer_markdown": [ "12 yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(5*a + 24, 7*a)", "answer_expr": "12" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(5*x + 24, 7*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.solve.num" ], "expectation": "X=12", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "24 ENTER 7 ENTER 5 − ÷" ], "calculator_value": "+12E+0", "printed_value": "12", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/4", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 4", "problem_latex": "A father gave his son four times as many dollars as he then\nhad, and his mother gave him \\$25, when he found that he had nine\ntimes as many dollars as at first. How many dollars had he at\nfirst?", "markdown": "A father gave his son four times as many dollars as he then had, and his mother gave him $25, when he found that he had nine times as many dollars as at first. How many dollars had he at first?", "answer_latex": [ "\\$6.25." ], "answer_markdown": [ "$6.25." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(x + 4*x + 25, 9*x)", "answer_expr": "Rational(25, 4)" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(5*x + 25, 9*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "25 ENTER 4 ÷" ], "constants": [ { "value": "25", "source": "the $25 from the mother in 'his mother gave him $25'" }, { "value": "4", "source": "the 4 in 'four times as many dollars' (the 4x in the expression Eq(x + 4*x + 25, 9*x))" } ], "calculator_value": "+625E-2", "printed_value": "25/4", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/5", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 5", "problem_latex": "A man had a certain amount of money; he earned three times\nas much the next week and found \\$32. If he then had eight times\nas much as at first, how much had he at first?", "markdown": "A man had a certain amount of money; he earned three times as much the next week and found $32. If he then had eight times as much as at first, how much had he at first?", "answer_latex": [ "\\$8." ], "answer_markdown": [ "$8." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(m + 3*m + 32, 8*m)", "answer_expr": "8" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(4*x + 32, 8*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.solve.num" ], "expectation": "X=8", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "32 ENTER 8 ENTER 4 −", "÷" ], "constants": [ { "value": "4", "source": "the working: m + 3m = 4m (the 1 of 'a certain amount' and the 3 of 'three times as much' combine to 4m), so 4m + 32 = 8m rearranges to 8m − 4m = 32, giving m = 32 ÷ (8 − 4)" } ], "calculator_value": "+8E+0", "printed_value": "8", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/6", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 6", "problem_latex": "A man, being asked how many sheep he had, said, \"If you will\ngive me 24 more than six times what I have now, I shall have ten\ntimes my present number.\" How many had he?", "markdown": "A man, being asked how many sheep he had, said, \"If you will give me 24 more than six times what I have now, I shall have ten times my present number.\" How many had he?", "answer_latex": [ "8 sheep." ], "answer_markdown": [ "8 sheep." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(s + 6*s + 24, 10*s)", "answer_expr": "8" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(7*x + 24, 10*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.solve.num" ], "expectation": "X=8", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "24 ENTER 10 ENTER 1 ENTER 6 + − ÷" ], "constants": [ { "value": "24", "source": "the 24 in '24 more than six times what I have now'" }, { "value": "10", "source": "the 10 in 'ten times my present number'" }, { "value": "1", "source": "the implicit 1 in 's' (what I have now, taken once) on the left side of s + 6s + 24 = 10s" }, { "value": "6", "source": "the 6 in 'six times what I have now'" } ], "calculator_value": "+8E+0", "printed_value": "8", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/7", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 7", "problem_latex": "Divide the number 726 into two parts such that one shall be\nfive times the other.", "markdown": "Divide the number 726 into two parts such that one shall be five times the other.", "answer_latex": [ "121; 605." ], "answer_markdown": [ "121; 605." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 121, y: 605}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, 5*a), Eq(a + b, 726))" ], "shape": [ "solve: (Eq(b, N*a), Eq(a + b, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/8", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 8", "problem_latex": "Find two numbers differing by 852, one of which is seven\ntimes the other.", "markdown": "Find two numbers differing by 852, one of which is seven times the other.", "answer_latex": [ "142; 994." ], "answer_markdown": [ "142; 994." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 142, y: 994}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, 7*a), Eq(-a + b, 852))" ], "shape": [ "solve: (Eq(b, N*a), Eq(-a + b, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-6/9", "set": "boyden-first-book-in-algebra-1895/ex-6", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 6, problem 9", "problem_latex": "A storekeeper received a certain amount the first month; the\nsecond month he received \\$50 less than three times as much, and\nthe third month twice as much as the second month. In the three\nmonths he received \\$4850. What did he receive each month?", "markdown": "A storekeeper received a certain amount the first month; the second month he received $50 less than three times as much, and the third month twice as much as the second month. In the three months he received $4850. What did he receive each month?", "answer_latex": [ "\\$500; \\$1450; \\$2900." ], "answer_markdown": [ "$500; $1450; $2900." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 500, b: 1450, c: 2900}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(b, 3*a - 50), Eq(c, 2*b), Eq(a + b + c, 4850))" ], "shape": [ "solve: (Eq(b, N*a + N), Eq(c, N*b), Eq(a + b + c, N))" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/1", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 1", "problem_latex": "Roger is one-fourth as old as his father, and the sum of\ntheir ages is 70 years. How old is each?", "markdown": "Roger is one-fourth as old as his father, and the sum of their ages is 70 years. How old is each?", "answer_latex": [ "14 yrs.; 56 yrs." ], "answer_markdown": [ "14 yrs.; 56 yrs." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{r: 14, f: 56}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a, 4*x), Eq(a + x, 70))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/10", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 10", "problem_latex": "Henry gave a third of his marbles to one boy, and a fourth\nto another boy. He finds that he gave to the boys in all 14\nmarbles. How many had he at first?", "markdown": "Henry gave a third of his marbles to one boy, and a fourth to another boy. He finds that he gave to the boys in all 14 marbles. How many had he at first?", "answer_latex": [ "24 marbles." ], "answer_markdown": [ "24 marbles." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/3 + x/4, 14)", "answer_expr": "24" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(7*x/12, 14)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X=24", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "14 ENTER 3 1/x 4 1/x + ÷" ], "constants": [ { "value": "3", "source": "the 3 in 'a third of his marbles'" }, { "value": "4", "source": "the 4 in 'a fourth' to another boy" }, { "value": "14", "source": "the 14 in 'in all 14 marbles'" } ], "calculator_value": "+2400000000000000000000000000000000E-32", "printed_value": "24", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/11", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 11", "problem_latex": "Two men own a third and two-fifths of a mill respectively.\nIf their part of the property is worth \\$22,000, what is the value\nof the mill?", "markdown": "Two men own a third and two-fifths of a mill respectively. If their part of the property is worth $22,000, what is the value of the mill?", "answer_latex": [ "\\$30,000." ], "answer_markdown": [ "$30,000." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/3 + 2*x/5, 22000)", "answer_expr": "30000" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(11*x/15, 22000)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X=30000", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "22000 ENTER 3 1/x", "2 ENTER 5 ÷ +", "÷" ], "constants": [ { "value": "22000", "source": "the $22,000 in 'their part of the property is worth $22,000'" }, { "value": "3", "source": "the 3 in 'a third' (x/3)" }, { "value": "2", "source": "the 2 in 'two-fifths' (2x/5)" }, { "value": "5", "source": "the 5 in 'two-fifths' (2x/5)" } ], "calculator_value": "+3000000000000000000000000000000000E-29", "printed_value": "30000", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/12", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 12", "problem_latex": "A fruit-seller sold one-fourth of his oranges in the\nforenoon, and three-fifths of them in the afternoon. If he sold in\nall 255 oranges, how many had he at the start?", "markdown": "A fruit-seller sold one-fourth of his oranges in the forenoon, and three-fifths of them in the afternoon. If he sold in all 255 oranges, how many had he at the start?", "answer_latex": [ "300 oranges." ], "answer_markdown": [ "300 oranges." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/4 + 3*x/5, 255)", "answer_expr": "300" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(17*x/20, 255)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X=300", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "255 ENTER 1 ENTER 4 ÷", "3 ENTER 5 ÷ +", "÷" ], "constants": [ { "value": "1", "source": "the numerator of 'one-fourth' in the problem text (x/4 = 1/4 · x)" }, { "value": "4", "source": "the denominator of 'one-fourth' in the problem text (x/4)" }, { "value": "3", "source": "the numerator of 'three-fifths' in the problem text (3x/5)" }, { "value": "5", "source": "the denominator of 'three-fifths' in the problem text (3x/5)" } ], "calculator_value": "+3E+2", "printed_value": "300", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/13", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 13", "problem_latex": "The half, third, and fifth of a number are together equal to\n93. Find the number.", "markdown": "The half, third, and fifth of a number are together equal to 93. Find the number.", "answer_latex": [ "90." ], "answer_markdown": [ "90." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/2 + x/3 + x/5, 93)", "answer_expr": "90" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(31*x/30, 93)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X=90", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "93 ENTER 2 1/x 3 1/x + 5 1/x +", "÷" ], "calculator_value": "+9000000000000000000000000000000003E-32", "printed_value": "90", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/14", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 14", "problem_latex": "Mr. A bought one-fourth of an estate, Mr. B one-half, and\nMr. C one-sixth. If they together bought 55,000 feet, how large\nwas the estate?", "markdown": "Mr. A bought one-fourth of an estate, Mr. B one-half, and Mr. C one-sixth. If they together bought 55,000 feet, how large was the estate?", "answer_latex": [ "60,000ft." ], "answer_markdown": [ "60,000ft." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/4 + x/2 + x/6, 55000)", "answer_expr": "60000" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(11*x/12, 55000)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num", "core.units" ], "expectation": "X=60000", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "4 1/x 2 1/x +", "6 1/x +", "55000 x↔y ÷" ], "calculator_value": "+6000000000000000000000000000000000E-29", "printed_value": "60000", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/15", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 15", "problem_latex": "The wind broke off two-sevenths of a pine tree, and\nafterwards two-fifths more. If the parts broken off measured 48\nfeet, how high was the tree at first?", "markdown": "The wind broke off two-sevenths of a pine tree, and afterwards two-fifths more. If the parts broken off measured 48 feet, how high was the tree at first?", "answer_latex": [ "70ft." ], "answer_markdown": [ "70ft." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(2*x/7 + 2*x/5, 48)", "answer_expr": "70" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(24*x/35, 48)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num", "core.units" ], "expectation": "X=70", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "48 ENTER 2 ENTER 7 ÷ 2 ENTER 5 ÷ +", "÷" ], "constants": [ { "value": "2", "source": "the 2 in 'two-sevenths' (numerator of 2x/7)" }, { "value": "7", "source": "the 7 in 'two-sevenths' (denominator of 2x/7)" }, { "value": "2", "source": "the 2 in 'two-fifths' (numerator of 2x/5)" }, { "value": "5", "source": "the 5 in 'two-fifths' (denominator of 2x/5)" }, { "value": "48", "source": "the 48 in 'the parts broken off measured 48 feet' (right side of Eq(2*x/7 + 2*x/5, 48))" } ], "calculator_value": "+7000000000000000000000000000000000E-32", "printed_value": "70", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/16", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 16", "problem_latex": "A man spaded up three-eighths of his garden, and his son\nspaded two-ninths of it. In all they spaded 43 square rods. How\nlarge was the garden?", "markdown": "A man spaded up three-eighths of his garden, and his son spaded two-ninths of it. In all they spaded 43 square rods. How large was the garden?", "answer_latex": [ "72 sq. rds." ], "answer_markdown": [ "72 sq. rds." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(3*x/8 + 2*x/9, 43)", "answer_expr": "72" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(43*x/72, 43)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num", "core.units" ], "expectation": "X=72", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "3 ENTER 8 ÷ 2 ENTER 9 ÷ +", "43 x↔y ÷" ], "constants": [ { "value": "3", "source": "the 3 in 'three-eighths' (3x/8)" }, { "value": "8", "source": "the 8 in 'three-eighths' (3x/8)" }, { "value": "2", "source": "the 2 in 'two-ninths' (2x/9)" }, { "value": "9", "source": "the 9 in 'two-ninths' (2x/9)" }, { "value": "43", "source": "the 43 square rods in 'In all they spaded 43 square rods' (right side of the equation)" } ], "calculator_value": "+7200000000000000000000000000000000E-32", "printed_value": "72", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/17", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 17", "problem_latex": "Mr. A's investment in business is \\$15,000 more than Mr.\nB's. If Mr. A invests three times as much as Mr. B, how much is\neach man's investment?", "markdown": "Mr. A’s investment in business is $15,000 more than Mr. B’s. If Mr. A invests three times as much as Mr. B, how much is each man’s investment?", "answer_latex": [ "A, \\$22,500; B, \\$7500." ], "answer_markdown": [ "A, $22,500; B, $7500." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{A: 22500, B: 7500}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(x, 3*a), Eq(x, a + 15000))" ], "shape": [ "solve: (Eq(x, N*a), Eq(x, N + a))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/18", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 18", "problem_latex": "A man drew out of the bank \\$27, in half-dollars, quarters,\ndimes, and nickels, of each the same number. What was the number?", "markdown": "A man drew out of the bank $27, in half-dollars, quarters, dimes, and nickels, of each the same number. What was the number?", "answer_latex": [ "30." ], "answer_markdown": [ "30." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(n*(Rational(1, 2) + Rational(1, 4) + Rational(1, 10) + Rational(1, 20)), 27)", "answer_expr": "30" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(9*x/10, 27)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.frac", "core.solve.num", "core.units" ], "expectation": "X=30", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "27 ENTER 100 ×", "50 ENTER 25 + 10 + 5 +", "÷" ], "constants": [ { "value": "100", "source": "cents in a dollar, converting the $27 to cents; the problem prints the dollar sign, not this number, so it comes from the unit" }, { "value": "50", "source": "cents in a half-dollar; from the coin name, not a printed number" }, { "value": "25", "source": "cents in a quarter; from the coin name, not a printed number" }, { "value": "10", "source": "cents in a dime; from the coin name, not a printed number" }, { "value": "5", "source": "cents in a nickel; from the coin name, not a printed number" } ], "calculator_value": "+30E+0", "printed_value": "30", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/2", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 2", "problem_latex": "In a mixture of 360 bushels of grain, there is one-fifth as\nmuch corn as wheat. How many bushels of each?", "markdown": "In a mixture of 360 bushels of grain, there is one-fifth as much corn as wheat. How many bushels of each?", "answer_latex": [ "Corn, 60; wheat, 300." ], "answer_markdown": [ "Corn, 60; wheat, 300." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{c: 60, w: 300}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(x, a/5), Eq(a + x, 360))" ], "shape": [ "solve: (Eq(x, N*a), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/3", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 3", "problem_latex": "A man bought a farm and buildings for \\$12,000. The\nbuildings were valued at one-third as much as the farm. What was\nthe value of each?", "markdown": "A man bought a farm and buildings for $12,000. The buildings were valued at one-third as much as the farm. What was the value of each?", "answer_latex": [ "\\$3000; \\$9000." ], "answer_markdown": [ "$3000; $9000." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{b: 3000, f: 9000}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(x, a/3), Eq(a + x, 12000))" ], "shape": [ "solve: (Eq(x, N*a), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/4", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 4", "problem_latex": "A bicyclist rode 105 miles in a day. If he rode one-half as\nfar in the afternoon as in the forenoon, how far did he ride in\neach part of the day?", "markdown": "A bicyclist rode 105 miles in a day. If he rode one-half as far in the afternoon as in the forenoon, how far did he ride in each part of the day?", "answer_latex": [ "70 miles; 35 miles." ], "answer_markdown": [ "70 miles; 35 miles." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 70, p: 35}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a, x/2), Eq(a + x, 105))" ], "shape": [ "solve: (Eq(a, N*x), Eq(a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/5", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 5", "problem_latex": "Two numbers differ by 675, and one is one-sixteenth of the\nother. What are the numbers?", "markdown": "Two numbers differ by 675, and one is one-sixteenth of the other. What are the numbers?", "answer_latex": [ "45; 720." ], "answer_markdown": [ "45; 720." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{L: 720, s: 45}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a, x/16), Eq(-a + x, 675))" ], "shape": [ "solve: (Eq(a, N*x), Eq(-a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/6", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 6", "problem_latex": "What number is that which being diminished by one-seventh of\nitself will equal 162?", "markdown": "What number is that which being diminished by one-seventh of itself will equal 162?", "answer_latex": [ "189." ], "answer_markdown": [ "189." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x - x/7, 162)", "answer_expr": "189" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(6*x/7, 162)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X=189", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "162 ENTER 1 ENTER 7 1/x −", "÷" ], "constants": [ { "value": "1", "source": "the 'one' in 'one-seventh' of itself: x − x/7 = x(1 − 1/7), so x = 162 ÷ (1 − 1/7)" }, { "value": "7", "source": "the 7 in 'one-seventh' of itself (the 1/x key on 7 gives 1/7)" } ], "calculator_value": "+1890000000000000000000000000000000E-31", "printed_value": "189", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/7", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 7", "problem_latex": "Jane is one-fifth as old as Mary, and the difference of\ntheir ages is 12 years. How old is each?", "markdown": "Jane is one-fifth as old as Mary, and the difference of their ages is 12 years. How old is each?", "answer_latex": [ "J, 3 yrs.; M, 15 yrs." ], "answer_markdown": [ "J, 3 yrs.; M, 15 yrs." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": null, "answer_expr": "{J: 3, M: 15}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: (Eq(a, x/5), Eq(-a + x, 12))" ], "shape": [ "solve: (Eq(a, N*x), Eq(-a + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/8", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 8", "problem_latex": "The fourth and eighth of a number are together equal to 36.\nWhat is the number?", "markdown": "The fourth and eighth of a number are together equal to 36. What is the number?", "answer_latex": [ "96." ], "answer_markdown": [ "96." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/4 + x/8, 36)", "answer_expr": "96" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(3*x/8, 36)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X=96", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "36 ENTER 4 1/x ENTER 8 1/x +", "÷" ], "constants": [ { "value": "4", "source": "the 'fourth' in 'the fourth and eighth of a number' (the number is divided by 4, so its reciprocal 1/x is taken)" }, { "value": "8", "source": "the 'eighth' in 'the fourth and eighth of a number' (the number is divided by 8, so its reciprocal 1/x is taken)" }, { "value": "36", "source": "the 'equal to 36' on the right-hand side of the problem" } ], "calculator_value": "+96E+0", "printed_value": "96", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/9", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem 9", "problem_latex": "A man left half his estate to his widow, and a fifth to his\ndaughter. If they both together received \\$28,000, what was the\nvalue of his estate?", "markdown": "A man left half his estate to his widow, and a fifth to his daughter. If they both together received $28,000, what was the value of his estate?", "answer_latex": [ "\\$40,000." ], "answer_markdown": [ "$40,000." ], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/2 + x/5, 28000)", "answer_expr": "40000" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS" ] }, "form": [ "solve: Eq(7*x/10, 28000)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": "X=40000", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "28000 ENTER 2 1/x 5 1/x +", "÷" ], "constants": [ { "value": "2", "source": "the 2 in 'half' (one half is 1/2, via 1/x)" }, { "value": "5", "source": "the 5 in 'a fifth' (one fifth is 1/5, via 1/x)" } ], "calculator_value": "+4000E+1", "printed_value": "40000", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-7/none", "set": "boyden-first-book-in-algebra-1895/ex-7", "number": null, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 7, problem None", "problem_latex": "\\textit{ Illustrative Example}. Divide the number 72 into two\nparts such that one part shall be one-eighth of the other.", "markdown": "*Illustrative Example*. Divide the number 72 into two parts such that one part shall be one-eighth of the other.", "answer_latex": [], "answer_markdown": [], "checks": [ { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x + x/8, 72)", "answer_expr": "64" }, { "task": "solve", "verdict": "PASS", "judge_why": null, "problem_expr": "Eq(x/2 + x/4, 75)", "answer_expr": "100" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS", "PASS" ] }, "form": [ "solve: Eq(9*x/8, 72)", "solve: Eq(3*x/4, 75)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "72 ENTER 1 ENTER 8 1/x + ÷" ], "constants": [ { "value": "1", "source": "the coefficient of the first x in the expression x + x/8 (x written with no numeral means 1x); the working is x(1 + 1/8) = 72, so x = 72 ÷ (1 + 1/8)" }, { "value": "8", "source": "the 8 in 'x/8' in the expression Eq(x + x/8, 72), from 'one-eighth' in the text" } ], "calculator_value": "+64E+0", "printed_value": "64", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" }, { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "2 1/x 4 1/x +", "75 x↔y ÷" ], "calculator_value": "+1E+2", "printed_value": "100", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/1", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 1", "problem_latex": "Three times a certain number increased by one-half of the\nnumber is equal to 14. What is the number?", "markdown": "Three times a certain number increased by one-half of the number is equal to 14. What is the number?", "answer_latex": [ "4." ], "answer_markdown": [ "4." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 4}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(7*x/2, 14)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "14 ENTER 3 ENTER 1 ENTER 2 ÷ + ÷" ], "constants": [ { "value": "3", "source": "the 3 in 'Three times a certain number'" }, { "value": "1", "source": "the 1 in 'one-half'" }, { "value": "2", "source": "the 2 in 'one-half' and in the expression x/2" }, { "value": "14", "source": "the right-hand side, 'is equal to 14'" } ], "calculator_value": "+4E+0", "printed_value": "4", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/10", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 10", "problem_latex": "A man, owning a lot of land, bought 3 other lots adjoining,\n-- one three-eighths, another one-third as large as his lot, and\nthe third containing 14,000 feet, -- when he found that he had\njust twice as much land as at first. How large was his original\nlot?", "markdown": "A man, owning a lot of land, bought 3 other lots adjoining, -- one three-eighths, another one-third as large as his lot, and the third containing 14,000 feet, -- when he found that he had just twice as much land as at first. How large was his original lot?", "answer_latex": [ "48,000 ft." ], "answer_markdown": [ "48,000 ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 48000}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(41*x/24 + 14000, 2*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num", "core.units" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "1 ENTER 3 ENTER 8 ÷ −", "1 ENTER 3 ÷ −", "1/x 14000 ×" ], "constants": [ { "value": "1", "source": "the 1 in 'x + 3x/8 + x/3 + 14000': the original lot itself, coefficient 1" }, { "value": "3", "source": "the 3 in '3x/8' (one three-eighths of the lot)" }, { "value": "8", "source": "the 8 in '3x/8' (three-eighths)" }, { "value": "3", "source": "the 3 in 'x/3' (one-third as large as the lot)" }, { "value": "14000", "source": "the 14000 feet of the third lot, as printed in the problem" } ], "calculator_value": "+4799999999999999999999999999999999E-29", "printed_value": "48000", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/11", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 11", "problem_latex": "What number is doubled by adding to it two-fifths of itself,\none-third of itself, and 8?", "markdown": "What number is doubled by adding to it two-fifths of itself, one-third of itself, and 8?", "answer_latex": [ "30." ], "answer_markdown": [ "30." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 30}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(26*x/15 + 8, 2*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "2 ENTER 5 ÷ 1 ENTER 3 ÷ + 1 + 2 −", "8 +/− x↔y ÷" ], "constants": [ { "value": "2", "source": "the 2 in 'doubled' (2*x) and 'two-fifths'" }, { "value": "1", "source": "the 'one' in 'one-third of itself' (the coefficient of x on the left side)" }, { "value": "5", "source": "the 5 in 'two-fifths' (2*x/5)" }, { "value": "3", "source": "the 3 in 'one-third' (x/3)" }, { "value": "8", "source": "the 8 in 'and 8' (the constant added)" } ], "calculator_value": "+2999999999999999999999999999999996E-32", "printed_value": "30", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/12", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 12", "problem_latex": "There are three numbers whose sum is 90; the second is equal\nto one-half of the first, and the third is equal to the second\nplus three times the first. What are the numbers?", "markdown": "There are three numbers whose sum is 90; the second is equal to one-half of the first, and the third is equal to the second plus three times the first. What are the numbers?", "answer_latex": [ "18; 9; 63." ], "answer_markdown": [ "18; 9; 63." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 18, y: 9, z: 63}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, x/2), Eq(b, a + 3*x), Eq(a + b + x, 90))" ], "shape": [ "solve: (Eq(a, N*x), Eq(b, N*x + a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/13", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 13", "problem_latex": "Divide 84 into three parts, so that the third part shall be\none-third of the second, and the first part equal to twice the\nthird plus twice the second part.", "markdown": "Divide 84 into three parts, so that the third part shall be one-third of the second, and the first part equal to twice the third plus twice the second part.", "answer_latex": [ "56; 21; 7." ], "answer_markdown": [ "56; 21; 7." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 56, y: 21, z: 7}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, 2*a + 2*b), Eq(b, a/3), Eq(a + b + x, 84))" ], "shape": [ "solve: (Eq(x, N*a + N*b), Eq(b, N*a), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/14", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 14", "problem_latex": "Divide 112 into four parts, so that the second part shall be\none-fourth of the first, the third part equal to twice the second\nplus three times the first, and the fourth part equal to the\nsecond plus twice the first part.", "markdown": "Divide 112 into four parts, so that the second part shall be one-fourth of the first, the third part equal to twice the second plus three times the first, and the fourth part equal to the second plus twice the first part.", "answer_latex": [ "16; 4; 56; 36." ], "answer_markdown": [ "16; 4; 56; 36." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 16, y: 4, z: 56, w: 36}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b + 2*x), Eq(b, x/4), Eq(c, 2*b + 3*x), Eq(a + b + c + x, 112))" ], "shape": [ "solve: (Eq(a, N*x + b), Eq(b, N*x), Eq(c, N*b + N*x), Eq(a + b + c + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/15", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 15", "problem_latex": "A grocer sold 62 pounds of tea, coffee, and cocoa. Of tea he\nsold 2 pounds more than of coffee, and of cocoa 4 pounds more than\nof tea. How many pounds of each did he sell?", "markdown": "A grocer sold 62 pounds of tea, coffee, and cocoa. Of tea he sold 2 pounds more than of coffee, and of cocoa 4 pounds more than of tea. How many pounds of each did he sell?", "answer_latex": [ "Coffee, 18 lbs.; tea, 20 lbs.; cocoa, 24 lbs." ], "answer_markdown": [ "Coffee, 18 lbs.; tea, 20 lbs.; cocoa, 24 lbs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{c: 18, t: 20, k: 24}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, b + 4), Eq(b, x + 2), Eq(a + b + x, 62))" ], "shape": [ "solve: (Eq(a, N + b), Eq(b, N + x), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/16", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 16", "problem_latex": "Three houses are together worth six times as much as the\nfirst house, the second is worth twice as much as the first, and\nthe third is worth \\$7500. How much is each worth?", "markdown": "Three houses are together worth six times as much as the first house, the second is worth twice as much as the first, and the third is worth $7500. How much is each worth?", "answer_latex": [ "\\$2500; \\$5000; \\$7500." ], "answer_markdown": [ "$2500; $5000; $7500." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{a: 2500, b: 5000, c: 7500}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(b, 7500), Eq(a + b + x, 6*x))" ], "shape": [ "solve: (Eq(a, N*x), Eq(b, N), Eq(a + b + x, N*x))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/17", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 17", "problem_latex": "John has one-ninth as much money as Peter, but if his father\nshould give him 72 cents, he would have just the same as Peter.\nHow much money has each boy?", "markdown": "John has one-ninth as much money as Peter, but if his father should give him 72 cents, he would have just the same as Peter. How much money has each boy?", "answer_latex": [ "J, 9 cents; P, 81 cents." ], "answer_markdown": [ "J, 9 cents; P, 81 cents." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{j: 9, p: 81}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(x, a/9), Eq(x + 72, a))" ], "shape": [ "solve: (Eq(x, N*a), Eq(N + x, a))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/18", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 18, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 18", "problem_latex": "Mr. James lost two-fifteenths of his property in\nspeculation, and three-eighths by fire. If his loss was \\$6100,\nwhat was his property worth?", "markdown": "Mr. James lost two-fifteenths of his property in speculation, and three-eighths by fire. If his loss was $6100, what was his property worth?", "answer_latex": [ "\\$12,000." ], "answer_markdown": [ "$12,000." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 12000}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(61*x/120, 6100)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num", "core.units" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "6100 ENTER 2 ENTER 15 ÷", "3 ENTER 8 ÷ +", "÷" ], "constants": [ { "value": "2", "source": "the 2 in 'two-fifteenths' (SymPy 2*x/15)" }, { "value": "15", "source": "the 15 in 'two-fifteenths' (SymPy 2*x/15)" }, { "value": "3", "source": "the 3 in 'three-eighths' (SymPy 3*x/8)" }, { "value": "8", "source": "the 8 in 'three-eighths' (SymPy 3*x/8)" }, { "value": "6100", "source": "the loss '\\$6100' in the problem text and the right-hand side of Eq(2*x/15 + 3*x/8, 6100)" } ], "calculator_value": "+1200000000000000000000000000000000E-29", "printed_value": "12000", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/2", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 2", "problem_latex": "Three boys have an equal number of marbles. John buys\ntwo-thirds of Henry's and two-fifths of Robert's marbles, and\nfinds that he then has 93 marbles. How many had he at first?", "markdown": "Three boys have an equal number of marbles. John buys two-thirds of Henry’s and two-fifths of Robert’s marbles, and finds that he then has 93 marbles. How many had he at first?", "answer_latex": [ "45 marbles." ], "answer_markdown": [ "45 marbles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{m: 45}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(31*x/15, 93)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "2 ENTER 3 ÷", "1 +", "2 ENTER 5 ÷ +", "93 x↔y ÷" ], "constants": [ { "value": "2", "source": "the 2 in 'two-thirds' and 'two-fifths' (2m/3, 2m/5)" }, { "value": "3", "source": "the 3 in 'two-thirds' (2m/3)" }, { "value": "5", "source": "the 5 in 'two-fifths' (2m/5)" }, { "value": "1", "source": "the implied coefficient of the first term m in 'John ... has m' (m + 2m/3 + 2m/5), since the equation's first term is m with no printed coefficient" }, { "value": "93", "source": "'he then has 93 marbles' in the problem text and Eq(..., 93)" } ], "calculator_value": "+4499999999999999999999999999999999E-32", "printed_value": "45", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/3", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 3", "problem_latex": "In three pastures there are 42 cows. In the second there are\ntwice as many as in the first, and in the third there are one-half\nas many as in the first. How many cows are there in each pasture?", "markdown": "In three pastures there are 42 cows. In the second there are twice as many as in the first, and in the third there are one-half as many as in the first. How many cows are there in each pasture?", "answer_latex": [ "12; 24; 6 cows." ], "answer_markdown": [ "12; 24; 6 cows." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 12, y: 24, z: 6}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: (Eq(a, 2*x), Eq(b, x/2), Eq(a + b + x, 42))" ], "shape": [ "solve: (Eq(a, N*x), Eq(b, N*x), Eq(a + b + x, N))" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/4", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 4", "problem_latex": "What number is that which being increased by one-half and\none-fourth of itself, and 5 more, equals 33?", "markdown": "What number is that which being increased by one-half and one-fourth of itself, and 5 more, equals 33?", "answer_latex": [ "16." ], "answer_markdown": [ "16." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 16}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(7*x/4 + 5, 33)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "1 ENTER 2 1/x +", "4 1/x +", "33 ENTER 5 −", "x↔y ÷" ], "constants": [ { "value": "1", "source": "the coefficient of x in 'x + x/2 + x/4 + 5 = 33' (the number itself plus its one-half and one-fourth)" }, { "value": "2", "source": "the 2 in 'one-half' (x/2)" }, { "value": "4", "source": "the 4 in 'one-fourth' (x/4)" }, { "value": "33", "source": "the 33 in 'equals 33'" }, { "value": "5", "source": "the 5 in '5 more'" } ], "calculator_value": "+16E+0", "printed_value": "16", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/5", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 5", "problem_latex": "One-third and two-fifths of a number, and 11, make 44. What\nis the number?", "markdown": "One-third and two-fifths of a number, and 11, make 44. What is the number?", "answer_latex": [ "45." ], "answer_markdown": [ "45." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 45}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(11*x/15 + 11, 44)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "44 ENTER 11 −", "ENTER 3 ENTER 5 × ×", "5 ENTER 2 ENTER 3 × + ÷" ], "constants": [ { "value": "44", "source": "the 44 in 'make 44'" }, { "value": "11", "source": "the 11 in 'and 11, make 44'" }, { "value": "3", "source": "the 3 in 'One-third'" }, { "value": "5", "source": "the 5 in 'two-fifths'" }, { "value": "2", "source": "the 2 in 'two-fifths'" } ], "calculator_value": "+45E+0", "printed_value": "45", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/6", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 6", "problem_latex": "What number increased by three-sevenths of itself will\namount to 8640?", "markdown": "What number increased by three-sevenths of itself will amount to 8640?", "answer_latex": [ "6048." ], "answer_markdown": [ "6048." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 6048}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(10*x/7, 8640)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "8640 ENTER 7 ×", "7 ENTER 3 + ÷" ], "constants": [ { "value": "7", "source": "the 7 in 'three-sevenths' (3x/7)" }, { "value": "3", "source": "the 3 in 'three-sevenths' (3x/7)" } ], "calculator_value": "+6048E+0", "printed_value": "6048", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/7", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 7", "problem_latex": "A man invested a certain amount in business. His gain the\nfirst year was three-tenths of his capital, the second year\nfive-sixths of his original capital, and the third year \\$3600. At\nthe end of the third year he was worth \\$10,000. What was his\noriginal investment?", "markdown": "A man invested a certain amount in business. His gain the first year was three-tenths of his capital, the second year five-sixths of his original capital, and the third year $3600. At the end of the third year he was worth $10,000. What was his original investment?", "answer_latex": [ "\\$3000." ], "answer_markdown": [ "$3000." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 3000}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(32*x/15 + 3600, 10000)" ], "shape": [ "solve: Eq(N*x + N, N)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num", "core.units" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "10000 ENTER 3600 −", "1 ENTER 3 ENTER 10 ÷ +", "5 ENTER 6 ÷ +", "÷" ], "constants": [ { "value": "10000", "source": "'At the end of the third year he was worth $10,000' (the right side of Eq(x + 3*x/10 + 5*x/6 + 3600, 10000))" }, { "value": "3600", "source": "'the third year $3600' (the 3600 in the equation)" }, { "value": "1", "source": "the coefficient of x for his capital itself (the leading x in x + 3*x/10 + 5*x/6 = 10000 − 3600, i.e. one whole capital)" }, { "value": "3", "source": "'three-tenths of his capital' (the 3 in 3*x/10)" }, { "value": "10", "source": "'three-tenths' (the 10 in 3*x/10)" }, { "value": "5", "source": "'five-sixths of his original capital' (the 5 in 5*x/6)" }, { "value": "6", "source": "'five-sixths' (the 6 in 5*x/6)" } ], "calculator_value": "+3000000000000000000000000000000000E-30", "printed_value": "3000", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/8", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 8", "problem_latex": "Find the number which, being increased by its third, its\nfourth, and 34, will equal three times the number itself.", "markdown": "Find the number which, being increased by its third, its fourth, and 34, will equal three times the number itself.", "answer_latex": [ "24." ], "answer_markdown": [ "24." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 24}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(19*x/12 + 34, 3*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "34 ENTER 3 ENTER 1 −", "1 ENTER 3 ÷ −", "1 ENTER 4 ÷ −", "÷" ], "constants": [ { "value": "34", "source": "the 34 in 'and 34'" }, { "value": "3", "source": "the 3 in 'its third' (as 1/3) and 'three times the number itself'" }, { "value": "1", "source": "the implicit coefficient of the number itself: x = 1·x, from 'the number itself' and the leading x in x + x/3 + x/4 + 34 = 3x" }, { "value": "4", "source": "the 4 in 'its fourth' (as 1/4)" } ], "calculator_value": "+2399999999999999999999999999999999E-32", "printed_value": "24", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-8/9", "set": "boyden-first-book-in-algebra-1895/ex-8", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 8, problem 9", "problem_latex": "One-half of a number, two-sevenths of the number, and 31,\nadded to the number itself, will equal four times the number. What\nis the number?", "markdown": "One-half of a number, two-sevenths of the number, and 31, added to the number itself, will equal four times the number. What is the number?", "answer_latex": [ "14." ], "answer_markdown": [ "14." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": "{x: 14}" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(25*x/14 + 31, 4*x)" ], "shape": [ "solve: Eq(N*x + N, N*x)" ], "same_problem_in": [], "needs": [ "core.eqn", "core.frac", "core.solve.num" ], "expectation": null, "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "31 ENTER 4 ENTER 1 ENTER 2 ÷ −", "2 ENTER 7 ÷ −", "1 −", "÷" ], "constants": [ { "value": "31", "source": "the 31 in 'added to the number ... will equal'" }, { "value": "4", "source": "the 4 in 'four times the number'" }, { "value": "1", "source": "the 1 in 'one-half of a number' (1/2)" }, { "value": "2", "source": "the 2 in 'one-half' (divisor) and the 2 in 'two-sevenths' (numerator)" }, { "value": "7", "source": "the 7 in 'two-sevenths' (divisor)" }, { "value": "1", "source": "the coefficient 1 of 'the number itself' (x), moved to the right side as 4x - x - x/2 - 2x/7 - 31 with the x-terms collected: x(4 - 1/2 - 2/7 - 1) = 31" } ], "calculator_value": "+1400000000000000000000000000000000E-32", "printed_value": "14", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/1", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 1, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 1", "problem_latex": "Divide the number 56 into two parts, such that one part is\nthree-fifths of the other.", "markdown": "Divide the number 56 into two parts, such that one part is three-fifths of the other.", "answer_latex": [ "35; 21." ], "answer_markdown": [ "35; 21." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "x": 35, "y": 21 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/10", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 10, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 10", "problem_latex": "A man bought a lot of lemons for \\$5; for one-third he paid\n4 cents apiece, and for the rest 3 cents apiece. How many lemons\ndid he buy?", "markdown": "A man bought a lot of lemons for $5; for one-third he paid 4 cents apiece, and for the rest 3 cents apiece. How many lemons did he buy?", "answer_latex": [ "150 lemons." ], "answer_markdown": [ "150 lemons." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(4*n/3 + 3*(2*n/3), 500)", "answer_expr": "150" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(10*x/3, 500)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.frac", "core.solve.num", "core.units" ], "expectation": "X=150", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "4 ENTER 3 ÷ 2 +", "5 ENTER 100 × x↔y ÷" ], "constants": [ { "value": "2", "source": "the 2 in '2n/3' (the two-thirds of the lemons), which after multiplying by the 3 cents gives 3·(2n/3) = 2n, so the coefficient is 4/3 + 2" }, { "value": "100", "source": "the 100 in 'cents': one dollar is 100 cents, so the $5 must be converted to 500 cents to match the cent prices" } ], "calculator_value": "+1500000000000000000000000000000000E-31", "printed_value": "150", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/11", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 11, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 11", "problem_latex": "A lot of land contains 15,000 feet more than the adjacent\nlot, and twice the first lot is equal to seven times the second.\nHow large is each lot?", "markdown": "A lot of land contains 15,000 feet more than the adjacent lot, and twice the first lot is equal to seven times the second. How large is each lot?", "answer_latex": [ "21,000 ft.; 6000 ft." ], "answer_markdown": [ "21,000 ft.; 6000 ft." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "A": 21000, "B": 6000 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/12", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 12, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 12", "problem_latex": "A bicyclist, in going a journey of 52 miles, goes a certain\ndistance the first hour, three-fifths as far the second hour,\none-half as far the third hour, and 10 miles the fourth hour, thus\nfinishing the journey. How far did he travel each hour?", "markdown": "A bicyclist, in going a journey of 52 miles, goes a certain distance the first hour, three-fifths as far the second hour, one-half as far the third hour, and 10 miles the fourth hour, thus finishing the journey. How far did he travel each hour?", "answer_latex": [ "20; 12; 10; l0 miles." ], "answer_markdown": [ "20; 12; 10; l0 miles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "a": 20, "b": 12, "c": 10, "d": 10 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/13", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 13, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 13", "problem_latex": "One man carried off three-sevenths of a pile of loam,\nanother man four-ninths of the pile. In all they took 110 cubic\nyards of earth. How large was the pile at first?", "markdown": "One man carried off three-sevenths of a pile of loam, another man four-ninths of the pile. In all they took 110 cubic yards of earth. How large was the pile at first?", "answer_latex": [ "126 cu. yds." ], "answer_markdown": [ "126 cu. yds." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": "Eq(3*P/7 + 4*P/9, 110)", "answer_expr": "126" } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [ "solve: Eq(55*x/63, 110)" ], "shape": [ "solve: Eq(N*x, N)" ], "same_problem_in": [], "needs": [ "core.arith", "core.eqn", "core.frac", "core.solve.num", "core.units" ], "expectation": "X=126", "keys": [ { "kind": "keys", "mode": "STU", "entry": "rpn", "steps": [ "110 ENTER 3 ENTER 7 ÷ 4 ENTER 9 ÷ + ÷" ], "calculator_value": "+1260000000000000000000000000000000E-31", "printed_value": "126", "core_pins": { "firmware": "628c96c8634194ec8196315d8aa75f88f04d49e6", "casim": "dbb6d4c6f1014957b14a1711d2369aa70cb63b24", "stu32-tutor": "1fe14f61238f3b829624546f726f74b24a0b7b9a", "intel-dfp-sha256": "85dafd70f0fe2a8da218ade4233fca9d3228b0b04cd6d8527f7499926be01037", "builder": "gcc@sha256:9188ac751ca24431dc43dbd142a223c98ea74f01d2858e84d30ba342a0d67844", "base": "gcr.io/distroless/cc-debian13@sha256:e792ab3d241a468a4fd7519ddbbebe66b49b5f365771716ea688ad40b6c6f1c2" }, "records_checker": "stu32-tutor tools/records.py at fa8658e (vendor/records.py, copied unmodified)", "checked_by": "stu32-calc ran the keys; mpmath at 50 digits agrees to 1E-30; tutor's records.py accepted them" } ] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/14", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 14, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 14", "problem_latex": "Matthew had three times as many stamps as Herman, but after\nhe had lost 70, and Herman had bought 90, they put what they had\ntogether, and found that they had 540. How many had each at first?", "markdown": "Matthew had three times as many stamps as Herman, but after he had lost 70, and Herman had bought 90, they put what they had together, and found that they had 540. How many had each at first?", "answer_latex": [ "M, 390; H, 130." ], "answer_markdown": [ "M, 390; H, 130." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "H": 130, "M": 390 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/15", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 15, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 15", "problem_latex": "It is required to divide the number 139 into four parts,\nsuch that the first may be 2 less than the second, 7 more than the\nthird, and 12 greater than the fourth.", "markdown": "It is required to divide the number 139 into four parts, such that the first may be 2 less than the second, 7 more than the third, and 12 greater than the fourth.", "answer_latex": [ "39; 41; 32; 27." ], "answer_markdown": [ "39; 41; 32; 27." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "p1": 39, "p2": 41, "p3": 32, "p4": 27 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/16", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 16, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 16", "problem_latex": "In an election 7105 votes were cast for three candidates.\nOne candidate received 614 votes less, and the other 1896 votes\nless, than the winning candidate. How many votes did each receive?", "markdown": "In an election 7105 votes were cast for three candidates. One candidate received 614 votes less, and the other 1896 votes less, than the winning candidate. How many votes did each receive?", "answer_latex": [ "3205; 2591; 1309." ], "answer_markdown": [ "3205; 2591; 1309." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "S": 2591, "T": 1309, "W": 3205 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/17", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 17, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 17", "problem_latex": "There are four towns, A, B, C, and D, in a straight line.\nThe distance from B to C is one-fifth of the distance from A to B,\nand the distance from C to D is equal to twice the distance from A\nto C. The whole distance from A to D is 72 miles. Required the\ndistance from A to B, B to C, and C to D.", "markdown": "There are four towns, A, B, C, and D, in a straight line. The distance from B to C is one-fifth of the distance from A to B, and the distance from C to D is equal to twice the distance from A to C. The whole distance from A to D is 72 miles. Required the distance from A to B, B to C, and C to D.", "answer_latex": [ "20 miles; 4 miles; 48 miles." ], "answer_markdown": [ "20 miles; 4 miles; 48 miles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "AB": 20, "BC": 4, "CD": 48 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/2", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 2, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 2", "problem_latex": "If the sum of two numbers is 42, and one is three-fourths of\nthe other, what are the numbers?", "markdown": "If the sum of two numbers is 42, and one is three-fourths of the other, what are the numbers?", "answer_latex": [ "24; 18." ], "answer_markdown": [ "24; 18." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "a": 18, "b": 24 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/3", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 3, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 3", "problem_latex": "The village of C---- is situated directly between two cities\n72 miles apart, in such a way that it is five-sevenths as far from\none city as from the other. How far is it from each city?", "markdown": "The village of C---- is situated directly between two cities 72 miles apart, in such a way that it is five-sevenths as far from one city as from the other. How far is it from each city?", "answer_latex": [ "42; 30 miles." ], "answer_markdown": [ "42; 30 miles." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "x": 30, "y": 42 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/4", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 4, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 4", "problem_latex": "A son is five-ninths as old as his father. If the sum of\ntheir ages is 84 years, how old is each?", "markdown": "A son is five-ninths as old as his father. If the sum of their ages is 84 years, how old is each?", "answer_latex": [ "30; 54 yrs." ], "answer_markdown": [ "30; 54 yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "f": 54, "s": 30 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/5", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 5, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 5", "problem_latex": "Two boys picked 26 boxes of strawberries. If John picked\nfive-eighths as many as Henry, how many boxes did each pick?", "markdown": "Two boys picked 26 boxes of strawberries. If John picked five-eighths as many as Henry, how many boxes did each pick?", "answer_latex": [ "J, 10 boxes; H, 16 boxes." ], "answer_markdown": [ "J, 10 boxes; H, 16 boxes." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "H": 16, "J": 10 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/6", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 6, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 6", "problem_latex": "A man received 60-1/2 tons of coal in two carloads, one load\nbeing five-sixths as large as the other. How many tons in each\ncarload?", "markdown": "A man received 60-1/2 tons of coal in two carloads, one load being five-sixths as large as the other. How many tons in each carload?", "answer_latex": [ "33 tons; $27\\frac{1}{2}$ tons." ], "answer_markdown": [ "33 tons; $27\\frac{1}{2}$ tons." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "a": "55/2", "b": 33 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/7", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 7, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 7", "problem_latex": "John is seven-eighths as old as James, and the sum of their\nages is 60 years. How old is each?", "markdown": "John is seven-eighths as old as James, and the sum of their ages is 60 years. How old is each?", "answer_latex": [ "John, 28yrs.; James, 32yrs." ], "answer_markdown": [ "John, 28yrs.; James, 32yrs." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "J": 28, "M": 32 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/8", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 8, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 8", "problem_latex": "Two men invest \\$1625 in business, one putting in\nfive-eighths as much as the other. How much did each invest?", "markdown": "Two men invest $1625 in business, one putting in five-eighths as much as the other. How much did each invest?", "answer_latex": [ "\\$1000; \\$625." ], "answer_markdown": [ "$1000; $625." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "a": 625, "b": 1000 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys", "core.units" ], "expectation": null, "keys": [] }, { "id": "boyden-first-book-in-algebra-1895/ex-9/9", "set": "boyden-first-book-in-algebra-1895/ex-9", "number": 9, "part": null, "book": "boyden-first-book-in-algebra-1895", "edition": "Silver, Burdett and Company, 1895", "page": null, "location": "Exercise 9, problem 9", "problem_latex": "In a school containing 420 pupils, there are three-fourths\nas many boys as girls. How many are there of each?", "markdown": "In a school containing 420 pupils, there are three-fourths as many boys as girls. How many are there of each?", "answer_latex": [ "240 girls; 180 boys." ], "answer_markdown": [ "240 girls; 180 boys." ], "checks": [ { "task": "solve", "verdict": "PASS-INTERPRETED", "judge_why": null, "problem_expr": null, "answer_expr": { "b": 180, "g": 240 } } ], "verdict": "verified", "judge": { "commit": "4a88328", "verdicts": [ "PASS-INTERPRETED" ] }, "form": [], "shape": [], "same_problem_in": [], "needs": [ "core.arith", "core.frac", "core.linsys" ], "expectation": null, "keys": [] } ], "errata_statuses": [ "transcriber_marked", "candidate", "probable", "confirmed", "dismissed", "note" ], "errata": [ { "id": "boyden-first-book-in-algebra-1895/G001", "kind": "transcription", "status": "confirmed", "page": "77", "location": "Exercise 31, item 15 (Factor)", "printed": "4x^3 y - 12a x^2 - 8 x y^3", "corrected": "4x^3 y - 12x^2 y^2 - 8 x y^3", "class": "transcription (a term mis-set in the 2004 transcription; the book is right)", "evidence": "Status: confirmed against a scan. The book's answer 4xy(x^2-3xy-2y^2) expands to 4x^3y - 12x^2y^2 - 8xy^3, not to the transcription's problem (claudiverse judge.py, factor: FLAG-MISMATCH at seeded points). The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett 1894, University of California Libraries), leaf n80, printed page 77, reads \"15. 4x^3y - 12x^2y^2 - 8xy^3.\", read from the page image (evidence/scan-1894-p77-exercise-31.jpg). The scan is the 1894 printing; the transcription's title page says 1895, same publisher.", "found_by": "claudiverse shelf (Haiku 5.5 extractor flagged it in its notes; judge.py agreed); settled against the scan by qwenniverse-fermion; abacus concurred", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G002", "kind": "transcription", "status": "confirmed", "page": "44", "location": "Exercise 15, item 7 (Find the sum of)", "printed": "$5x^2$, $3ab$, $-2ab$, $-4a^2$, $5ab$, $-2a^2$", "corrected": "$5x^2$, $3ab$, $-2ab$, $-4x^2$, $5ab$, $-2x^2$", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 44 (leaf n47), reads \"7. 5x^2, 3ab, -2ab, -4x^2, 5ab, -2x^2\", read from the page image on 2026-10-10. The transcription has -4a^2 and -2a^2 for the page's -4x^2 and -2x^2; the page's x^2 terms sum to -x^2. The page's printed answer, printed page 157 (leaf n160), is \"6ab - x^2\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G003", "kind": "transcription", "status": "confirmed", "page": "45", "location": "Exercise 15, item 20 (Add)", "printed": "$3a^m - a^{m-1} - 1$, $3a^{m-1} + 1 - 2a^m$, $a^{m-1} + 1$", "corrected": "$3a^m - a^{m-1} - 1$, $3a^{m-1} + 1 - 2a^m$, $a^m - 2a^{m-1} + 1$", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 45 (leaf n48), reads \"20. 3a^m - a^(m-1) - 1, 3a^(m-1) + 1 - 2a^m, a^m - 2a^(m-1) + 1\", read from the page image on 2026-10-10. The transcription dropped \"a^m - 2\" from the third addend; the printed answer is right. The page's printed answer, printed page 157 (leaf n160), is \"2a^m + 1\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G004", "kind": "transcription", "status": "confirmed", "page": "45", "location": "Exercise 15, item 25 (Add)", "printed": "a^2b + b^3 - bc^2", "corrected": "a^2b + b^3 + bc^2", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 45 (leaf n48), reads item 25 as \"second addend: a^2b + b^3 + bc^2 - ab^2 - b^2c - abc (others as transcribed)\", read from the page image on 2026-10-10. The transcription has -bc^2 in the second addend where the page prints +bc^2. The page's printed answer, printed page 157 (leaf n160), is \"a^3 + b^3 + c^3 - 3abc\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G005", "kind": "transcription", "status": "confirmed", "page": "157", "location": "Answers, Exercise 16, answer 8 (subtraction)", "printed": "9 ax", "corrected": "9 a^2x", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 157 (leaf n160), prints answer 8 of Exercise 16 as \"9a^2x\", read from the page image on 2026-10-10; the problem, printed page 48 (leaf n51), reads \"From the difference between 5a^2x and -3a^2x take the sum of 2a^2x and -3a^2x\". The transcription dropped the exponent 2 from the answer. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G006", "kind": "transcription", "status": "confirmed", "page": "48", "location": "Exercise 16, item 11 (subtraction)", "printed": "from $11x^{4} - 2x^{3} -", "corrected": "from $11x^{4} - 2x^{3} + 3x^{2} -", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 48 (leaf n51), reads \"11. Subtract 3x^4 - x^2 + 7x - 14 from 11x^4 - 2x^3 + 3x^2 - 8x\", read from the page image on 2026-10-10. The transcription dropped \"+3x^2\" from the second polynomial; the printed answer is right. The page's printed answer, printed page 157 (leaf n160), is \"8x^4 - 2x^3 + 4x^2 - 15x + 14\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G007", "kind": "transcription", "status": "confirmed", "page": "49", "location": "Exercise 16, item 26 (subtraction)", "printed": "5a^2b - 6ab^3 - 7a^2b^2", "corrected": "5a^2b - 6ab^2 - 7a^2b^2", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 49 (leaf n52), reads item 26 as \"...and 5a^2b - 6ab^2 - 7a^2b^2... (rest as transcribed)\", read from the page image on 2026-10-10. The transcription has 6ab^3 where the page prints 6ab^2. The page's printed answer, printed page 157 (leaf n160), is \"-11a^2b + 4ab^2 - 12a^2b^2 - b^3\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G008", "kind": "transcription", "status": "confirmed", "page": "51", "location": "Exercise 17, item 7 (Remove the parentheses)", "printed": "a - (3b - 2c + a) - (2b - a - c) - (6 - c + a)", "corrected": "a - (3b - 2c + a) - (2b - a - c) - (b - c + a)", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 51 (leaf n54), reads \"7. a - (3b - 2c + a) - (2b - a - c) - (b - c + a)\", read from the page image on 2026-10-10. The transcription has (6 - c + a) for the page's (b - c + a). The page's printed answer, printed page 158 (leaf n161), is \"-6b + 4c\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G009", "kind": "transcription", "status": "confirmed", "page": "158", "location": "Answers, Exercise 18, answer 9 (Find the product of)", "printed": "-\\frac{2}{9}a^2cx^6y^4", "corrected": "-\\frac{2}{9}a^2cx^5y^4", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 158 (leaf n161), prints answer 9 of Exercise 18 as \"-2/9 a^2cx^5y^4\", read from the page image on 2026-10-10; the problem, printed page 54 (leaf n57), reads \"1/2 xy, -2/3 cx^2, -2/5 a^2y, and -5/3 x^2y^2\". The transcription has x^6 in the answer where the page prints x^5. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G010", "kind": "transcription", "status": "confirmed", "page": "61", "location": "Exercise 23, item 2 (Review)", "printed": "Multiply $b^4 - 2b^2$ by $b^4 + 2b^2 - 1$", "corrected": "Multiply $b^4 - 2b^2 + 1$ by $b^4 + 2b^2 + 1$", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 61 (leaf n64), reads \"2. Multiply b^4 - 2b^2 + 1 by b^4 + 2b^2 + 1\", read from the page image on 2026-10-10. Both factors are garbled in the transcription; the page's (b^4 - 1)^2 gives the printed answer. The page's printed answer, printed page 160 (leaf n163), is \"b^8 - 2b^4 + 1\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G011", "kind": "transcription", "status": "confirmed", "page": "63", "location": "Exercise 24, item 3 (Divide)", "printed": "$27a^3 b^3 c$ by $9ab^2 c$", "corrected": "$27a^3 b^2 c$ by $9ab^2 c$", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 63 (leaf n66), reads \"3. 27a^3b^2c by 9ab^2c\", read from the page image on 2026-10-10. The transcription has b^3 in the dividend where the page prints b^2. The page's printed answer, printed page 160 (leaf n163), is \"3a^2\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G012", "kind": "transcription", "status": "confirmed", "page": "63", "location": "Exercise 24, item 12 (Divide)", "printed": "$60a^4 bc^{11}$ by $-4ab^2 c^7$", "corrected": "$60a^4 bc^{11}$ by $-12a^2 bc^7$", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 63 (leaf n66), reads \"12. 60a^4bc^11 by -12a^2bc^7\", read from the page image on 2026-10-10. The transcription's divisor is -4ab^2c^7; the page prints -12a^2bc^7. The page's printed answer, printed page 160 (leaf n163), is \"-5a^2c^4\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G013", "kind": "transcription", "status": "confirmed", "page": "64", "location": "Exercise 24, item 19 (Divide)", "printed": "\\div 2x^{3}y^{3}z^{4}", "corrected": "\\div 2x^{3}y^{2}z^{4}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 64 (leaf n67), reads \"19. Simplify (-x^2y^3z^2) x (-x^4y^5z^4) ÷ 2x^3y^2z^4\", read from the page image on 2026-10-10. The transcription has y^3 in the divisor where the page prints y^2 (and y^3 in the answer where the page prints y^6: G014). The page's printed answer, printed page 160 (leaf n163), is \"1/2 x^3y^6z^2\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G014", "kind": "transcription", "status": "confirmed", "page": "160", "location": "Answers, Exercise 24, answer 19 (Divide)", "printed": "\\frac{1}{2} x^3 y^3 z^2", "corrected": "\\frac{1}{2} x^3 y^6 z^2", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 160 (leaf n163), prints answer 19 of Exercise 24 as \"1/2 x^3y^6z^2\", read from the page image on 2026-10-10; the problem, printed page 64 (leaf n67), reads \"Simplify (-x^2y^3z^2) x (-x^4y^5z^4) ÷ 2x^3y^2z^4\". The transcription has y^3 in the answer where the page prints y^6 (and y^3 in the divisor where the page prints y^2: G013). The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G015", "kind": "transcription", "status": "confirmed", "page": "160", "location": "Answers, Exercise 25, answer 7 (Divide)", "printed": "-4y^3 z^3 + 3x^2 y^3 z^4 - xy", "corrected": "-4y^3 z^6 + 3x^2 y^3 z^4 - xy", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 160 (leaf n163), prints answer 7 of Exercise 25 as \"-4y^3z^6 + 3x^2y^3z^4 - xy\", read from the page image on 2026-10-10; the problem, printed page 64 (leaf n67), reads \"32x^3y^4z^6 - 24x^5y^4z^4 + 8x^4y^2 by -8x^3y\". The transcription has z^3 in the answer's first term where the page prints z^6. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G016", "kind": "transcription", "status": "probable", "page": "161", "location": "Answers, Exercise 26, answer 10 (Divide)", "printed": "27x^5 + 9x^4y + 3x^2y^2 + y^3", "corrected": "27x^6 + 9x^4y + 3x^2y^2 + y^3", "class": "transcription (low confidence: a damaged character on the 1894 page, most likely a 6; the 2004 transcription reads 5)", "evidence": "Status: probable (the scan's character is damaged; read as a 6 by its shape and the book's own algebra). LOW CONFIDENCE. In the rich scan the first exponent of the answer is a broken, poorly inked character, open on the left; it lacks the flat top stroke of the other 5s on the page, and its shape matches the exponent in 26.18, which must be a 6. Two other 1894 copies split: afirstbookinalg00boydgoog (p.161) shows a closed 6, firstbookinalge00boydgoog shows the same broken 5-like shape. Most likely a damaged 6 that the transcriber read as 5; the page reading used here (27x^6) is that interpretation, not a clean reading. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 161 (leaf n164), prints answer 10 of Exercise 26 as \"27x^[damaged] + 9x^4y + 3x^2y^2 + y^3\", read from the page image on 2026-10-10; the problem, printed page 67 (leaf n70), reads \"81x^8 - y^4 by 3x^2 - y\". The transcription has 27x^5; the mathematics needs 27x^6. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G017", "kind": "transcription", "status": "confirmed", "page": "67", "location": "Exercise 26, item 12 (Divide)", "printed": "$a^5+a^4b-14a^3b^2+15a^2b^3-4b^3$ by $a^2-3ab+2b^2$", "corrected": "$a^5+a^4b-13a^3b^2+15a^2b^3-4b^5$ by $a^2-3ab+2b^2$", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 67 (leaf n70), reads \"12. a^5 + a^4b - 13a^3b^2 + 15a^2b^3 - 4b^5 by a^2 - 3ab + 2b^2\", read from the page image on 2026-10-10. Two figures differ in the transcription's dividend (-14a^3b^2 for the page's -13a^3b^2, -4b^3 for -4b^5); multiplying out the page's answer and divisor gives the page's dividend exactly. The page's printed answer, printed page 161 (leaf n164), is \"a^3 + 4a^2b - 3ab^2 - 2b^3\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G018", "kind": "transcription", "status": "confirmed", "page": "68", "location": "Exercise 26, item 19 (Divide)", "printed": "$x^4 + 4y^4$ by $x^2 - 2xy + y^2$", "corrected": "$x^4 + 4y^4$ by $x^2 - 2xy + 2y^2$", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 68 (leaf n71), reads \"19. x^4 + 4y^4 by x^2 - 2xy + 2y^2\", read from the page image on 2026-10-10. The transcription's divisor has y^2 where the page prints 2y^2. The page's printed answer, printed page 161 (leaf n164), is \"x^2 + 2xy + 2y^2\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G019", "kind": "transcription", "status": "confirmed", "page": "70", "location": "Exercise 27, item 17 (Simplify)", "printed": "\\sqrt[5]{\\frac{32}{243} a^{10} b^{15}}", "corrected": "\\sqrt[5]{-\\frac{32}{243} a^{10} b^{15}}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 70 (leaf n73), reads \"17. sqrt(1/9 a^4b^6) - cbrt(1/8 a^6b^9) - 5th-root(-32/243 a^10b^15) + cbrt(a^6b^9)\", read from the page image on 2026-10-10. The transcription dropped the minus inside the fifth root; 1/3 - 1/2 + 2/3 + 1 = 3/2. The page's printed answer, printed page 161 (leaf n164), is \"3/2 a^2b^3\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G020", "kind": "transcription", "status": "confirmed", "page": "163", "location": "Answers, Exercise 33, answer 6 (Factor)", "printed": "(xy^2z^2 + cdm^2)(x^2y^2z^2 - cdm^2)", "corrected": "(xy^2z^2 + cdm^2)(xy^2z^2 - cdm^2)", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 6 of Exercise 33 as \"(xy^2z^2 + cdm^2)(xy^2z^2 - cdm^2)\", read from the page image on 2026-10-10; the problem, printed page 79 (leaf n82), reads \"x^2y^4z^4 - c^2d^2m^4\". The transcription has x^2y^2z^2 in the second factor. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G021", "kind": "transcription", "status": "confirmed", "page": "163", "location": "Answers, Exercise 33, answer 11 (Factor)", "printed": "(9xy^2 - 5bd)(9xy^2 - 5bd)", "corrected": "(9xy^2 + 5bd)(9xy^2 - 5bd)", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 11 of Exercise 33 as \"(9xy^2 + 5bd)(9xy^2 - 5bd)\", read from the page image on 2026-10-10; the problem, printed page 79 (leaf n82), reads \"81x^2y^4 - 25b^2d^2\". The transcription has a minus in both factors. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G022", "kind": "transcription", "status": "confirmed", "page": "80", "location": "Exercise 33, item 16 (Factor)", "printed": "a^4b^8 - l", "corrected": "a^8b^8 - 1", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 80 (leaf n83), reads \"16. a^8b^8 - 1\", read from the page image on 2026-10-10. The transcription has a^4b^8 - l (the letter l) for the page's a^8b^8 - 1. The page's printed answer, printed page 163 (leaf n166), is \"(a^4b^4+1)(a^2b^2+1)(ab+1)(ab-1)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G023", "kind": "transcription", "status": "confirmed", "page": "80", "location": "Exercise 33, item 19 (Factor)", "printed": "a^4 - ax^2", "corrected": "a^3 - ax^2", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 80 (leaf n83), reads \"19. a^3 - ax^2\", read from the page image on 2026-10-10. The transcription has a^4 for the page's a^3. The page's printed answer, printed page 163 (leaf n166), is \"a(a + x)(a - x)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G024", "kind": "transcription", "status": "confirmed", "page": "163", "location": "Answers, Exercise 33, answer 22 (Factor)", "printed": "5a(a + y)(1 + a)(1 - a)", "corrected": "5a(x + y)(1 + a)(1 - a)", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 22 of Exercise 33 as \"5a(x + y)(1 + a)(1 - a)\", read from the page image on 2026-10-10; the problem, printed page 80 (leaf n83), reads \"5ax - 5a^3x + 5ay - 5a^3y\". The transcription has (a + y) for the page's (x + y). The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G025", "kind": "transcription", "status": "confirmed", "page": "163", "location": "Answers, Exercise 33, answer 24 (Factor)", "printed": "(a - x + 1)(a + x)", "corrected": "(a - x - 1)(a + x)", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 24 of Exercise 33 as \"(a - x - 1)(a + x)\", read from the page image on 2026-10-10; the problem, printed page 80 (leaf n83), reads \"a^2 - x^2 - a - x\". The transcription has (a - x + 1) for the page's (a - x - 1). The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G026", "kind": "transcription", "status": "confirmed", "page": "81", "location": "Exercise 34, item 1 (Factor)", "printed": "x^5 + y^5", "corrected": "x^3 + y^3", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 81 (leaf n84), reads \"1. x^3 + y^3\", read from the page image on 2026-10-10. The transcription has x^5 + y^5 for the page's x^3 + y^3. The page's printed answer, printed page 163 (leaf n166), is \"(x + y)(x^2 - xy + y^2)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G027", "kind": "transcription", "status": "confirmed", "page": "81", "location": "Exercise 34, item 5 (Factor)", "printed": "8a^5b^3c^6 + m^6", "corrected": "8a^3b^3c^6 + m^6", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 81 (leaf n84), reads \"5. 8a^3b^3c^6 + m^6\", read from the page image on 2026-10-10. The transcription has 8a^5 for the page's 8a^3. The page's printed answer, printed page 163 (leaf n166), is \"(2abc^2 + m^2)(4a^2b^2c^4 - 2abc^2m^2 + m^4)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G028", "kind": "transcription", "status": "confirmed", "page": "81", "location": "Exercise 34, item 6 (Factor)", "printed": "x^6y^3 + 216a^3", "corrected": "x^6y^9 + 216a^3", "class": "transcription (the 2004 transcription mis-set the problem; the book's problem is right, its answer is not: F004)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 81 (leaf n84), reads \"6. x^6y^9 + 216a^3\", read from the page image on 2026-10-10. The transcription has x^6y^3 for the page's x^6y^9. The page's printed answer, printed page 163 (leaf n166), is \"(x^2y^3 + 6a)(x^4y^3 - 6ax^2y^3 + 36a^2)\"; it is itself misprinted (F004), and the page's problem gives the corrected answer while the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G029", "kind": "transcription", "status": "confirmed", "page": "81", "location": "Exercise 34, item 12 (Factor)", "printed": "1 + b^3c^3", "corrected": "1 + b^3c^9", "class": "transcription (the 2004 transcription mis-set the problem; the book's problem is right, its answer is not: F005)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 81 (leaf n84), reads \"12. 1 + b^3c^9\", read from the page image on 2026-10-10. The transcription has c^3 for the page's c^9. The page's printed answer, printed page 163 (leaf n166), is \"(1 + bc^3)(1 - bc^3 + b^2c^5)\"; it is itself misprinted (F005), and the page's problem gives the corrected answer while the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G030", "kind": "transcription", "status": "confirmed", "page": "81", "location": "Exercise 34, item 13 (Factor)", "printed": "\\frac{1}{8}a^6b^3+ c^0", "corrected": "\\frac{1}{8}a^6b^3+ c^9", "class": "transcription (the 2004 transcription mis-set the problem; the book's problem is right, its answer is not: F006)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 81 (leaf n84), reads \"13. 1/8 a^6b^3 + c^9\", read from the page image on 2026-10-10. The transcription has c^0 for the page's c^9. The page's printed answer, printed page 163 (leaf n166), is \"(1/2 a^2b + c^3)(1/4 a^4b^2 - 1/2 a^2bc^3 + c^5)\"; it is itself misprinted (F006), and the page's problem gives the corrected answer while the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G031", "kind": "transcription", "status": "confirmed", "page": "163", "location": "Answers, Exercise 34, answer 14 (Factor)", "printed": "(\\frac{1}{4}x + 1)(\\frac{1}{2}x^2 - \\frac{1}{4}x + 1)", "corrected": "(\\frac{1}{3}x + 1)(\\frac{1}{9}x^2 - \\frac{1}{3}x + 1)", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 14 of Exercise 34 as \"(1/3 x + 1)(1/9 x^2 - 1/3 x + 1)\", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads \"1/27 x^3 + 1\". The transcription has 1/4, 1/2, 1/4 for the page's 1/3, 1/9, 1/3. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G032", "kind": "transcription", "status": "confirmed", "page": "164", "location": "Answers, Exercise 34, answer 16 (Factor)", "printed": "(1 - x - y)\\{1 - (x - y) + (x - y)^2\\}", "corrected": "(1 + x - y)\\{1 - (x - y) + (x - y)^2\\}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 164 (leaf n167), prints answer 16 of Exercise 34 as \"(1 + x - y){1 - (x - y) + (x - y)^2}\", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads \"1 + (x - y)^3\". The transcription has (1 - x - y) for the page's (1 + x - y). The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G033", "kind": "transcription", "status": "confirmed", "page": "164", "location": "Answers, Exercise 35, answer 8 (Factor)", "printed": "4a^2m^4x^4", "corrected": "4a^3m^4x^4", "class": "transcription (the 2004 transcription departs from the 1894 page, which is itself wrong here: F008)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 164 (leaf n167), prints answer 8 of Exercise 35 as \"27(bc^2y - 2a^3m^2x^2)(b^2c^4y^2 + 2a^3bc^2m^2x^2y + 4a^3m^4x^4)\", read from the page image on 2026-10-10; the problem, printed page 82 (leaf n85), reads \"27b^3c^6y^3 - 216a^9m^6x^6\". The transcription has 4a^2 in the last term where the page prints 4a^3 (faint, but shaped like a 3, and not a 2). The page is itself wrong here: the problem needs a^6, not the page's a^3 (F008); this entry records only where the transcription departs from the page. The printed exponent is faint, a 3 or a 5; the claim is only that the page does not print the required 6 (the sympy check rejects both readings).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G034", "kind": "transcription", "status": "confirmed", "page": "165", "location": "Answers, Exercise 36, answer 17 (Factor)", "printed": "\\left(4xy^2-3a^8\\right)^2", "corrected": "\\left(4xy^2-3a^3\\right)^2", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 165 (leaf n168), prints answer 17 of Exercise 36 as \"(4xy^2 - 3a^3)^2\", read from the page image on 2026-10-10; the problem, printed page 84 (leaf n87), reads \"16x^2y^4 - 24a^3xy^2 + 9a^6\". The transcription has 3a^8 for the page's 3a^3. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G035", "kind": "transcription", "status": "confirmed", "page": "84", "location": "Exercise 36, item 20 (Factor)", "printed": "\\frac{1}{9}x^4 - \\frac{2}{3}x^2y^2 + 4y^4", "corrected": "\\frac{1}{9}x^4 - \\frac{2}{3}x^2y^2 + y^4", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 84 (leaf n87), reads \"20. 1/9 x^4 - 2/3 x^2y^2 + y^4\", read from the page image on 2026-10-10. The transcription has 4y^4 for the page's y^4. The page's printed answer, printed page 165 (leaf n168), is \"(1/3 x^2 - y^2)^2\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G036", "kind": "transcription", "status": "confirmed", "page": "166", "location": "Answers, Exercise 38, answer 5 (Review: Expand)", "printed": "x^6y^3 - 12x^4y^2z^3a^4 + 48x^2yz^8a^8 - 64z^9a^{12}", "corrected": "x^6y^3 - 12x^4y^2z^3a^4 + 48x^2yz^6a^8 - 64z^9a^{12}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 166 (leaf n169), prints answer 5 of Exercise 38 as \"x^6y^3 - 12x^4y^2z^3a^4 + 48x^2yz^6a^8 - 64z^9a^12\", read from the page image on 2026-10-10; the problem, printed page 87 (leaf n90), reads \"Expand (x^2y - 4z^3a^4)^3\". The transcription has z^8 in the third term for the page's z^6. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G037", "kind": "transcription", "status": "confirmed", "page": "94", "location": "Exercise 42, item 3 (Reduce to lowest terms)", "printed": "\\frac{x^2-7x+12}{x^3+x-20}", "corrected": "\\frac{x^2-7x+12}{x^2+x-20}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 94 (leaf n97), reads \"3. (x^2 - 7x + 12)/(x^2 + x - 20)\", read from the page image on 2026-10-10. The transcription has x^3 in the denominator for the page's x^2. The page's printed answer, printed page 167 (leaf n170), is \"(x - 3)/(x + 5)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G038", "kind": "transcription", "status": "confirmed", "page": "97", "location": "Exercise 43, item 3 (Change to equivalent entire or mixed numbers)", "printed": "\\frac{x^2 + y^2 + 3}{x - y}", "corrected": "\\frac{x^2 - y^2 + 3}{x - y}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 97 (leaf n100), reads \"3. (x^2 - y^2 + 3)/(x - y)\", read from the page image on 2026-10-10. The transcription has x^2 + y^2 for the page's x^2 - y^2. The page's printed answer, printed page 167 (leaf n170), is \"x + y + 3/(x - y)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G039", "kind": "transcription", "status": "confirmed", "page": "97", "location": "Exercise 43, item 4 (Change to equivalent entire or mixed numbers)", "printed": "\\frac{a^3 + b^3 + 3}{x - y}", "corrected": "\\frac{a^3 + b^3 - 2}{a + b}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 97 (leaf n100), reads \"4. (a^3 + b^3 - 2)/(a + b)\", read from the page image on 2026-10-10. The transcription has (a^3 + b^3 + 3)/(x - y), the numerator's 3 and the denominator apparently carried over from the item above. The page's printed answer, printed page 167 (leaf n170), is \"a^2 - ab + b^2 - 2/(a + b)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G040", "kind": "transcription", "status": "confirmed", "page": "98", "location": "Exercise 43, item 25 (Change to equivalent fractions)", "printed": "\\frac{3x + 2}{x^2 + x + 2} - 1", "corrected": "\\frac{3x + 2}{x^2 - x + 2} - 1", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 98 (leaf n101), reads \"25. (3x + 2)/(x^2 - x + 2) - 1\", read from the page image on 2026-10-10. The transcription has x^2 + x + 2 in the denominator for the page's x^2 - x + 2. The page's printed answer, printed page 167 (leaf n170), is \"(4x - x^2)/(x^2 - x + 2)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G041", "kind": "transcription", "status": "confirmed", "page": "100", "location": "Exercise 44, item 3 (Find the value of)", "printed": "\\frac{2x}{3}-\\frac{3x}{4}-\\frac{4x}{5}", "corrected": "\\frac{2x}{3}-\\frac{3x}{4}+\\frac{4x}{5}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 100 (leaf n103), reads \"3. 2x/3 - 3x/4 + 4x/5\", read from the page image on 2026-10-10. The transcription has - 4x/5 for the page's + 4x/5. The page's printed answer, printed page 168 (leaf n171), is \"43x/60\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G042", "kind": "transcription", "status": "confirmed", "page": "100", "location": "Exercise 44, item 4 (Find the value of)", "printed": "\\frac{4a}{b}+\\frac{3x}{2m}", "corrected": "\\frac{2a}{b}+\\frac{3x}{2m}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 100 (leaf n103), reads \"4. 2a/b + 3x/2m\", read from the page image on 2026-10-10. The transcription has 4a/b for the page's 2a/b. The page's printed answer, printed page 168 (leaf n171), is \"(4am + 3bx)/(2bm)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G043", "kind": "transcription", "status": "confirmed", "page": "101", "location": "Exercise 44, item 19 (Find the value of)", "printed": "1} - \\frac{3x^3 + 3x^2 - x - 1}", "corrected": "1} + \\frac{3x^3 + 3x^2 - x - 1}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 101 (leaf n104), reads \"19. (3x^3-3x^2+x-1)/(3x^3-3x^2-x+1) + (3x^3+3x^2-x-1)/(3x^3+3x^2+x+1)\", read from the page image on 2026-10-10. The transcription has a minus between the fractions; the page prints +. The page's printed answer, printed page 168 (leaf n171), is \"2(9x^4 + 1)/(9x^4 - 1)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G044", "kind": "transcription", "status": "confirmed", "page": "105", "location": "Exercise 45, item 4 (Find the value of)", "printed": "\\frac{20a-4}{4a^2-1}+\\frac{3}{1-2a}-\\frac{6}{1-2a}", "corrected": "\\frac{20a-4}{4a^2-1}+\\frac{3}{1-2a}-\\frac{6}{1+2a}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 105 (leaf n108), reads \"4. (20a - 4)/(4a^2 - 1) + 3/(1 - 2a) - 6/(1 + 2a)\", read from the page image on 2026-10-10. The transcription has 6/(1 - 2a) for the page's 6/(1 + 2a). The page's printed answer, printed page 168 (leaf n171), is \"1/(2a + 1)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G045", "kind": "transcription", "status": "confirmed", "page": "105", "location": "Exercise 45, item 5 (Find the value of)", "printed": "\\frac{3y^3}{y^3-x^3}", "corrected": "\\frac{3y^2}{y^3-x^3}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 105 (leaf n108), reads \"5. 1/(x - y) + 3y^2/(y^3 - x^3) - (x - y)/(x^2 + xy + y^2)\", read from the page image on 2026-10-10. The transcription has 3y^3 in the second numerator for the page's 3y^2 (one of two slips in this item: G046). The page's printed answer, printed page 168 (leaf n171), is \"3y/(x^2 + xy + y^2)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G046", "kind": "transcription", "status": "confirmed", "page": "105", "location": "Exercise 45, item 5 (Find the value of)", "printed": "-\n\\frac{1}{3(1+a)}", "corrected": "-\n\\frac{x-y}{x^2+xy+y^2}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 105 (leaf n108), reads \"5. 1/(x - y) + 3y^2/(y^3 - x^3) - (x - y)/(x^2 + xy + y^2)\", read from the page image on 2026-10-10. The transcription's third term is garbled, 1/(3(1+a)) for the page's (x - y)/(x^2 + xy + y^2) (one of two slips in this item: G045). The page's printed answer, printed page 168 (leaf n171), is \"3y/(x^2 + xy + y^2)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G047", "kind": "transcription", "status": "confirmed", "page": "110", "location": "Exercise 49, item 4 (Simplify)", "printed": "\\frac{3a^3mn^2}{2x^3yz^2}", "corrected": "\\frac{3a^3mn^2}{2xy^3z^2}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 110 (leaf n113), reads \"4. 2am^3n^2/(3x^3yz^2) ÷ 3a^3mn^2/(2xy^3z^2)\", read from the page image on 2026-10-10. The transcription has 2x^3yz^2 in the divisor's denominator for the page's 2xy^3z^2. The page's printed answer, printed page 170 (leaf n173), is \"4m^2y^2/(9a^2x^2)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G048", "kind": "transcription", "status": "confirmed", "page": "170", "location": "Answers, Exercise 50, answer 2 (Find by inspection the values)", "printed": "\\frac{a^3b^9}{64y^3}", "corrected": "\\frac{a^6b^9}{64y^3}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 170 (leaf n173), prints answer 2 of Exercise 50 as \"a^6b^9/(64y^3)\", read from the page image on 2026-10-10; the problem, printed page 112 (leaf n115), reads \"(a^2b^3/4y)^3\". The transcription has a^3 in the answer for the page's a^6. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G049", "kind": "transcription", "status": "confirmed", "page": "170", "location": "Answers, Exercise 50, answer 5 (Find by inspection the values)", "printed": "-\\frac{125x^5y^3\\left(a+b^2\\right)^6}", "corrected": "-\\frac{125x^6y^3\\left(a+b^2\\right)^6}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 170 (leaf n173), prints answer 5 of Exercise 50 as \"-125x^6y^3(a+b^2)^6 / 8a^3b^9(x^2-y)^9\", read from the page image on 2026-10-10; the problem, printed page 112 (leaf n115), reads \"(-5x^2y(a+b^2)^2 / 2ab^3(x^2-y)^3)^3\". The transcription has x^5 in the answer for the page's x^6. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G050", "kind": "transcription", "status": "confirmed", "page": "112", "location": "Exercise 50, item 6 (Find by inspection the values)", "printed": "\\frac{3am^4(2a+3b)^3}{4x^2y^2(m-n)^2}", "corrected": "\\frac{3am^4(2a+3b)^3}{4x^2y^3(m-n)^2}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 112 (leaf n115), reads \"6. (-3am^4(2a+3b)^3 / 4x^2y^3(m-n)^2)^3\", read from the page image on 2026-10-10. The transcription has y^2 in the problem for the page's y^3, so the answer's y^9 is correct. The page's printed answer, printed page 170 (leaf n173), is \"-27a^3m^12(2a+3b)^9 / 64x^6y^9(m-n)^6\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G051", "kind": "transcription", "status": "confirmed", "page": "113", "location": "Exercise 50, item 19 (Find by inspection the values)", "printed": "\\frac{x^2}{2mn}", "corrected": "\\frac{x^2y}{2mn}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 113 (leaf n116), reads \"19. 3ab(2x/ab + x^2y/2mn - ax/3mb)\", read from the page image on 2026-10-10. The transcription dropped the y from the problem's second term, not from the answer. The page's printed answer, printed page 170 (leaf n173), is \"6x + 3abx^2y/(2mn) - a^2x/m\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G052", "kind": "transcription", "status": "confirmed", "page": "113", "location": "Exercise 50, item 22 (Find by inspection the values)", "printed": "\\frac{9y^2}{25m^1}", "corrected": "\\frac{9y^2}{25m^2}", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 113 (leaf n116), reads \"22. (x^2/16 + 9y^2/25m^2)(x/4 + 3y/5m)(x/4 - 3y/5m)\", read from the page image on 2026-10-10. The transcription has m^1 for the page's m^2. The page's printed answer, printed page 170 (leaf n173), is \"x^4/256 - 81y^4/(625m^4)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/G053", "kind": "transcription", "status": "confirmed", "page": "113", "location": "Exercise 50, item 25 (Find by inspection the values)", "printed": "\\frac{3a^2}{2b}\n\\right)$", "corrected": "\\frac{3a^2}{2b}\n\\right)^2$", "class": "transcription (the 2004 transcription departs from the 1894 page; the book is right)", "evidence": "Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 113 (leaf n116), reads \"25. (x/y - 3a^2/2b)^2\", read from the page image on 2026-10-10. The transcription dropped the square from the problem. The page's printed answer, printed page 170 (leaf n173), is \"x^2/y^2 - 3a^2x/(by) + 9a^4/(4b^2)\"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F001", "kind": "found-by-us", "status": "confirmed", "page": "157", "location": "Answers, Exercise 15, answer 22 (Add)", "printed": "23x^3 - 20x^2 + 27x + 6", "corrected": "23x^3 + 20x^2 + 27x + 6", "class": "content (sign): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 157 (leaf n160), prints answer 22 of Exercise 15 as \"23x^3 - 20x^2 + 27x + 6\", read from the page image on 2026-10-10; the problem, printed page 45 (leaf n48), reads \"22. 15x^3 + 35x^2 + 3x + 7, 7x^3 + 15x - 11x^2 + 9, 9x - 10 + x^3 - 4x^2\". 35 - 11 - 4 = +20, so the sum's x^2 term is +20x^2; the page prints -20x^2. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here.", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F002", "kind": "found-by-us", "status": "confirmed", "page": "158", "location": "Answers, Exercise 19, answer 11 (Multiply)", "printed": "a^6 + b^6", "corrected": "a^6 - b^6", "class": "content (sign): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 158 (leaf n161), prints answer 11 of Exercise 19 as \"a^6 + b^6\", read from the page image on 2026-10-10; the problem, printed page 56 (leaf n59), reads \"11. a^5 - a^4b + a^3b^2 - a^2b^3 + ab^4 - b^5 by a + b\". (a + b)(a^5 - a^4b + a^3b^2 - a^2b^3 + ab^4 - b^5) = a^6 - b^6; the page prints a^6 + b^6. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here. The rich scan has a faint grey smudge over the sign, but the + strokes are clear; two other 1894 copies (Google scans afirstbookinalg00boydgoog p.158 and firstbookinalge00boydgoog) also print a clean +.", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F003", "kind": "found-by-us", "status": "confirmed", "page": "163", "location": "Answers, Exercise 33, answer 5 (Factor)", "printed": "(a^3bx^2 + m^2c^4y^{10})(a^3bx^2 - m^2c^4y^{10})", "corrected": "(a^3bx^2 + m^2c^4y^5)(a^3bx^2 - m^2c^4y^5)", "class": "content (exponent): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 5 of Exercise 33 as \"(a^3bx^2 + m^2c^4y^10)(a^3bx^2 - m^2c^4y^10)\", read from the page image on 2026-10-10; the problem, printed page 79 (leaf n82), reads \"5. a^6b^2x^4 - m^4c^8y^10\". a^6b^2x^4 - m^4c^8y^10 = (a^3bx^2)^2 - (m^2c^4y^5)^2, so both factors need y^5; the page prints y^10 in each. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here. A reader of this copy pencilled \"5\" over both 10s.", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F004", "kind": "found-by-us", "status": "confirmed", "page": "163", "location": "Answers, Exercise 34, answer 6 (Factor)", "printed": "(x^2y^3 + 6a)(x^4y^3 - 6ax^2y^3 + 36a^2)", "corrected": "(x^2y^3 + 6a)(x^4y^6 - 6ax^2y^3 + 36a^2)", "class": "content (exponent): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 6 of Exercise 34 as \"(x^2y^3 + 6a)(x^4y^3 - 6ax^2y^3 + 36a^2)\", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads \"6. x^6y^9 + 216a^3\". (x^2y^3 + 6a)(x^4y^6 - 6ax^2y^3 + 36a^2) = x^6y^9 + 216a^3; the page prints y^3 for y^6 in the second factor. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The 2004 transcription silently has the correct y^6 here (13309-t.tex line 8152), so printed above is what the page prints, written in the transcription's notation, and corrected is the transcription as it stands. The transcription also mis-sets this problem (G028).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F005", "kind": "found-by-us", "status": "confirmed", "page": "163", "location": "Answers, Exercise 34, answer 12 (Factor)", "printed": "(1 + bc^3)(1 - bc^3 + b^2c^5)", "corrected": "(1 + bc^3)(1 - bc^3 + b^2c^6)", "class": "content (exponent): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 12 of Exercise 34 as \"(1 + bc^3)(1 - bc^3 + b^2c^5)\", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads \"12. 1 + b^3c^9\". 1 + b^3c^9 = (1 + bc^3)(1 - bc^3 + b^2c^6); the page prints c^5. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here. The transcription also mis-sets this problem (G029). The printed exponent is faint, a 3 or a 5; the claim is only that the page does not print the required 6 (the sympy check rejects both readings).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F006", "kind": "found-by-us", "status": "confirmed", "page": "163", "location": "Answers, Exercise 34, answer 13 (Factor)", "printed": "- \\frac{1}{2}a^2bc^3 + c^5)", "corrected": "- \\frac{1}{2}a^2bc^3 + c^6)", "class": "content (exponent): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 13 of Exercise 34 as \"(1/2 a^2b + c^3)(1/4 a^4b^2 - 1/2 a^2bc^3 + c^5)\", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads \"13. 1/8 a^6b^3 + c^9\". 1/8 a^6b^3 + c^9 = (1/2 a^2b + c^3)(1/4 a^4b^2 - 1/2 a^2bc^3 + c^6); the page prints c^5. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here. The transcription also mis-sets this problem (G030). The printed exponent is faint, a 3 or a 5; the claim is only that the page does not print the required 6 (the sympy check rejects both readings).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F007", "kind": "found-by-us", "status": "confirmed", "page": "164", "location": "Answers, Exercise 34, answer 21 (Factor)", "printed": "(27x^3 + 4y^3)(27x^3 - 4y^3)", "corrected": "(27x^3 + 8y^3)(27x^3 - 8y^3)", "class": "content (coefficient): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 164 (leaf n167), prints answer 21 of Exercise 34 as \"(27x^3 + 4y^3)(27x^3 - 4y^3)\", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads \"21. 729x^6 - 64y^6\". 729x^6 - 64y^6 = (27x^3)^2 - (8y^3)^2; the page prints 4y^3. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here. The 4 is clear both times.", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F008", "kind": "found-by-us", "status": "confirmed", "page": "164", "location": "Answers, Exercise 35, answer 8 (Factor)", "printed": "4a^3m^4x^4", "corrected": "4a^6m^4x^4", "class": "content (exponent): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 164 (leaf n167), prints answer 8 of Exercise 35 as \"27(bc^2y - 2a^3m^2x^2)(b^2c^4y^2 + 2a^3bc^2m^2x^2y + 4a^3m^4x^4)\", read from the page image on 2026-10-10; the problem, printed page 82 (leaf n85), reads \"8. 27b^3c^6y^3 - 216a^9m^6x^6\". 27(bc^2y - 2a^3m^2x^2)(b^2c^4y^2 + 2a^3bc^2m^2x^2y + 4a^6m^4x^4) = 27b^3c^6y^3 - 216a^9m^6x^6; the page prints a^3 in the last term. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The 2004 transcription has 4a^2m^4x^4 here (13309-t.tex line 8206; G033), so printed above is what the page prints, written in the transcription's notation, not the text of 13309-t.tex. The printed exponent is faint, a 3 or a 5; the claim is only that the page does not print the required 6 (the sympy check rejects both readings).", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F009", "kind": "found-by-us", "status": "confirmed", "page": "164", "location": "Answers, Exercise 35, answer 15 (Factor)", "printed": "(\\frac{1}{3}xy^2 - b^3)(\\frac{1}{9}x^3y^4 + \\frac{1}{3}xy^2b^3 + b^6)", "corrected": "(\\frac{1}{3}xy^2 - b^3)(\\frac{1}{9}x^2y^4 + \\frac{1}{3}xy^2b^3 + b^6)", "class": "content (exponent): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 164 (leaf n167), prints answer 15 of Exercise 35 as \"(1/3 xy^2 - b^3)(1/9 x^3y^4 + 1/3 xy^2b^3 + b^6)\", read from the page image on 2026-10-10; the problem, printed page 82 (leaf n85), reads \"15. 1/27 x^3y^6 - b^9\". (1/3 xy^2)^2 = 1/9 x^2y^4, so the second factor begins 1/9 x^2y^4; the page prints 1/9 x^3y^4. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here.", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F010", "kind": "found-by-us", "status": "confirmed", "page": "169", "location": "Answers, Exercise 48, answer 2 (Simplify)", "printed": "\\frac{2}{3}", "corrected": "\\frac{3}{4}", "class": "content (value): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 169 (leaf n172), prints answer 2 of Exercise 48 as \"2/3\", read from the page image on 2026-10-10; the problem, printed page 109 (leaf n112), reads \"2. 9a^2b^2/(8nx^3y^2) x 5x^2y^2/(2am^2n) x 24m^2n^2x/(90ab^2)\". (9 x 5 x 24)/(8 x 2 x 90) = 1080/1440 = 3/4, and every letter cancels; the page prints 2/3. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here.", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F011", "kind": "found-by-us", "status": "confirmed", "page": "170", "location": "Answers, Exercise 49, answer 2 (Simplify)", "printed": "\\frac{21ab^2y^2}{16mnz^3}", "corrected": "\\frac{21a^2b^2y^2}{16mnz^3}", "class": "content (exponent): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 170 (leaf n173), prints answer 2 of Exercise 49 as \"21ab^2y^2/(16mnz^3)\", read from the page image on 2026-10-10; the problem, printed page 110 (leaf n113), reads \"2. 7axy^2/(8m^2n) ÷ 2xz^3/(3ab^2m)\". 7axy^2/(8m^2n) x 3ab^2m/(2xz^3) = 21a^2b^2y^2/(16mnz^3); the page prints 21ab^2y^2. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here.", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" }, { "id": "boyden-first-book-in-algebra-1895/F012", "kind": "found-by-us", "status": "confirmed", "page": "171", "location": "Answers, Exercise 50, answer 35 (Factor)", "printed": "\\left(\\frac{m}{y}-5\\right)\\left(\\frac{m}{y}+3\\right)", "corrected": "\\left(\\frac{m}{y}+5\\right)\\left(\\frac{m}{y}-3\\right)", "class": "content (sign): the book's own error; the 1894 page prints it", "evidence": "Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 171 (leaf n174), prints answer 35 of Exercise 50 as \"(m/y - 5)(m/y + 3)\", read from the page image on 2026-10-10; the problem, printed page 114 (leaf n117), reads \"35. m^2/y^2 + 2m/y - 15\". (m/y + 5)(m/y - 3) = m^2/y^2 + 2m/y - 15; the printed (m/y - 5)(m/y + 3) gives -2m/y. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here.", "found_by": "claudiverse shelf (Haiku 5.5 extractor, judge.py, Opus 5.5 adjudicator; abacus's scan list); settled against the scan by qwenniverse-fermion's scan check; book misprint verified on the page image by qwenniverse-fermion", "date": "2026-10-10" } ] }