m81329 Solve a Formula for a Specific Variable By the end of this section, you will be able to: Use the distance, rate, and time formula Solve a formula for a specific variable fdecc523-30c3-46a7-a168-c24302d65420 Before you get started, take this readiness quiz. Write 35 miles per gallon as a unit rate. If you missed this problem, review . 35 miles1 gallon Solve 6x+24=96. If you missed this problem, review . 12 Find the simple interest earned after 5 years on $1,000 at an interest rate of 4%. If you missed this problem, review . $200

One formula you’ll use often in algebra and in everyday life is the formula for distance traveled by an object moving at a constant speed. The basic idea is probably already familiar to you. Do you know what distance you travel if you drove at a steady rate of 60 miles per hour for 2 hours? (This might happen if you use your car’s cruise control while driving on the Interstate.) If you said 120 miles, you already know how to use this formula! The math to calculate the distance might look like this: distance=(60miles1hour)(2hours)distance=120milesIn general, the formula relating distance, rate, and time is distance=rate·time For an object moving in at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula d=rt where d= distance, r= rate, and t= time. Notice that the units we used above for the rate were miles per hour, which we can write as a ratio mileshour. Then when we multiplied by the time, in hours, the common units ‘hour’ divided out. The answer was in miles. Jamal rides his bike at a uniform rate of 12 miles per hour for 312 hours. How much distance has he traveled? Step 1. Read the problem.You may want to create a mini-chart to summarize the information in the problem. d=?r=12mpht=312hours Step 2. Identify what you are looking for. distance traveled Step 3. Name. Choose a variable to represent it. let d = distance Step 4. Translate.Write the appropriate formula for the situation.Substitute in the given information. d=rtd=12⋅312 Step 5. Solve the equation. d=42miles Step 6. Check: Does 42 miles make sense? Step 7. Answer the question with a complete sentence. Jamal rode 42 miles. Lindsay drove for 512 hours at 60 miles per hour. How much distance did she travel? 330 mi Trinh walked for 213 hours at 3 miles per hour. How far did she walk? 7 mi Rey is planning to drive from his house in San Diego to visit his grandmother in Sacramento, a distance of 520 miles. If he can drive at a steady rate of 65 miles per hour, how many hours will the trip take? Step 1. Read the problem.Summarize the information in the problem. d=520milesr=65mpht=? Step 2. Identify what you are looking for. how many hours (time) Step 3. Name:Choose a variable to represent it. let t = time Step 4. Translate.Write the appropriate formula.Substitute in the given information. d=rt520=65t Step 5. Solve the equation. t=8 Step 6. Check:Substitute the numbers into the formula and make sure the result is a true statement.d=rt520=?65⋅8520=520>✓ Step 7. Answer the question with a complete sentence.We know the units of time will be hours because we divided miles by miles per hour. Rey's trip will take 8 hours. Lee wants to drive from Phoenix to his brother’s apartment in San Francisco, a distance of 770 miles. If he drives at a steady rate of 70 miles per hour, how many hours will the trip take? 11 hours Yesenia is 168 miles from Chicago. If she needs to be in Chicago in 3 hours, at what rate does she need to drive? 56 mph

In this chapter, you became familiar with some formulas used in geometry. Formulas are also very useful in the sciences and social sciences—fields such as chemistry, physics, biology, psychology, sociology, and criminal justice. Healthcare workers use formulas, too, even for something as routine as dispensing medicine. The widely used spreadsheet program Microsoft Excel^TM relies on formulas to do its calculations. Many teachers use spreadsheets to apply formulas to compute student grades. It is important to be familiar with formulas and be able to manipulate them easily. In and , we used the formula d=rt. This formula gives the value of d when you substitute in the values of r and t. But in , we had to find the value of t. We substituted in values of d and r and then used algebra to solve to t. If you had to do this often, you might wonder why there isn’t a formula that gives the value of t when you substitute in the values of d and r. We can get a formula like this by solving the formula d=rt for t. To solve a formula for a specific variable means to get that variable by itself with a coefficient of 1 on one side of the equation and all the other variables and constants on the other side. We will call this solving an equation for a specific variable in general. This process is also called solving a literal equation. The result is another formula, made up only of variables. The formula contains letters, or literals.Let’s try a few examples, starting with the distance, rate, and time formula we used above. Solve the formula d=rt for t:ⓐ when d=520 and r=65ⓑ in general. We’ll write the solutions side-by-side so you can see that solving a formula in general uses the same steps as when we have numbers to substitute. ⓐ when d = 520 and r = 65 ⓑ in general Write the forumla. Substitute any given values. Divide to isolate t. Simplify. Notice that the solution for ⓐ is the same as that in . We say the formula t=dr is solved for t. We can use this version of the formula anytime we are given the distance and rate and need to find the time. Solve the formula d=rt for r:ⓐ when d=180 and t=4ⓐ in general ⓐ r=45ⓑ r=dt Solve the formula d=rt for r:ⓐ when d=780 and t=12ⓑ in general ⓐ r=65ⓑ r=dt We used the formula A=12bh in Use Properties of Rectangles, Triangles, and Trapezoids to find the area of a triangle when we were given the base and height. In the next example, we will solve this formula for the height. The formula for area of a triangle is A=12bh. Solve this formula for h: ⓐ when A=90 and b=15ⓑ in general ⓐ when A = 90 and b = 15 ⓑ in general Write the forumla. Substitute any given values. Clear the fractions. Simplify. Solve for h. We can now find the height of a triangle, if we know the area and the base, by using the formula h=2Ab Use the formula A=12bh to solve for h:ⓐ when A=170 and b=17 ⓑ in general ⓐ h=20 ⓑ h=2Ab Use the formula A=12bh to solve for b: ⓐ when A=62 and h=31 ⓑ in general ⓐ b=4ⓑ b=2Ah In Solve Simple Interest Applications, we used the formula I=Prt to calculate simple interest, where I is interest, P is principal, r is rate as a decimal, and t is time in years. Solve the formula I=Prt to find the principal, P: ⓐ when I=$5,600,r=4%,t=7yearsⓑ in general I = $5600, r = 4%, t = 7 years in general Write the forumla. Substitute any given values. Multiply r ⋅ t. Divide to isolate P. Simplify. State the answer. The principal is $20,000. Use the formula I=Prt. Find t: ⓐ when I=$2,160,r=6%,P=$12,000; ⓑ in general ⓐ t=3 yearsⓑ t=IPr Use the formula I=Prt. Find r: ⓐ when I=$5,400,P=$9,000,t=5years ⓑ in general ⓐ r=0.12=12%ⓑ r=IPt Later in this class, and in future algebra classes, you’ll encounter equations that relate two variables, usually x and y. You might be given an equation that is solved for y and need to solve it for x, or vice versa. In the following example, we’re given an equation with both x and y on the same side and we’ll solve it for y. To do this, we will follow the same steps that we used to solve a formula for a specific variable. Solve the formula 3x+2y=18 for y:ⓐ when x=4ⓑ in general when x = 4 in general Write the equation. Substitute any given values. Simplify if possible. Subtract to isolate the y-term. Simplify. Divide. Simplify. Solve the formula 3x+4y=10 for y:ⓐ when x=2ⓑ in general ⓐ y=1ⓑ y=10−3x4 Solve the formula 5x+2y=18 for y: ⓐ when x=4ⓑ in general ⓐ y=−1ⓑ y=18−5x2 In the previous examples, we used the numbers in part (a) as a guide to solving in general in part (b). Do you think you’re ready to solve a formula in general without using numbers as a guide? Solve the formula P=a+b+c for a. We will isolate a on one side of the equation. We will isolate a on one side of the equation. Write the equation. P=a+b+c Subtract b and c from both sides to isolate a. Simplify. P−b−c=a So, a=P−b−c Solve the formula P=a+b+c for b. b = P − a − c Solve the formula P=a+b+c for c. c = P − a − b Solve the equation 3x+y=10 for y. We will isolate y on one side of the equation. We will isolate y on one side of the equation. Write the equation. 3x+y=10 Subtract 3x from both sides to isolate y. Simplify. y=10−3x Solve the formula 7x+y=11 for y. y = 11 − 7x Solve the formula 11x+y=8 for y. y = 8 − 11x Solve the equation 6x+5y=13 for y. We will isolate y on one side of the equation. We will isolate y on one side of the equation. Write the equation. Subtract to isolate the term with y. Simplify. Divide 5 to make the coefficient 1. Simplify. Solve the formula 4x+7y=9 for y. y=9−4x7 Solve the formula 5x+8y=1 for y. y=1−5x8 The Links to Literacy activity What's Faster than a Speeding Cheetah? will provide you with another view of the topics covered in this section.Distance=RatexTime Distance, Rate, Time Simple Interest Solving a Formula for a Specific Variable Solving a Formula for a Specific Variable

Distance, Rate, and Time d=rt

Use the Distance, Rate, and Time Formula In the following exercises, solve. Steve drove for 812 hours at 72 miles per hour. How much distance did he travel? 612 mi Socorro drove for 456 hours at 60 miles per hour. How much distance did she travel? Yuki walked for 134 hours at 4 miles per hour. How far did she walk? 7 mi Francie rode her bike for 212 hours at 12 miles per hour. How far did she ride? Connor wants to drive from Tucson to the Grand Canyon, a distance of 338 miles. If he drives at a steady rate of 52 miles per hour, how many hours will the trip take? 6.5 hours Megan is taking the bus from New York City to Montreal. The distance is 384 miles and the bus travels at a steady rate of 64 miles per hour. How long will the bus ride be? Aurelia is driving from Miami to Orlando at a rate of 65 miles per hour. The distance is 235 miles. To the nearest tenth of an hour, how long will the trip take? 3.6 hours Kareem wants to ride his bike from St. Louis, Missouri to Champaign, Illinois. The distance is 180 miles. If he rides at a steady rate of 16 miles per hour, how many hours will the trip take? Javier is driving to Bangor, Maine, which is 240 miles away from his current location. If he needs to be in Bangor in 4 hours, at what rate does he need to drive? 60 mph Alejandra is driving to Cincinnati, Ohio, 450 miles away. If she wants to be there in 6 hours, at what rate does she need to drive? Aisha took the train from Spokane to Seattle. The distance is 280 miles, and the trip took 3.5 hours. What was the speed of the train? 80 mph Philip got a ride with a friend from Denver to Las Vegas, a distance of 750 miles. If the trip took 10 hours, how fast was the friend driving? Solve a Formula for a Specific Variable In the following exercises, use the formula. d=rt. Solve for t: ⓐ when d=350 and r=70ⓑ in general ⓐ t=5ⓑ t=dr Solve for t:ⓐ when d=240 and r=60ⓑ in general Solve for t:ⓐ when d=510 and r=60ⓑ in general ⓐ t=8.5ⓑ t=dr Solve for t:ⓐ when d=175 and r=50ⓑ in general Solve for r:ⓐ when d=204 and t=3ⓑ in general ⓐ r=68ⓑ r=dt Solve for r:ⓐ when d=420 and t=6ⓑ in general Solve for r:ⓐ when d=160 and t=2.5ⓑ in general ⓐ r=64ⓑ r=dt Solve for r:ⓐ when d=180 and t=4.5ⓑ in general. In the following exercises, use the formula A=12bh. Solve for b:ⓐ when A=126 and h=18ⓑ in general ⓐ b=14ⓑ b=2Ah Solve for h:ⓐ when A=176 and b=22ⓑ in general Solve for h:ⓐ when A=375 and b=25ⓑ in general ⓐ h=30ⓑ h=2Ab Solve for b:ⓐ when A=65 and h=13ⓑ in general In the following exercises, use the formula I=Prt. Solve for the principal, P for: ⓐ I=$5,480, r=4%, t=7yearsⓑ in general ⓐ P=$19,571.43ⓑ P=Irt Solve for the principal, P for: ⓐ I=$3,950, r=6%, t=5yearsⓑ in general Solve for the time, t for: ⓐ I=$2,376, P=$9,000, r=4.4%ⓑ in general ⓐ t=6yearsⓑ t=IPr Solve for the time, t for: ⓐ I=$624, P=$6,000, r=5.2%ⓑ in general In the following exercises, solve. Solve the formula 2x+3y=12 for y:ⓐ when x=3ⓑ in general ⓐ y=2ⓑ y=12−2x3 Solve the formula 5x+2y=10 for y:ⓐ when x=4ⓑ in general Solve the formula 3x+y=7 for y:ⓐ when x=−2ⓑ in general ⓐ y = 13ⓑ y = 7 − 3x Solve the formula 4x+y=5 for y:ⓐ when x=−3 ⓑ in general Solve a+b=90 for b. b = 90 − a Solve a+b=90 for a. Solve 180=a+b+c for a. a = 180 − b − c Solve 180=a+b+c for c. Solve the formula 8x+y=15 for y. y = 15 − 8x Solve the formula 9x+y=13 for y. Solve the formula −4x+y=−6 for y. y = −6 + 4x Solve the formula −5x+y=−1 for y. Solve the formula 4x+3y=7 for y. y=7−4x3 Solve the formula 3x+2y=11 for y. Solve the formula x−y=−4 for y. y = 4 + x Solve the formula x−y=−3 for y. Solve the formula P=2L+2W for L. L=P−2W2 Solve the formula P=2L+2W for W. Solve the formula C=πd for d. d=Cπ Solve the formula C=πd for π. Solve the formula V=LWH for L. L=VWH Solve the formula V=LWH for H.

Converting temperature While on a tour in Greece, Tatyana saw that the temperature was 40° Celsius. Solve for F in the formula C=59(F−32) to find the temperature in Fahrenheit. 104° F Converting temperature Yon was visiting the United States and he saw that the temperature in Seattle was 50° Fahrenheit. Solve for C in the formula F=95C+32 to find the temperature in Celsius.

Solve the equation 2x+3y=6 for y:ⓐ when x=−3ⓑ in generalⓒ Which solution is easier for you? Explain why. Answers will vary Solve the equation 5x−2y=10 for x:ⓐ when y=10ⓑ in generalⓒ Which solution is easier for you? Explain why.

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

Approach Word Problems with a Positive Attitude In the following exercises, solve. How has your attitude towards solving word problems changed as a result of working through this chapter? Explain. Answers will vary. Did the Problem Solving Strategy help you solve word problems in this chapter? Explain. Use a Problem Solving Strategy for Word Problems In the following exercises, solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question. Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert? There are 116 people at the concert. There are 9 saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players. Reza was very sick and lost 15% of his original weight. He lost 27 pounds. What was his original weight? His original weight was 180 pounds. Dolores bought a crib on sale for $350. The sale price was 40% of the original price. What was the original price of the crib? Solve Number Problems In the following exercises, solve each number word problem. The sum of a number and three is forty-one. Find the number. 38 Twice the difference of a number and ten is fifty-four. Find the number. One number is nine less than another. Their sum is twenty-seven. Find the numbers. 18, 9 The sum of two consecutive integers is −135. Find the numbers.

Solve Coin Word Problems In the following exercises, solve each coin word problem. Francie has $4.35 in dimes and quarters. The number of dimes is 5 more than the number of quarters. How many of each coin does she have? 16 dimes, 11 quarters Scott has $0.39 in pennies and nickels. The number of pennies is 8 times the number of nickels. How many of each coin does he have? Paulette has $140 in $5 and $10 bills. The number of $10 bills is one less than twice the number of $5 bills. How many of each does she have? 6 of $5 bills, 11 of $10 bills Lenny has $3.69 in pennies, dimes, and quarters. The number of pennies is 3 more than the number of dimes. The number of quarters is twice the number of dimes. How many of each coin does he have? Solve Ticket and Stamp Word Problems In the following exercises, solve each ticket or stamp word problem. A church luncheon made $842. Adult tickets cost $10 each and children’s tickets cost $6 each. The number of children was 12 more than twice the number of adults. How many of each ticket were sold? 35 adults, 82 children Tickets for a basketball game cost $2 for students and $5 for adults. The number of students was 3 less than 10 times the number of adults. The total amount of money from ticket sales was $619. How many of each ticket were sold? Ana spent $4.06 buying stamps. The number of $0.41 stamps she bought was 5 more than the number of $0.26 stamps. How many of each did she buy? 3 of 26 -cent stamps, 8 of 41 -cent stamps Yumi spent $34.15 buying stamps. The number of $0.56 stamps she bought was 10 less than 4 times the number of $0.41 stamps. How many of each did she buy?

Use Properties of Angles In the following exercises, solve using properties of angles. What is the supplement of a 48° angle? 132° What is the complement of a 61° angle? Two angles are complementary. The smaller angle is 24° less than the larger angle. Find the measures of both angles. 33°, 57° Two angles are supplementary. The larger angle is 45° more than the smaller angle. Find the measures of both angles. Use Properties of Triangles In the following exercises, solve using properties of triangles. The measures of two angles of a triangle are 22 and 85 degrees. Find the measure of the third angle. 73° One angle of a right triangle measures 41.5 degrees. What is the measure of the other small angle? One angle of a triangle is 30° more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles. 30°, 60°, 90° One angle of a triangle is twice the measure of the smallest angle. The third angle is 60° more than the measure of the smallest angle. Find the measures of all three angles. In the following exercises, ΔABC is similar to ΔXYZ. Find the length of the indicated side. side x 15 side b Use the Pythagorean Theorem In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary. 26 8 8.1 In the following exercises, solve. Approximate to the nearest tenth, if necessary. Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is 8 feet tall and Sergio has 10 feet of wire. How far from the base of the antenna can he attach the wire? 6 feet Seong is building shelving in his garage. The shelves are 36 inches wide and 15 inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?

Understand Linear, Square, Cubic Measure In the following exercises, would you measure each item using linear, square, or cubic measure? amount of sand in a sandbag cubic height of a tree size of a patio square length of a highway In the following exercises, find ⓐ the perimeterⓑ the area of each figure ⓐ 8 unitsⓑ 3 sq. units Use Properties of Rectangles In the following exercises, find the ⓐ perimeter ⓑ area of each rectangle The length of a rectangle is 42 meters and the width is 28 meters. ⓐ 140 mⓑ 1176 sq. m The length of a rectangle is 36 feet and the width is 19 feet. A sidewalk in front of Kathy’s house is in the shape of a rectangle 4 feet wide by 45 feet long. ⓐ 98 ft.ⓑ 180 sq. ft. A rectangular room is 16 feet wide by 12 feet long. In the following exercises, solve. Find the length of a rectangle with perimeter of 220 centimeters and width of 85 centimeters. 25 cm Find the width of a rectangle with perimeter 39 and length 11. The area of a rectangle is 2356 square meters. The length is 38 meters. What is the width? 62 m The width of a rectangle is 45 centimeters. The area is 2700 square centimeters. What is the length? The length of a rectangle is 12 centimeters more than the width. The perimeter is 74 centimeters. Find the length and the width. 24.5 cm., 12.5 cm. The width of a rectangle is 3 more than twice the length. The perimeter is 96 inches. Find the length and the width. Use Properties of Triangles In the following exercises, solve using the properties of triangles. Find the area of a triangle with base 18 inches and height 15 inches. 135 sq. in. Find the area of a triangle with base 33 centimeters and height 21 centimeters. A triangular road sign has base 30 inches and height 40 inches. What is its area? 600 sq. in. If a triangular courtyard has sides 9 feet and 12 feet and the perimeter is 32 feet, how long is the third side? A tile in the shape of an isosceles triangle has a base of 6 inches. If the perimeter is 20 inches, find the length of each of the other sides. 7 in., 7 in. Find the length of each side of an equilateral triangle with perimeter of 81 yards. The perimeter of a triangle is 59 feet. One side of the triangle is 3 feet longer than the shortest side. The third side is 5 feet longer than the shortest side. Find the length of each side. 17 ft., 20 ft., 22 ft. One side of a triangle is three times the smallest side. The third side is 9 feet more than the shortest side. The perimeter is 39 feet. Find the lengths of all three sides. Use Properties of Trapezoids In the following exercises, solve using the properties of trapezoids. The height of a trapezoid is 8 feet and the bases are 11 and 14 feet. What is the area? 100 sq. ft. The height of a trapezoid is 5 yards and the bases are 7 and 10 yards. What is the area? Find the area of the trapezoid with height 25 meters and bases 32.5 and 21.5 meters. 675 sq. m A flag is shaped like a trapezoid with height 62 centimeters and the bases are 91.5 and 78.1 centimeters. What is the area of the flag?

Use Properties of Circles In the following exercises, solve using the properties of circles. Round answers to the nearest hundredth. A circular mosaic has radius 3 meters. Find theⓐ circumferenceⓑ area of the mosaic ⓐ 18.84 mⓑ 28.26 sq. m A circular fountain has radius 8 feet. Find theⓐ circumferenceⓑ area of the fountain Find the diameter of a circle with circumference 150.72 inches. 48 in. Find the radius of a circle with circumference 345.4 centimeters Find the Area of Irregular Figures In the following exercises, find the area of each shaded region. 30 sq. units 300 sq. units 199.25 sq. units

Find Volume and Surface Area of Rectangular Solids In the following exercises, find the ⓐ volumeⓑ surface area of the rectangular solid a rectangular solid with length 14 centimeters, width 4.5 centimeters, and height 10 centimeters ⓐ 630 cu. cmⓑ 496 sq. cm a cube with sides that are 3 feet long a cube of tofu with sides 2.5 inches ⓐ 15.625 cu. in.ⓑ 37.5 sq. in. a rectangular carton with length 32 inches, width 18 inches, and height 10 inches Find Volume and Surface Area of Spheres In the following exercises, find theⓐ volumeⓑ surface area of the sphere. a sphere with radius 4 yards ⓐ 267.95 cu. yd.ⓑ 200.96 sq. yd. a sphere with radius 12 meters a baseball with radius 1.45 inches ⓐ 12.76 cu. in.ⓑ 26.41 sq. in. a soccer ball with radius 22 centimeters Find Volume and Surface Area of Cylinders In the following exercises, find the ⓐ volumeⓑ surface area of the cylinder a cylinder with radius 2 yards and height 6 yards ⓐ 75.36 cu. yd.ⓑ 100.48 sq. yd. a cylinder with diameter 18 inches and height 40 inches a juice can with diameter 8 centimeters and height 15 centimeters ⓐ 753.6 cu. cmⓑ 477.28 sq. cm a cylindrical pylon with diameter 0.8 feet and height 2.5 feet Find Volume of Cones In the following exercises, find the volume of the cone. a cone with height 5 meters and radius 1 meter 5.233 cu. m a cone with height 24 feet and radius 8 feet a cone-shaped water cup with diameter 2.6 inches and height 2.6 inches 4.599 cu. in. a cone-shaped pile of gravel with diameter 6 yards and height 5 yards

Use the Distance, Rate, and Time Formula In the following exercises, solve using the formula for distance, rate, and time. A plane flew 4 hours at 380 miles per hour. What distance was covered? 1520 miles Gus rode his bike for 112 hours at 8 miles per hour. How far did he ride? Jack is driving from Bangor to Portland at a rate of 68 miles per hour. The distance is 107 miles. To the nearest tenth of an hour, how long will the trip take? 1.6 hours Jasmine took the bus from Pittsburgh to Philadelphia. The distance is 305 miles and the trip took 5 hours. What was the speed of the bus? Solve a Formula for a Specific Variable In the following exercises, use the formula d=rt. Solve for t: ⓐ when d=403 and r=65ⓑ in general ⓐ t=6.2ⓑ t=dr Solve for r: ⓐ when d=750 and t=15 ⓑ in general In the following exercises, use the formula A=12bh. Solve for b: ⓐ when A=416 and h=32 ⓑ in general ⓐ b=26ⓑ b=2Ah Solve for h: ⓐ when A=48 and b=8 ⓑ in general In the following exercises, use the formula I=Prt. Solve for the principal, P, for: ⓐ I=$720, r=4%, t=3years ⓑ in general ⓐ P=$6000ⓑ P=I(r⋅t) Solve for the time, t for: ⓐ I=$3630, P=$11,000, r=5.5% ⓑ in general In the following exercises, solve. Solve the formula 6x+5y=20 for y:ⓐ when x=0ⓑ in general ⓐ y=4ⓑ y=20−6x5 Solve the formula 2x+y=15 for y:ⓐ when x=−5ⓑ in general Solve a+b=90 for a. a = 90 − b Solve 180=a+b+c for a. Solve the formula 4x+y=17 for y. y = 17 − 4x Solve the formula −3x+y=−6 for y. Solve the formula P=2L+2W for W. W=P−2L2 Solve the formula V=LWH for H. Describe how you have used two topics from this chapter in your life outside of math class during the past month.

Four-fifths of the people on a hike are children. If there are 12 children, what is the total number of people on the hike? The sum of 13 and twice a number is −19. Find the number. −16 One number is 3 less than another number. Their sum is 65. Find the numbers. Bonita has $2.95 in dimes and quarters in her pocket. If she has 5 more dimes than quarters, how many of each coin does she have? 7 quarters, 12 dimes At a concert, $1600 in tickets were sold. Adult tickets were $9 each and children’s tickets were $4 each. If the number of adult tickets was 30 fewer than twice the number of children’s tickets, how many of each kind were sold? Find the complement of a 52° angle. 38° The measure of one angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is 14 more than the measure of the smallest angle. Find the measures of all three angles. The perimeter of an equilateral triangle is 145 feet. Find the length of each side. 48.3 ΔABC is similar to ΔXYZ. Find the length of side c. Find the length of the missing side. Round to the nearest tenth, if necessary. 10 Find the length of the missing side. Round to the nearest tenth, if necessary. A baseball diamond is shaped like a square with sides 90 feet long. How far is it from home plate to second base, as shown? 127.3 ft The length of a rectangle is 2 feet more than five times the width. The perimeter is 40 feet. Find the dimensions of the rectangle. A triangular poster has base 80 centimeters and height 55 centimeters. Find the area of the poster. 2200 square centimeters A trapezoid has height 14 inches and bases 20 inches and 23 inches. Find the area of the trapezoid. A circular pool has diameter 90 inches. What is its circumference? Round to the nearest tenth. 282.6 inches Find the area of the shaded region. Round to the nearest tenth. Find the volume of a rectangular room with width 12 feet, length 15 feet, and height 8 feet. 1440 A coffee can is shaped like a cylinder with height 7 inches and radius 5 inches. Find (a) the surface area and (b) the volume of the can. Round to the nearest tenth. A traffic cone has height 75 centimeters. The radius of the base is 20 centimeters. Find the volume of the cone. Round to the nearest tenth. 31,400 cubic inches Leon drove from his house in Cincinnati to his sister’s house in Cleveland. He drove at a uniform rate of 63 miles per hour and the trip took 4 hours. What was the distance? The Catalina Express takes 112 hours to travel from Long Beach to Catalina Island, a distance of 22 miles. To the nearest tenth, what is the speed of the boat? 14.7 miles per hour Use the formula I=Prt to solve for the principal, P, for: ⓐ I=$1380,r=5%,t=3 yearsⓑ in general Solve the formula A=12bh for h:ⓐ when A=1716 and b=66ⓑ in general ⓐ height=52ⓑ h=2Ab Solve x+5y=14 for y.