m81311 Solve Proportions and their Applications By the end of this section, you will be able to: Use the definition of proportion Solve proportions Solve applications using proportions Write percent equations as proportions Translate and solve percent proportions 202c212c-f1f5-467e-b7e7-cf6fde5172da Before you get started, take this readiness quiz. Simplify: 134. If you missed this problem, review . 112 Solve: x4=20. If you missed this problem, review . 80 Write as a rate: Sale rode his bike 24 miles in 2 hours. If you missed this problem, review . 24 miles2 hours

In the section on Ratios and Rates we saw some ways they are used in our daily lives. When two ratios or rates are equal, the equation relating them is called a proportion. A proportion is an equation of the form ab=cd, where b≠0,d≠0. The proportion states two ratios or rates are equal. The proportion is read “a is to b, as c is to d”. The equation 12=48 is a proportion because the two fractions are equal. The proportion 12=48 is read “1 is to 2 as 4 is to 8”. If we compare quantities with units, we have to be sure we are comparing them in the right order. For example, in the proportion 20 students1 teacher=60 students3 teachers we compare the number of students to the number of teachers. We put students in the numerators and teachers in the denominators. Write each sentence as a proportion: ⓐ 3 is to 7 as 15 is to 35. ⓑ 5 hits in 8 at bats is the same as 30 hits in 48 at-bats. ⓒ $1.50 for 6 ounces is equivalent to $2.25 for 9 ounces. ⓐ 3 is to 7 as 15 is to 35. Write as a proportion. 37=1535 ⓑ 5 hits in 8 at-bats is the same as 30 hits in 48 at-bats. Write each fraction to compare hits to at-bats. hitsat-bats=hitsat-bats Write as a proportion. 58=3048 ⓒ $1.50 for 6 ounces is equivalent to $2.25 for 9 ounces. Write each fraction to compare dollars to ounces. $ounces=$ounces Write as a proportion. 1.506=2.259 Write each sentence as a proportion: ⓐ 5 is to 9 as 20 is to 36. ⓑ 7 hits in 11 at-bats is the same as 28 hits in 44 at-bats. ⓒ $2.50 for 8 ounces is equivalent to $3.75 for 12 ounces. ⓐ 59=2036 ⓑ 711=2844 ⓒ 2.508=3.7512 Write each sentence as a proportion: ⓐ 6 is to 7 as 36 is to 42. ⓑ 8 adults for 36 children is the same as 12 adults for 54 children. ⓒ $3.75 for 6 ounces is equivalent to $2.50 for 4 ounces. ⓐ 67=3642 ⓑ 836=1254 ⓒ 3.756=2.504 Look at the proportions 12=48 and 23=69. From our work with equivalent fractions we know these equations are true. But how do we know if an equation is a proportion with equivalent fractions if it contains fractions with larger numbers? To determine if a proportion is true, we find the cross products of each proportion. To find the cross products, we multiply each denominator with the opposite numerator (diagonally across the equal sign). The results are called a cross product because of the cross formed. If, and only if, the given proportion is true, that is, the two sides are equal, then the cross products of a proportion will be equal. For any proportion of the form ab=cd, where b≠0,d≠0, its cross products are equal. Cross products can be used to test whether a proportion is true. To test whether an equation makes a proportion, we find the cross products. If they are both equal, we have a proportion. Determine whether each equation is a proportion: ⓐ 49=1228 ⓑ 17.537.5=715 To determine if the equation is a proportion, we find the cross products. If they are equal, the equation is a proportion. ⓐ Find the cross products. 28⋅4=1129⋅12=108 Since the cross products are not equal, 28·4≠9·12, the equation is not a proportion. ⓑ Find the cross products. 15⋅17.5=262.537.5⋅7=262.5 Since the cross products are equal, 15·17.5=37.5·7, the equation is a proportion. Determine whether each equation is a proportion: ⓐ 79=5472 ⓑ 24.545.5=713 ⓐ noⓑ yes Determine whether each equation is a proportion: ⓐ 89=5673 ⓑ 28.552.5=815 ⓐ no ⓑ no

To solve a proportion containing a variable, we remember that the proportion is an equation. All of the techniques we have used so far to solve equations still apply. In the next example, we will solve a proportion by multiplying by the Least Common Denominator (LCD) using the Multiplication Property of Equality. Solve: x63=47. To isolate x, multiply both sides by the LCD, 63. Simplify. Divide the common factors. Check: To check our answer, we substitute into the original proportion. Show common factors. Simplify. Solve the proportion: n84=1112. 77 Solve the proportion: y96=1312. 104 When the variable is in a denominator, we’ll use the fact that the cross products of a proportion are equal to solve the proportions. We can find the cross products of the proportion and then set them equal. Then we solve the resulting equation using our familiar techniques. Solve: 144a=94. Notice that the variable is in the denominator, so we will solve by finding the cross products and setting them equal. Find the cross products and set them equal. Simplify. Divide both sides by 9. Simplify. Check your answer. Show common factors.. Simplify. Another method to solve this would be to multiply both sides by the LCD, 4a. Try it and verify that you get the same solution. Solve the proportion: 91b=75. 65 Solve the proportion: 39c=138. 24 Solve: 5291=−4y. Find the cross products and set them equal. Simplify. Divide both sides by 52. Simplify. Check: Show common factors. Simplify. Solve the proportion: 8498=−6x. −7 Solve the proportion: −7y=105135. −9

The strategy for solving applications that we have used earlier in this chapter, also works for proportions, since proportions are equations. When we set up the proportion, we must make sure the units are correct—the units in the numerators match and the units in the denominators match. When pediatricians prescribe acetaminophen to children, they prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of the child’s weight. If Zoe weighs 80 pounds, how many milliliters of acetaminophen will her doctor prescribe? Identify what you are asked to find. How many ml of acetaminophen the doctor will prescribe Choose a variable to represent it. Let a= ml of acetaminophen. Write a sentence that gives the information to find it. If 5 ml is prescribed for every 25 pounds, how much will be prescribed for 80 pounds? Translate into a proportion. Substitute given values—be careful of the units. Multiply both sides by 80. Multiply and show common factors. Simplify. Check if the answer is reasonable. Yes. Since 80 is about 3 times 25, the medicine should be about 3 times 5. Write a complete sentence. The pediatrician would prescribe 16 ml of acetaminophen to Zoe. You could also solve this proportion by setting the cross products equal. Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Emilia, who weighs 60 pounds? 12 ml For every 1 kilogram (kg) of a child’s weight, pediatricians prescribe 15 milligrams (mg) of a fever reducer. If Isabella weighs 12 kg, how many milligrams of the fever reducer will the pediatrician prescribe? 180 mg One brand of microwave popcorn has 120 calories per serving. A whole bag of this popcorn has 3.5 servings. How many calories are in a whole bag of this microwave popcorn? Identify what you are asked to find. How many calories are in a whole bag of microwave popcorn? Choose a variable to represent it. Let c= number of calories. Write a sentence that gives the information to find it. If there are 120 calories per serving, how many calories are in a whole bag with 3.5 servings? Translate into a proportion. Substitute given values. Multiply both sides by 3.5. Multiply. Check if the answer is reasonable. Yes. Since 3.5 is between 3 and 4, the total calories should be between 360 (3⋅120) and 480 (4⋅120). Write a complete sentence. The whole bag of microwave popcorn has 420 calories. Marissa loves the Caramel Macchiato at the coffee shop. The 16 oz. medium size has 240 calories. How many calories will she get if she drinks the large 20 oz. size? 300 Yaneli loves Starburst candies, but wants to keep her snacks to 100 calories. If the candies have 160 calories for 8 pieces, how many pieces can she have in her snack? 5 pieces Josiah went to Mexico for spring break and changed $325 dollars into Mexican pesos. At that time, the exchange rate had $1 U.S. is equal to 12.54 Mexican pesos. How many Mexican pesos did he get for his trip? Identify what you are asked to find. How many Mexican pesos did Josiah get? Choose a variable to represent it. Let p= number of pesos. Write a sentence that gives the information to find it. If $1 U.S. is equal to 12.54 Mexican pesos, then $325 is how many pesos? Translate into a proportion. Substitute given values. The variable is in the denominator, so find the cross products and set them equal. Simplify. Check if the answer is reasonable. Yes, $100 would be $1,254 pesos. $325 is a little more than 3 times this amount. Write a complete sentence. Josiah has 4075.5 pesos for his spring break trip. Yurianna is going to Europe and wants to change $800 dollars into Euros. At the current exchange rate, $1 US is equal to 0.738 Euro. How many Euros will she have for her trip? 590 Euros Corey and Nicole are traveling to Japan and need to exchange $600 into Japanese yen. If each dollar is 94.1 yen, how many yen will they get? 56,460 yen

Previously, we solved percent equations by applying the properties of equality we have used to solve equations throughout this text. Some people prefer to solve percent equations by using the proportion method. The proportion method for solving percent problems involves a percent proportion. A percent proportion is an equation where a percent is equal to an equivalent ratio.For example, 60%=60100 and we can simplify 60100=35. Since the equation 60100=35 shows a percent equal to an equivalent ratio, we call it a percent proportion. Using the vocabulary we used earlier:amountbase=percent100 35=60100 The amount is to the base as the percent is to 100. amountbase=percent100 If we restate the problem in the words of a proportion, it may be easier to set up the proportion: The amount is to the base as the percent is to one hundred. We could also say: The amount out of the base is the same as the percent out of one hundred. First we will practice translating into a percent proportion. Later, we’ll solve the proportion. Translate to a proportion. What number is 75% of 90? If you look for the word "of", it may help you identify the base. Identify the parts of the percent proportion. Restate as a proportion. Set up the proportion. Let n=number. n90=75100 Translate to a proportion: What number is 60% of 105? n105=60100 Translate to a proportion: What number is 40% of 85? n85=40100 Translate to a proportion. 19 is 25% of what number? Identify the parts of the percent proportion. Restate as a proportion. Set up the proportion. Let n=number. 19n=25100 Translate to a proportion: 36 is 25% of what number? 36n=25100 Translate to a proportion: 27 is 36% of what number? 27n=36100 Translate to a proportion. What percent of 27 is 9? Identify the parts of the percent proportion. Restate as a proportion. Set up the proportion. Let p=percent. 927=p100 Translate to a proportion: What percent of 52 is 39? n100=3952 Translate to a proportion: What percent of 92 is 23? n100=2392

Now that we have written percent equations as proportions, we are ready to solve the equations. Translate and solve using proportions: What number is 45% of 80? Identify the parts of the percent proportion. Restate as a proportion. Set up the proportion. Let n= number. Find the cross products and set them equal. Simplify. Divide both sides by 100. Simplify. Check if the answer is reasonable. Yes. 45 is a little less than half of 100 and 36 is a little less than half 80. Write a complete sentence that answers the question. 36 is 45% of 80. Translate and solve using proportions: What number is 65% of 40? n40=65100;n=26 Translate and solve using proportions: What number is 85% of 40? n40=85100;n=34 In the next example, the percent is more than 100, which is more than one whole. So the unknown number will be more than the base. Translate and solve using proportions: 125% of 25 is what number? Identify the parts of the percent proportion. Restate as a proportion. Set up the proportion. Let n= number. Find the cross products and set them equal. Simplify. Divide both sides by 100. Simplify. Check if the answer is reasonable. Yes. 125 is more than 100 and 31.25 is more than 25. Write a complete sentence that answers the question. 125% of 25 is 31.25. Translate and solve using proportions: 125% of 64 is what number? n64=125100;n=80 Translate and solve using proportions: 175% of 84 is what number? n84=175100;n=147 Percents with decimals and money are also used in proportions. Translate and solve: 6.5% of what number is $1.56? Identify the parts of the percent proportion. Restate as a proportion. Set up the proportion. Letn= number. Find the cross products and set them equal. Simplify. Divide both sides by 6.5 to isolate the variable. Simplify. Check if the answer is reasonable. Yes. 6.5% is a small amount and $1.56 is much less than $24. Write a complete sentence that answers the question. 6.5% of $24 is $1.56. Translate and solve using proportions: 8.5% of what number is $3.23? 3.23n=8.5100;n=38 Translate and solve using proportions: 7.25% of what number is $4.64? 4.64n=7.25100;n=64 Translate and solve using proportions: What percent of 72 is 9? Identify the parts of the percent proportion. Restate as a proportion. Set up the proportion. Let n= number. Find the cross products and set them equal. Simplify. Divide both sides by 72. Simplify. Check if the answer is reasonable. Yes. 9 is 18 of 72 and 18 is 12.5%. Write a complete sentence that answers the question. 12.5% of 72 is 9. Translate and solve using proportions: What percent of 72 is 27? 2772=n100;n=37.5% Translate and solve using proportions: What percent of 92 is 23? 2392=n100;n=25%

Proportion A proportion is an equation of the form ab=cd, where b≠0, d≠0.The proportion states two ratios or rates are equal. The proportion is read “a is to b, as c is to d”. Cross Products of a Proportion For any proportion of the form ab=cd, where b≠0, its cross products are equal: a⋅d=b⋅c. Percent Proportion The amount is to the base as the percent is to 100. amountbase=percent100

Use the Definition of Proportion In the following exercises, write each sentence as a proportion. 4 is to 15 as 36 is to 135. 415=36135 7 is to 9 as 35 is to 45. 12 is to 5 as 96 is to 40. 125=9640 15 is to 8 as 75 is to 40. 5 wins in 7 games is the same as 115 wins in 161 games. 57=115161 4 wins in 9 games is the same as 36 wins in 81 games. 8 campers to 1 counselor is the same as 48 campers to 6 counselors. 81=486 6 campers to 1 counselor is the same as 48 campers to 8 counselors. $9.36 for 18 ounces is the same as $2.60 for 5 ounces. 9.3618=2.605 $3.92 for 8 ounces is the same as $1.47 for 3 ounces. $18.04 for 11 pounds is the same as $4.92 for 3 pounds. 18.0411=4.923 $12.42 for 27 pounds is the same as $5.52 for 12 pounds. In the following exercises, determine whether each equation is a proportion. 715=56120 yes 512=45108 116=2116 no 94=3934 1218=4.997.56 no 916=2.163.89 13.58.5=31.0519.55 yes 10.18.4=3.032.52 Solve Proportions In the following exercises, solve each proportion. x56=78 x = 49 n91=813 4963=z9 z = 7 5672=y9 5a=65117 a = 9 4b=64144 98154=−7p p = −11 72156=−6q a−8=−4248 a = 7 b−7=−3042 2.63.9=c3 c = 2 2.73.6=d4 2.7j=0.90.2 j = 0.6 2.8k=2.11.5 121=m8 m = 4 133=9n Solve Applications Using Proportions In the following exercises, solve the proportion problem. Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs 45 pounds? 9 ml Brianna, who weighs 6 kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at 15 milligrams (mg) for every 1 kilogram (kg) of the child’s weight. How many milligrams will the doctor prescribe? At the gym, Carol takes her pulse for 10 sec and counts 19 beats. How many beats per minute is this? Has Carol met her target heart rate of 140 beats per minute? 114 beats/minute. Carol has not met her target heart rate. Kevin wants to keep his heart rate at 160 beats per minute while training. During his workout he counts 27 beats in 10 seconds. How many beats per minute is this? Has Kevin met his target heart rate? A new energy drink advertises 106 calories for 8 ounces. How many calories are in 12 ounces of the drink? 159 cal One 12 ounce can of soda has 150 calories. If Josiah drinks the big 32 ounce size from the local mini-mart, how many calories does he get? Karen eats 12 cup of oatmeal that counts for 2 points on her weight loss program. Her husband, Joe, can have 3 points of oatmeal for breakfast. How much oatmeal can he have? 34cup An oatmeal cookie recipe calls for 12 cup of butter to make 4 dozen cookies. Hilda needs to make 10 dozen cookies for the bake sale. How many cups of butter will she need? Janice is traveling to Canada and will change $250 US dollars into Canadian dollars. At the current exchange rate, $1 US is equal to $1.01 Canadian. How many Canadian dollars will she get for her trip? $252.50 Todd is traveling to Mexico and needs to exchange $450 into Mexican pesos. If each dollar is worth 12.29 pesos, how many pesos will he get for his trip? Steve changed $600 into 480 Euros. How many Euros did he receive per US dollar? 0.8 Euros Martha changed $350 US into 385 Australian dollars. How many Australian dollars did she receive per US dollar? At the laundromat, Lucy changed $12.00 into quarters. How many quarters did she get? 48 quarters When she arrived at a casino, Gerty changed $20 into nickels. How many nickels did she get? Jesse’s car gets 30 miles per gallon of gas. If Las Vegas is 285 miles away, how many gallons of gas are needed to get there and then home? If gas is $3.09 per gallon, what is the total cost of the gas for the trip? 19 gallons, $58.71 Danny wants to drive to Phoenix to see his grandfather. Phoenix is 370 miles from Danny’s home and his car gets 18.5 miles per gallon. How many gallons of gas will Danny need to get to and from Phoenix? If gas is $3.19 per gallon, what is the total cost for the gas to drive to see his grandfather? Hugh leaves early one morning to drive from his home in Chicago to go to Mount Rushmore, 812 miles away. After 3 hours, he has gone 190 miles. At that rate, how long will the whole drive take? 12.8 hours Kelly leaves her home in Seattle to drive to Spokane, a distance of 280 miles. After 2 hours, she has gone 152 miles. At that rate, how long will the whole drive take? Phil wants to fertilize his lawn. Each bag of fertilizer covers about 4,000 square feet of lawn. Phil’s lawn is approximately 13,500 square feet. How many bags of fertilizer will he have to buy? 4 bags April wants to paint the exterior of her house. One gallon of paint covers about 350 square feet, and the exterior of the house measures approximately 2000 square feet. How many gallons of paint will she have to buy? Write Percent Equations as Proportions In the following exercises, translate to a proportion. What number is 35% of 250? n250=35100 What number is 75% of 920? What number is 110% of 47? n47=110100 What number is 150% of 64? 45 is 30% of what number? 45n=30100 25 is 80% of what number? 90 is 150% of what number? 90n=150100 77 is 110% of what number? What percent of 85 is 17? 1785=p100 What percent of 92 is 46? What percent of 260 is 340? 340260=p100 What percent of 180 is 220? Translate and Solve Percent Proportions In the following exercises, translate and solve using proportions. What number is 65% of 180? n180=65100; 117 What number is 55% of 300? 18% of 92 is what number? n92=18100; 16.56 22% of 74 is what number? 175% of 26 is what number? n26=175100; 45.5 250% of 61 is what number? What is 300% of 488? n488=300100; 1464 What is 500% of 315? 17% of what number is $7.65? 7.65n=17100; 45 19% of what number is $6.46? $13.53 is 8.25% of what number? 13.53n=8.25100; 164 $18.12 is 7.55% of what number? What percent of 56 is 14? 1456=p100; 25% What percent of 80 is 28? What percent of 96 is 12? 1296=p100; 12.5% What percent of 120 is 27?

Mixing a concentrate Sam bought a large bottle of concentrated cleaning solution at the warehouse store. He must mix the concentrate with water to make a solution for washing his windows. The directions tell him to mix 3 ounces of concentrate with 5 ounces of water. If he puts 12 ounces of concentrate in a bucket, how many ounces of water should he add? How many ounces of the solution will he have altogether? He must add 20 oz of water to obtain a final solution of 32 oz. Mixing a concentrate Travis is going to wash his car. The directions on the bottle of car wash concentrate say to mix 2 ounces of concentrate with 15 ounces of water. If Travis puts 6 ounces of concentrate in a bucket, how much water must he mix with the concentrate?

To solve “what number is 45% of 350” do you prefer to use an equation like you did in the section on Decimal Operations or a proportion like you did in this section? Explain your reason. Answers will vary. To solve “what percent of 125 is 25” do you prefer to use an equation like you did in the section on Decimal Operations or a proportion like you did in this section? Explain your reason.

ⓐ 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?

In the following exercises, write each percent as a ratio. 32% admission rate for the university 32100 53.3% rate of college students with student loans In the following exercises, write as a ratio and then as a percent. 13 out of 100 architects are women. 13100,13% 9 out of every 100 nurses are men. In the following exercises, convert each percent to a fraction. 48% 1225 175% 64.1% 6411000 814% In the following exercises, convert each percent to a decimal. 6% 0.06 23% 128% 1.28 4.9% In the following exercises, convert each percent to ⓐ a simplified fraction and ⓑ a decimal. In 2012,13.5% of the United States population was age 65 or over. (Source: www.census.gov) ⓐ 27200 ⓑ 0.135 In 2012,6.5% of the United States population was under 5 years old. (Source: www.census.gov) When a die is tossed, the probability it will land with an even number of dots on the top side is 50%. ⓐ 12 ⓑ 0.5 A couple plans to have three children. The probability they will all be girls is 12.5%. In the following exercises, convert each decimal to a percent. 0.04 4% 0.15 2.82 282% 3 0.003 0.3% 1.395 In the following exercises, convert each fraction to a percent. 34 75% 115 358 362.5% 29 According to the Centers for Disease Control, 25 of adults do not take a vitamin or supplement. 40% According to the Centers for Disease Control, among adults who do take a vitamin or supplement, 34 take a multivitamin. In the following exercises, translate and solve. What number is 46% of 350? 161 120% of 55 is what number? 84 is 35% of what number? 240 15 is 8% of what number? 200% of what number is 50? 25 7.9% of what number is $4.74? What percent of 120 is 81.6? 68% What percent of 340 is 595?

In the following exercises, solve. When Aurelio and his family ate dinner at a restaurant, the bill was $83.50. Aurelio wants to leave 20% of the total bill as a tip. How much should the tip be? $16.70 One granola bar has 2 grams of fiber, which is 8% of the recommended daily amount. What is the total recommended daily amount of fiber? The nutrition label on a package of granola bars says that each granola bar has 190 calories, and 54 calories are from fat. What percent of the total calories is from fat? 28.4% Elsa gets paid $4,600 per month. Her car payment is $253. What percent of her monthly pay goes to her car payment? In the following exercises, solve. Jorge got a raise in his hourly pay, from $19.00 to $19.76. Find the percent increase. 4% Last year Bernard bought a new car for $30,000. This year the car is worth $24,000. Find the percent decrease.

In the following exercises, find ⓐ the sales tax ⓑ the total cost. The cost of a lawn mower was $750. The sales tax rate is 6% of the purchase price. ⓐ $45ⓑ $795 The cost of a water heater is $577. The sales tax rate is 8.75% of the purchase price. In the following exercises, find the sales tax rate. Andy bought a piano for $4,600. The sales tax on the purchase was $333.50. 7.25% Nahomi bought a purse for $200. The sales tax on the purchase was $16.75. In the following exercises, find the commission. Ginny is a realtor. She receives 3% commission when she sells a house. How much commission will she receive for selling a house for $380,000? $11,400 Jackson receives 16.5% commission when he sells a dinette set. How much commission will he receive for selling a dinette set for $895? In the following exercises, find the rate of commission. Ruben received $675 commission when he sold a $4,500 painting at the art gallery where he works. What was the rate of commission? 15% Tori received $80.75 for selling a $950 membership at her gym. What was her rate of commission? In the following exercises, find the sale price. Aya bought a pair of shoes that was on sale for $30 off. The original price of the shoes was $75. $45 Takwanna saw a cookware set she liked on sale for $145 off. The original price of the cookware was $312. In the following exercises, find ⓐ the amount of discount and ⓑ the sale price. Nga bought a microwave for her office. The microwave was discounted 30% from an original price of $84.90. ⓐ $25.47 ⓑ $59.43 Jarrett bought a tie that was discounted 65% from an original price of $45. In the following exercises, find ⓐ the amount of discount ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.) Hilda bought a bedspread on sale for $37. The original price of the bedspread was $50. ⓐ $13ⓑ 26% Tyler bought a phone on sale for $49.99. The original price of the phone was $79.99. In the following exercises, find ⓐ the amount of the mark-up ⓑ the list price Manny paid $0.80 a pound for apples. He added 60% mark-up before selling them at his produce stand. What price did he charge for the apples? ⓐ $0.48 ⓑ $1.28 It cost Noelle $17.40 for the materials she used to make a purse. She added a 325% mark-up before selling it at her friend’s store. What price did she ask for the purse?

In the following exercises, solve the simple interest problem. Find the simple interest earned after 4 years on $2,250 invested at an interest rate of 5%. $450 Find the simple interest earned after 7 years on $12,000 invested at an interest rate of 8.5%. Find the principal invested if $660 interest was earned in 5 years at an interest rate of 3%. $4400 Find the interest rate if $2,898 interest was earned from a principal of $23,000 invested for 3 years. Kazuo deposited $10,000 in a bank account with interest rate 4.5%. How much interest was earned in 2 years? $900 Brent invested $23,000 in a friend’s business. In 5 years the friend paid him the $23,000 plus $9,200 interest. What was the rate of interest? Fresia lent her son $5,000 for college expenses. Three years later he repaid her the $5,000 plus $375 interest. What was the rate of interest? 2.5% In 6 years, a bond that paid 5.5% earned $594 interest. What was the principal of the bond?

In the following exercises, write each sentence as a proportion. 3 is to 8 as 12 is to 32. 38=1232 95 miles to 3 gallons is the same as 475 miles to 15 gallons. 1 teacher to 18 students is the same as 23 teachers to 414 students. 118=23414 $7.35 for 15 ounces is the same as $2.94 for 6 ounces. In the following exercises, determine whether each equation is a proportion. 513=3078 yes 167=4823 1218=6.9910.99 no 11.69.2=37.1229.44 In the following exercises, solve each proportion. x36=59 20 7a=−684 1.21.8=d6 4 122=m20 In the following exercises, solve the proportion problem. The children’s dosage of acetaminophen is 5 milliliters (ml) for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will be prescribed for a 60 pound child? 12 ml After a workout, Dennis takes his pulse for 10 sec and counts 21 beats. How many beats per minute is this? An 8 ounce serving of ice cream has 272 calories. If Lavonne eats 10 ounces of ice cream, how many calories does she get? 340 calories Alma is going to Europe and wants to exchange $1,200 into Euros. If each dollar is 0.75 Euros, how many Euros will Alma get? Zack wants to drive from Omaha to Denver, a distance of 494 miles. If his car gets 38 miles to the gallon, how many gallons of gas will Zack need to get to Denver? 13 gallons Teresa is planning a party for 100 people. Each gallon of punch will serve 18 people. How many gallons of punch will she need? In the following exercises, translate to a proportion. What number is 62% of 395? n395=62100 42 is 70% of what number? What percent of 1,000 is 15? 151000=p100 What percent of 140 is 210? In the following exercises, translate and solve using proportions. What number is 85% of 900? n900=85100,765 6% of what number is $24? $3.51 is 4.5% of what number? 3.51n=4.5100,$78 What percent of 3,100 is 930?

In the following exercises, convert each percent to ⓐ a decimal ⓑ a simplified fraction. 24% 0.24,625 5% 350% 3.5,72 In the following exercises, convert each fraction to a percent. (Round to 3 decimal places if needed.) 78 13 33.3¯%or3313% 1112 In the following exercises, solve the percent problem. 65 is what percent of 260? 25% What number is 27% of 3,000? 150% of what number is 60? 40 Yuki’s monthly paycheck is $3,825. She pays $918 for rent. What percent of her paycheck goes to rent? The total number of vehicles on one freeway dropped from 84,000 to 74,000. Find the percent decrease (round to the nearest tenth of a percent). 11.9% Kyle bought a bicycle in Denver where the sales tax was 7.72% of the purchase price. The purchase price of the bicycle was $600. What was the total cost? Mara received $31.80 commission when she sold a $795 suit. What was her rate of commission? 4% Kiyoshi bought a television set on sale for $899. The original price was $1,200. Find: ⓐ the amount of discountⓑ the discount rate (round to the nearest tenth of a percent) Oxana bought a dresser at a garage sale for $20. She refinished it, then added a 250% markup before advertising it for sale. What price did she ask for the dresser? $70 Find the simple interest earned after 5 years on $3000 invested at an interest rate of 4.2%. Brenda borrowed $400 from her brother. Two years later, she repaid the $400 plus $50 interest. What was the rate of interest? 6.25% Write as a proportion: 4 gallons to 144 miles is the same as 10 gallons to 360 miles. Solve for a: 12a=−1565 −52 Vin read 10 pages of a book in 12 minutes. At that rate, how long will it take him to read 35 pages?

proportion A proportion is an equation of the form ab=cd, where b≠0, d≠0.The proportion states two ratios or rates are equal. The proportion is read “a is to b, as c is to d”.