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מדריכי לימוד > Prealgebra

Problem Set 7: Percents

Practice Makes Perfect

Use the Definition of Percents In the following exercises, write each percent as a ratio. In 20142014, the unemployment rate for those with only a high school degree was \text{6.0%}. 6100\frac{6}{100} In 20152015, among the unemployed, \text{29%} were long-term unemployed. The unemployment rate for those with Bachelor's degrees was \text{3.2%} in 20142014. 321000\frac{32}{1000} The unemployment rate in Michigan in 20142014 was \text{7.3%}. In the following exercises, write as ⓐ a ratio and ⓑ a percent 5757 out of 100100 nursing candidates received their degree at a community college. ⓐ 57100\frac{57}{100} ⓑ \text{57%} 8080 out of 100100 firefighters and law enforcement officers were educated at a community college. 4242 out of 100100 first-time freshmen students attend a community college. ⓐ 42100\frac{42}{100} ⓑ \text{42%} 7171 out of 100100 full-time community college faculty have a master's degree. Convert Percents to Fractions and Decimals In the following exercises, convert each percent to a fraction and simplify all fractions. \text{4%} 125\frac{1}{25} \text{8%} \text{17%} 17100\frac{17}{100} \text{19%} \text{52%} 1325\frac{13}{25} \text{78%} \text{125%} 54\frac{5}{4} \text{135%} \text{37.5%} 38\frac{3}{8} \text{42.5%} \text{18.4%} 23125\frac{23}{125} \text{46.4%} 9129\frac{1}{2}% 19200\frac{19}{200} 8128\frac{1}{2}% 5135\frac{1}{3}% 475\frac{4}{75} 6236\frac{2}{3}% In the following exercises, convert each percent to a decimal. \text{5%} 0.05 \text{9%} \text{1%} 0.01 \text{2%} \text{63%} 0.63 \text{71%} \text{40%} 0.4 \text{50%} \text{115%} 1.15 \text{125%} \text{150%} 1.5 \text{250%} \text{21.4%} 0.214 \text{39.3%} \text{7.8%} 0.078 \text{6.4%} In the following exercises, convert each percent to ⓐ a simplified fraction and ⓑ a decimal In 2010,\text{1.5%} of home sales had owner financing. (Source: Bloomberg Businessweek, 5/23–29/2011) ⓐ 3200\frac{3}{200} ⓑ 0.0150.015 In 2000,\text{4.2%} of the United States population was of Asian descent. (Source: www.census.gov) According to government data, in 20132013 the number of cell phones in India was \text{70.23%} of the population. ⓐ 702310,000\frac{7023}{10,000} ⓑ 0.70230.7023 According to the U.S. Census Bureau, among Americans age 2525 or older who had doctorate degrees in 2014,\text{37.1%} are women. A couple plans to have two children. The probability they will have two girls is \text{25%}. ⓐ 14\frac{1}{4} ⓑ 0.250.25 Javier will choose one digit at random from 00 through 99. The probability he will choose 33 is \text{10%}. According to the local weather report, the probability of thunderstorms in New York City on July 1515 is \text{60%}. ⓐ 35\frac{3}{5} ⓑ 0.60.6 A club sells 5050 tickets to a raffle. Osbaldo bought one ticket. The probability he will win the raffle is \text{2%}. Convert Decimals and Fractions to Percents In the following exercises, convert each decimal to a percent. 0.010.01 1% 0.030.03 0.180.18 18% 0.150.15 1.351.35 135% 1.561.56 33 300% 44 0.0090.009 0.9% 0.0080.008 0.08750.0875 8.75% 0.06250.0625 1.51.5 150% 2.22.2 2.2542.254 225.4% 2.3172.317 In the following exercises, convert each fraction to a percent. 14\frac{1}{4} 25% 15\frac{1}{5} 38\frac{3}{8} 37.5% 58\frac{5}{8} 74\frac{7}{4} 175% 98\frac{9}{8} 6456\frac{4}{5} 680% 5145\frac{1}{4} 512\frac{5}{12} 41.7% 1112\frac{11}{12} 2232\frac{2}{3} 266.\stackrel{-}{6}\text{%} 1231\frac{2}{3} 37\frac{3}{7} 42.9% 67\frac{6}{7} 59\frac{5}{9} 55.6% 49\frac{4}{9} In the following exercises, convert each fraction to a percent. 14\frac{1}{4} of washing machines needed repair. 25% 15\frac{1}{5} of dishwashers needed repair. In the following exercises, convert each fraction to a percent. According to the National Center for Health Statistics, in 2012,7202012,\frac{7}{20} of American adults were obese. 35% The U.S. Census Bureau estimated that in 2013,\text{85%} of Americans lived in the same house as they did 11 year before. In the following exercises, complete the table.
Fraction Decimal Percent
12\frac{1}{2}
0.450.45
1818%
13\frac{1}{3}
0.00080.0008
22
Fraction Decimal Percent
14\frac{1}{4}
0.650.65
2222%
23\frac{2}{3}
0.00040.0004
33

Everyday Math

Sales tax Felipa says she has an easy way to estimate the sales tax when she makes a purchase. The sales tax in her city is \text{9.05%}. She knows this is a little less than \text{10%}. ⓐ Convert \text{10%} to a fraction. ⓑ Use your answer from ⓐ to estimate the sales tax Felipa would pay on a \text{$95} dress. ⓐ 110\frac{1}{10} ⓑ \text{approximately $9.50} Savings Ryan has \text{25%} of each paycheck automatically deposited in his savings account. ⓐ Write \text{25%} as a fraction. ⓑ Use your answer from ⓐ to find the amount that goes to savings from Ryan's \text{$2,400} paycheck. Amelio is shopping for textbooks online. He found three sellers that are offering a book he needs for the same price, including shipping. To decide which seller to buy from he is comparing their customer satisfaction ratings. The ratings are given in the chart.
Seller Rating
A\text{A} 4/5\text{4/5}
B\text{B} 3.5/4\text{3.5/4}
C\text{C} \text{85%}
Write seller C’s\text{C's} rating as a fraction and a decimal. 1720;0.85\frac{17}{20};0.85 Write seller B’s\text{B's} rating as a percent and a decimal. Write seller A’s\text{A's} rating as a percent and a decimal. 80%; 0.8 Which seller should Amelio buy from and why?

Writing Exercises

Convert \text{25%},\text{50%},\text{75%},\text{and}\text{100%} to fractions. Do you notice a pattern? Explain what the pattern is. 14,12,34,1\frac{1}{4},\frac{1}{2},\frac{3}{4},1. Convert 110,210,310,410,510,610,710,810\frac{1}{10},\frac{2}{10},\frac{3}{10},\frac{4}{10},\frac{5}{10},\frac{6}{10},\frac{7}{10},\frac{8}{10}, and 910\frac{9}{10} to percents. Do you notice a pattern? Explain what the pattern is. When the Szetos sold their home, the selling price was \text{500%} of what they had paid for the house 30 years\text{30 years} ago. Explain what \text{500%} means in this context. The Szetos sold their home for five times what they paid 30 years ago. According to cnn.com, cell phone use in 20082008 was \text{600%} of what it had been in 20012001. Explain what \text{600%} means in this context.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . ⓑ If most of your checks were: …confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific. …with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved? …no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.  

Practice Makes Perfect

Translate and Solve Basic Percent Equations In the following exercises, translate and solve. What number is \text{45%} of 120?120? 54 What number is \text{65%} of 100?100? What number is \text{24%} of 112?112? 26.88 What number is \text{36%} of 124?124? \text{250%} of 6565 is what number? 162.5 \text{150%} of 9090 is what number? \text{800%} of 2,2502,250 is what number? 18,000 \text{600%} of 1,7401,740 is what number? 2828 is \text{25%} of what number? 112 3636 is \text{25%} of what number? 8181 is \text{75%} of what number? 108 9393 is \text{75%} of what number? \text{8.2%}[/latex] of what number is [latex]\text{$2.87}? $35 \text{6.4%}[/latex] of what number is [latex]\text{$2.88}? \text{11.5%}[/latex] of what number is [latex]\text{$108.10}? $940 \text{12.3%}[/latex] of what number is [latex]\text{$92.25}? What percent of 260260 is 78?78? 30% What percent of 215215 is 86?86? What percent of 1,5001,500 is 540?540? 36% What percent of 1,8001,800 is 846?846? 30[/latex]iswhatpercentof[latex]20?30[/latex] is what percent of [latex]20? 150% 50[/latex]iswhatpercentof[latex]40?50[/latex] is what percent of [latex]40? 840[/latex]iswhatpercentof[latex]480?840[/latex] is what percent of [latex]480? 175% 790[/latex]iswhatpercentof[latex]395?790[/latex] is what percent of [latex]395? Solve Applications of Percents In the following exercises, solve the applications of percents. Geneva treated her parents to dinner at their favorite restaurant. The bill was \text{$74.25}. She wants to leave \text{16%} of the total bill as a tip. How much should the tip be? $11.88 When Hiro and his co-workers had lunch at a restaurant the bill was \text{$90.50}. They want to leave \text{18%} of the total bill as a tip. How much should the tip be? Trong has \text{12%} of each paycheck automatically deposited to his savings account. His last paycheck was \text{$2,165}. How much money was deposited to Trong's savings account? $259.80 Cherise deposits \text{8%} of each paycheck into her retirement account. Her last paycheck was \text{$1,485}. How much did Cherise deposit into her retirement account? One serving of oatmeal has 88 grams of fiber, which is \text{33%} of the recommended daily amount. What is the total recommended daily amount of fiber? 24.2 grams One serving of trail mix has 6767 grams of carbohydrates, which is \text{22%} of the recommended daily amount. What is the total recommended daily amount of carbohydrates? A bacon cheeseburger at a popular fast food restaurant contains 2,0702,070 milligrams (mg) of sodium, which is \text{86%} of the recommended daily amount. What is the total recommended daily amount of sodium? 2,407 grams A grilled chicken salad at a popular fast food restaurant contains 650650 milligrams (mg) of sodium, which is \text{27%} of the recommended daily amount. What is the total recommended daily amount of sodium? The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380380 calories, and 171171 calories are from fat. What percent of the total calories is from fat? 45% The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190190 calories, and 114114 calories are from fat. What percent of the total calories is from fat? Emma gets paid \text{$3,000} per month. She pays \text{$750} a month for rent. What percent of her monthly pay goes to rent? 25% Dimple gets paid \text{$3,200} per month. She pays \text{$960} a month for rent. What percent of her monthly pay goes to rent? Find Percent Increase and Percent Decrease In the following exercises, find the percent increase or percent decrease. Tamanika got a raise in her hourly pay, from \text{$15.50} to \text{$17.55}. Find the percent increase. 13.2% Ayodele got a raise in her hourly pay, from \text{$24.50} to \text{$25.48}. Find the percent increase. Annual student fees at the University of California rose from about \text{$4,000} in 20002000 to about \text{$9,000} in 20142014. Find the percent increase. 125% The price of a share of one stock rose from \text{$12.50} to \text{$50}. Find the percent increase. According to Time magazine (7/19/2011)\left(\text{7/19/2011}\right) annual global seafood consumption rose from 2222 pounds per person in 19601960 to 3838 pounds per person today. Find the percent increase. (Round to the nearest tenth of a percent.) 72.7% In one month, the median home price in the Northeast rose from \text{$225,400} to \text{$241,500}. Find the percent increase. (Round to the nearest tenth of a percent.) A grocery store reduced the price of a loaf of bread from \text{$2.80} to \text{$2.73}. Find the percent decrease. 2.5% The price of a share of one stock fell from \text{$8.75} to \text{$8.54}. Find the percent decrease. Hernando's salary was \text{$49,500} last year. This year his salary was cut to \text{$44,055}. Find the percent decrease. 11% From 20002000 to 20102010, the population of Detroit fell from about 951,000951,000 to about 714,000714,000. Find the percent decrease. (Round to the nearest tenth of a percent.) In one month, the median home price in the West fell from \text{$203,400} to \text{$192,300}. Find the percent decrease. (Round to the nearest tenth of a percent.) 5.5% Sales of video games and consoles fell from \text{$1,150} million to \text{$1,030} million in one year. Find the percent decrease. (Round to the nearest tenth of a percent.)

Everyday Math

Tipping At the campus coffee cart, a medium coffee costs \text{$1.65}. MaryAnne brings \text{$2.00} with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave? 21.2% Late Fees Alison was late paying her credit card bill of \text{$249}. She was charged a \text{5%} late fee. What was the amount of the late fee?

Writing Exercises

Without solving the problem "44"44 is \text{80%} of what number", think about what the solution might be. Should it be a number that is greater than 4444 or less than 44?44? Explain your reasoning. The original number should be greater than 44.80% is less than 100%, so when 80% is converted to a decimal and multiplied to the base in the percent equation, the resulting amount of 44 is less. 44 is only the larger number in cases where the percent is greater than 100%. Without solving the problem "What is \text{20%} of 300?"300?" think about what the solution might be. Should it be a number that is greater than 300300 or less than 300?300? Explain your reasoning. After returning from vacation, Alex said he should have packed \text{50%} fewer shorts and \text{200%} more shirts. Explain what Alex meant. Alex should have packed half as many shorts and twice as many shirts. Because of road construction in one city, commuters were advised to plan their Monday morning commute to take \text{150%} of their usual commuting time. Explain what this means.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . ⓑ After reviewing this checklist, what will you do to become confident for all objectives?

Practice Makes Perfect

Solve Sales Tax Applications In the following exercises, find ⓐ the sales tax and ⓑ the total cost. The cost of a pair of boots was \text{$84}. The sales tax rate is \text{5%} of the purchase price. ⓐ $4.20 ⓑ $$88.20 The cost of a refrigerator was \text{$1,242}. The sales tax rate is \text{8%} of the purchase price. The cost of a microwave oven was \text{$129}. The sales tax rate is \text{7.5%} of the purchase price. ⓐ $9.68 ⓑ $138.68 The cost of a tablet computer is \text{$350}. The sales tax rate is \text{8.5%} of the purchase price. The cost of a file cabinet is \text{$250}. The sales tax rate is \text{6.85%} of the purchase price. ⓐ $17.13 ⓑ $267.13 The cost of a luggage set \text{$400}. The sales tax rate is \text{5.75%} of the purchase price. The cost of a 6 -drawer\text{6 -drawer} dresser \text{$1,199}. The sales tax rate is \text{5.125%} of the purchase price. ⓐ $61.45 ⓑ $1,260.45 The cost of a sofa is \text{$1,350}. The sales tax rate is \text{4.225%} of the purchase price. In the following exercises, find the sales tax rate. Shawna bought a mixer for \text{$300}. The sales tax on the purchase was \text{$19.50}. 6.5% Orphia bought a coffee table for \text{$400}. The sales tax on the purchase was \text{$38}. Bopha bought a bedroom set for \text{$3,600}. The sales tax on the purchase was \text{$246.60}. 6.85% Ruth bought a washer and dryer set for \text{$2,100}. The sales tax on the purchase was \text{$152.25}. Solve Commission Applications In the following exercises, find the commission. Christopher sold his dinette set for \text{$225} through an online site, which charged him \text{9%} of the selling price as commission. How much was the commission? $20.25 Michele rented a booth at a craft fair, which charged her \text{8%} commission on her sales. One day her total sales were \text{$193}. How much was the commission? Farrah works in a jewelry store and receives \text{12%} commission when she makes a sale. How much commission will she receive for selling a \text{$8,125} ring? $975 Jamal works at a car dealership and receives \text{9%} commission when he sells a car. How much commission will he receive for selling a \text{$32,575} car? Hector receives \text{17.5%} commission when he sells an insurance policy. How much commission will he receive for selling a policy for \text{$4,910}? $859.25 Denise receives \text{10.5%} commission when she books a tour at the travel agency. How much commission will she receive for booking a tour with total cost \text{$7,420}? In the following exercises, find the rate of commission. Dontay is a realtor and earned \text{$11,250} commission on the sale of a \text{$375,000} house. What is his rate of commission? 3% Nevaeh is a cruise specialist and earned \text{$364} commission after booking a cruise that cost \text{$5,200}. What is her rate of commission? As a waitress, Emily earned \text{$420} in tips on sales of \text{$2,625} last Saturday night. What was her rate of commission? 16% Alejandra earned \text{$1,393.74} commission on weekly sales of \text{$15,486} as a salesperson at the computer store. What is her rate of commission? Maureen earned \text{$7,052.50} commission when she sold a \text{$45,500} car. What was the rate of commission? 15.5% Lucas earned \text{$4,487.50} commission when he brought a \text{$35,900} job to his office. What was the rate of commission? Solve Discount Applications In the following exercises, find the sale price. Perla bought a cellphone that was on sale for \text{$50} off. The original price of the cellphone was \text{$189}. $139 Sophie saw a dress she liked on sale for \text{$15} off. The original price of the dress was \text{$96}. $81 Rick wants to buy a tool set with original price \text{$165}. Next week the tool set will be on sale for \text{40%} off. $125 Angelo's store is having a sale on TV sets. One set, with an original price of \text{$859}, is selling for \text{$125} off. In the following exercises, find ⓐ the amount of discount and ⓑ the sale price. Janelle bought a beach chair on sale at \text{60%} off. The original price was \text{$44.95} ⓐ $26.97 ⓑ $17.98 Errol bought a skateboard helmet on sale at \text{40%} off. The original price was \text{$49.95}. Kathy wants to buy a camera that lists for \text{$389}. The camera is on sale with a \text{33%} discount. ⓐ $128.37 ⓑ $260.63 Colleen bought a suit that was discounted \text{25%} from an original price of \text{$245}. Erys bought a treadmill on sale at \text{35%} off. The original price was \text{$949.95}. ⓐ $332.48 ⓑ $617.50 Jay bought a guitar on sale at \text{45%} off. The original price was \text{$514.75}. In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.) Larry and Donna bought a sofa at the sale price of \text{$1,344}. The original price of the sofa was \text{$1,920}. ⓐ $576 ⓑ 30% Hiroshi bought a lawnmower at the sale price of \text{$240}. The original price of the lawnmower is \text{$300}. Patty bought a baby stroller on sale for \text{$301.75}. The original price of the stroller was \text{$355.} ⓐ $53.25 ⓑ 15% Bill found a book he wanted on sale for \text{$20.80}. The original price of the book was \text{$32}. Nikki bought a patio set on sale for \text{$480}. The original price was \text{$850}. ⓐ $370 ⓑ 43.5% Stella bought a dinette set on sale for \text{$725}. The original price was \text{$1,299}. Solve Mark-up Applications In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price. Daria bought a bracelet at wholesale cost \text{$16} to sell in her handicraft store. She marked the price up \text{45%}. ⓐ $7.20 ⓑ $23.20 Regina bought a handmade quilt at wholesale cost \text{$120} to sell in her quilt store. She marked the price up \text{55%}. Tom paid \text{$0.60} a pound for tomatoes to sell at his produce store. He added a \text{33%} mark-up. ⓐ $0.20 ⓑ 44.2% Flora paid her supplier \text{$0.74} a stem for roses to sell at her flower shop. She added an \text{85%} mark-up. Alan bought a used bicycle for \text{$115}. After re-conditioning it, he added \text{225%} mark-up and then advertised it for sale. ⓐ $258.75 ⓑ $373.75 Michael bought a classic car for \text{$8,500}. He restored it, then added \text{150%} mark-up before advertising it for sale.

Everyday Math

Coupons Yvonne can use two coupons for the same purchase at her favorite department store. One coupon gives her \text{$20} off and the other gives her \text{25%} off. She wants to buy a bedspread that sells for \text{$195}. ⓐ Calculate the discount price if Yvonne uses the \text{$20} coupon first and then takes \text{25%} off. ⓑ Calculate the discount price if Yvonne uses the \text{25%} off coupon first and then uses the \text{20%} coupon. ⓒ In which order should Yvonne use the coupons? ⓐ $131.25 ⓑ $126.25 ⓒ 25% off first, then $20 off Cash Back Jason can buy a bag of dog food for \text{$35} at two different stores. One store offers \text{6%} cash back on the purchase plus \text{$5} off his next purchase. The other store offers \text{20%} cash back. ⓐ Calculate the total savings from the first store, including the savings on the next purchase. ⓑ Calculate the total savings from the second store. ⓒ Which store should Jason buy the dog food from? Why?

Writing Exercises

Priam bought a jacket that was on sale for \text{40%} off. The original price of the jacket was \text{$150}. While the sales clerk figured the price by calculating the amount of discount and then subtracting that amount from \text{$150}, Priam found the price faster by calculating \text{60%} of \text{$150}. ⓐ Explain why Priam was correct. ⓑ Will Priam's method work for any original price? ⓐ Priam is correct. The original price is 100%. Since the discount rate was 40%, the sale price was 60% of the original price. ⓑ Yes. Roxy bought a scarf on sale for \text{50%} off. The original price of the scarf was \text{$32.90}. Roxy claimed that the price she paid for the scarf was the same as the amount she saved. Was Roxy correct? Explain.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?  

Practice Makes Perfect

Use the Simple Interest Formula In the following exercises, use the simple interest formula to fill in the missing information.
Interest Principal Rate Time (years)
\text{$1200} \text{3%} 55
$180
Interest Principal Rate Time (years)
\text{$1500} \text{2%} 4\text{4}
Interest Principal Rate Time (years)
$4410 \text{4.5%} 7\text{7}
$14,000
Interest Principal Rate Time (years)
$2212 \text{3.2%} 6\text{6}
Interest Principal Rate Time (years)
$577.08 \text{$4580} 2\text{2}
6.3%
Interest Principal Rate Time (years)
$528.12 \text{$3260} 3\text{3}
In the following exercises, solve the problem using the simple interest formula. Find the simple interest earned after 55 years on \text{$600} at an interest rate of \text{3%.} $90 Find the simple interest earned after 44 years on \text{$900} at an interest rate of \text{6%.} Find the simple interest earned after 22 years on \text{$8,950} at an interest rate of \text{3.24%}. $579.96 Find the simple interest earned after 33 years on \text{$6,510} at an interest rate of \text{2.85%}. Find the simple interest earned after 88 years on \text{$15,500} at an interest rate of \text{11.425%}. $14,167 Find the simple interest earned after 66 years on \text{$23,900} at an interest rate of \text{12.175%}. Find the principal invested if \text{$656} interest was earned in 55 years at an interest rate of \text{4%}. $3,280 Find the principal invested if \text{$177} interest was earned in 22 years at an interest rate of \text{3%}. Find the principal invested if \text{$70.95} interest was earned in 33 years at an interest rate of \text{2.75%.} $860 Find the principal invested if \text{$636.84} interest was earned in 66 years at an interest rate of \text{4.35%.} Find the principal invested if \text{$15,222.57} interest was earned in 66 years at an interest rate of \text{10.28%}. $24,679.91 Find the principal invested if \text{$10,953.70} interest was earned in 55 years at an interest rate of \text{11.04%.} Find the rate if a principal of \text{$5,400} earned \text{$432} interest in 22 years. 4% Find the rate if a principal of \text{$2,600} earned \text{$468} interest in 66 years. Find the rate if a principal of \text{$11,000} earned \text{$1,815} interest in 33 years. 5.5% Find the rate if a principal of \text{$8,500} earned \text{$3,230} interest in 44 years. Solve Simple Interest Applications In the following exercises, solve the problem using the simple interest formula. Casey deposited \text{$1,450} in a bank account with interest rate \text{4%.} How much interest was earned in 22 years? $116 Terrence deposited \text{$5,720} in a bank account with interest rate \text{6%.} How much interest was earned in 44 years? Robin deposited \text{$31,000} in a bank account with interest rate \text{5.2%}. How much interest was earned in 33 years? $4,836 Carleen deposited \text{$16,400} in a bank account with interest rate \text{3.9%}. How much interest was earned in 88 years? Hilaria borrowed \text{$8,000} from her grandfather to pay for college. Five years later, she paid him back the \text{$8,000}, plus \text{$1,200} interest. What was the rate of interest? 3% Kenneth lent his niece \text{$1,200} to buy a computer. Two years later, she paid him back the \text{$1,200}, plus \text{$96} interest. What was the rate of interest? Lebron lent his daughter \text{$20,000} to help her buy a condominium. When she sold the condominium four years later, she paid him the \text{$20,000}, plus \text{$3,000} interest. What was the rate of interest? 3.75% Pablo borrowed \text{$50,000} to start a business. Three years later, he repaid the \text{$50,000}, plus \text{$9,375} interest. What was the rate of interest? In 1010 years, a bank account that paid \text{5.25%} earned \text{$18,375} interest. What was the principal of the account? $35,000 In 2525 years, a bond that paid \text{4.75%} earned \text{$2,375} interest. What was the principal of the bond? Joshua's computer loan statement said he would pay \text{$1,244.34} in interest for a 33 year loan at \text{12.4%}. How much did Joshua borrow to buy the computer? $3,345 Margaret's car loan statement said she would pay \text{$7,683.20} in interest for a 55 year loan at \text{9.8%.} How much did Margaret borrow to buy the car? Caitlin invested \text{$8,200} in an 18-month\text{18-month} certificate of deposit paying \text{2.7%} interest. How much interest did she earn form this investment? $332.10 Diego invested \text{$6,100} in a 9-month\text{9-month} certificate of deposit paying \text{1.8%} interest. How much interest did he earn form this investment? Airin borrowed \text{$3,900} from her parents for the down payment on a car and promised to pay them back in 1515 months at a \text{4%} rate of interest. How much interest did she owe her parents? $195.00 Yuta borrowed \text{$840} from his brother to pay for his textbooks and promised to pay him back in 55 months at a \text{6%} rate of interest. How much interest did Yuta owe his brother?

Everyday Math

Interest on savings Find the interest rate your local bank pays on savings accounts. ⓐ What is the interest rate? ⓑ Calculate the amount of interest you would earn on a principal of \text{$8,000} for 55 years. Answers will vary. Interest on a loan Find the interest rate your local bank charges for a car loan. ⓐ What is the interest rate? ⓑ Calculate the amount of interest you would pay on a loan of \text{$8,000} for 55 years.

Writing Exercises

Why do banks pay interest on money deposited in savings accounts? Answers will vary. Why do banks charge interest for lending money?

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Practice Makes Perfect

Use the Definition of Proportion In the following exercises, write each sentence as a proportion. 44 is to 1515 as 3636 is to 135135. 415=36135\frac{4}{15}=\frac{36}{135} 77 is to 99 as 3535 is to 4545. 1212 is to 55 as 9696 is to 4040. 125=9640\frac{12}{5}=\frac{96}{40} 1515 is to 88 as 7575 is to 4040. 55 wins in 77 games is the same as 115115 wins in 161161 games. 57=115161\frac{5}{7}=\frac{115}{161} 44 wins in 99 games is the same as 3636 wins in 8181 games. 88 campers to 11 counselor is the same as 4848 campers to 66 counselors. 81=486\frac{8}{1}=\frac{48}{6} 66 campers to 11 counselor is the same as 4848 campers to 88 counselors. \text{$9.36} for 1818 ounces is the same as \text{$2.60} for 55 ounces. 9.3618=2.605\frac{9.36}{18}=\frac{2.60}{5} \text{$3.92} for 88 ounces is the same as \text{$1.47} for 33 ounces. \text{$18.04} for 1111 pounds is the same as \text{$4.92} for 33 pounds. 18.0411=4.923\frac{18.04}{11}=\frac{4.92}{3} \text{$12.42} for 2727 pounds is the same as \text{$5.52} for 1212 pounds. In the following exercises, determine whether each equation is a proportion. 715=56120\frac{7}{15}=\frac{56}{120} yes 512=45108\frac{5}{12}=\frac{45}{108} 116=2116\frac{11}{6}=\frac{21}{16} no 94=3934\frac{9}{4}=\frac{39}{34} 1218=4.997.56\frac{12}{18}=\frac{4.99}{7.56} no 916=2.163.89\frac{9}{16}=\frac{2.16}{3.89} 13.58.5=31.0519.55\frac{13.5}{8.5}=\frac{31.05}{19.55} yes 10.18.4=3.032.52\frac{10.1}{8.4}=\frac{3.03}{2.52} Solve Proportions In the following exercises, solve each proportion. x56=78\frac{x}{56}=\frac{7}{8} 49 n91=813\frac{n}{91}=\frac{8}{13} 4963=z9\frac{49}{63}=\frac{z}{9} 7 5672=y9\frac{56}{72}=\frac{y}{9} 5a=65117\frac{5}{a}=\frac{65}{117} 9 4b=64144\frac{4}{b}=\frac{64}{144} 98154=−7p\frac{98}{154}=\frac{-7}{p} −11 72156=−6q\frac{72}{156}=\frac{-6}{q} a−8=−4248\frac{a}{-8}=\frac{-42}{48} 7 b−7=−3042\frac{b}{-7}=\frac{-30}{42} 2.63.9=c3\frac{2.6}{3.9}=\frac{c}{3} 2 2.73.6=d4\frac{2.7}{3.6}=\frac{d}{4} 2.7j=0.90.2\frac{2.7}{j}=\frac{0.9}{0.2} 0.6 2.8k=2.11.5\frac{2.8}{k}=\frac{2.1}{1.5} 121=m8\frac{\frac{1}{2}}{1}=\frac{m}{8} 4 133=9n\frac{\frac{1}{3}}{3}=\frac{9}{n} Solve Applications Using Proportions In the following exercises, solve the proportion problem. Pediatricians prescribe 55 milliliters (ml) of acetaminophen for every 2525 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs 4545 pounds? 9 ml Brianna, who weighs 66 kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at 1515 milligrams (mg) for every 11 kilogram (kg) of the child’s weight. How many milligrams will the doctor prescribe? At the gym, Carol takes her pulse for 1010 sec and counts 1919 beats. How many beats per minute is this? Has Carol met her target heart rate of 140140 beats per minute? 114, no Kevin wants to keep his heart rate at 160160 beats per minute while training. During his workout he counts 2727 beats in 1010 seconds. How many beats per minute is this? Has Kevin met his target heart rate? A new energy drink advertises 106106 calories for 88 ounces. How many calories are in 1212 ounces of the drink? 159 cal One 1212 ounce can of soda has 150150 calories. If Josiah drinks the big 3232 ounce size from the local mini-mart, how many calories does he get? Karen eats 12\frac{1}{2} cup of oatmeal that counts for 22 points on her weight loss program. Her husband, Joe, can have 33 points of oatmeal for breakfast. How much oatmeal can he have? 34cup\frac{3}{4}\text{cup} An oatmeal cookie recipe calls for 12\frac{1}{2} cup of butter to make 44 dozen cookies. Hilda needs to make 1010 dozen cookies for the bake sale. How many cups of butter will she need? Janice is traveling to Canada and will change \text{$250} US dollars into Canadian dollars. At the current exchange rate, \text{$1} US is equal to \text{$1.01} Canadian. How many Canadian dollars will she get for her trip? $252.50 Todd is traveling to Mexico and needs to exchange \text{$450} into Mexican pesos. If each dollar is worth 12.2912.29 pesos, how many pesos will he get for his trip? Steve changed \text{$600} into 480480 Euros. How many Euros did he receive per US dollar? 1.25 Martha changed \text{$350} US into 385385 Australian dollars. How many Australian dollars did she receive per US dollar? At the laundromat, Lucy changed \text{$12.00} into quarters. How many quarters did she get? 48 quarters When she arrived at a casino, Gerty changed \text{$20} into nickels. How many nickels did she get? Jesse’s car gets 3030 miles per gallon of gas. If Las Vegas is 285285 miles away, how many gallons of gas are needed to get there and then home? If gas is \text{$3.09} per gallon, what is the total cost of the gas for the trip? 19, $58.71 Danny wants to drive to Phoenix to see his grandfather. Phoenix is 370370 miles from Danny’s home and his car gets 18.518.5 miles per gallon. How many gallons of gas will Danny need to get to and from Phoenix? If gas is \text{$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, 812812 miles away. After 33 hours, he has gone 190190 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 280280 miles. After 22 hours, she has gone 152152 miles. At that rate, how long will the whole drive take? Phil wants to fertilize his lawn. Each bag of fertilizer covers about 4,0004,000 square feet of lawn. Phil’s lawn is approximately 13,50013,500 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 350350 square feet, and the exterior of the house measures approximately 20002000 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 \text{35%} of 250?250? n250=35100\frac{n}{250}=\frac{35}{100} What number is \text{75%} of 920?920? What number is \text{110%} of 47?47? n47=110100\frac{n}{47}=\frac{110}{100} What number is \text{150%} of 64?64? 4545 is \text{30%} of what number? 45n=30100\frac{45}{n}=\frac{30}{100} 2525 is \text{80%} of what number? 9090 is \text{150%} of what number? 90n=150100\frac{90}{n}=\frac{150}{100} 7777 is \text{110%} of what number? What percent of 8585 is 17?17? 1785=p100\frac{17}{85}=\frac{p}{100} What percent of 9292 is 46?46? What percent of 260260 is 340?340? 340260=p100\frac{340}{260}=\frac{p}{100} What percent of 180180 is 220?220? Translate and Solve Percent Proportions In the following exercises, translate and solve using proportions. What number is \text{65%} of 180?180? 117 What number is \text{55%} of 300?300? 165 \text{18%} of 9292 is what number? 16.56 \text{22%} of 7474 is what number? \text{175%} of 2626 is what number? 45.5 \text{250%} of 6161 is what number? What is \text{300%} of 488?488? 1464 What is \text{500%} of 315?315? \text{17%}[/latex] of what number is [latex]\text{$7.65}? $45 \text{19%}[/latex] of what number is [latex]\text{$6.46}? \text{$13.53} is \text{8.25%} of what number? $164 \text{$18.12} is \text{7.55%} of what number? What percent of 5656 is 14?14? 25% What percent of 8080 is 28?28? What percent of 9696 is 12?12? 12.5% What percent of 120120 is 27?27?

Everyday Math

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 33 ounces of concentrate with 55 ounces of water. If he puts 1212 ounces of concentrate in a bucket, how many ounces of water should he add? How many ounces of the solution will he have altogether? 20, 32 Mixing a concentrate Travis is going to wash his car. The directions on the bottle of car wash concentrate say to mix 22 ounces of concentrate with 1515 ounces of water. If Travis puts 66 ounces of concentrate in a bucket, how much water must he mix with the concentrate?

Writing Exercises

To solve "what number is \text{45%} of 350"350\text{"} 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 125125 is 25"25\text{"} 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.

Self Check

ⓐ 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?

Understand Percent

In the following exercises, write each percent as a ratio. \text{32%} admission rate for the university 32100\frac{32}{100} \text{53.3%} rate of college students with student loans In the following exercises, write as a ratio and then as a percent. 1313 out of 100100 architects are women. \frac{13}{100},\text{13%} 99 out of every 100100 nurses are men. In the following exercises, convert each percent to a fraction. \text{48%} 1225\frac{12}{25} \text{175%} \text{64.1%} 6411000\frac{641}{1000} 8148\frac{1}{4}% In the following exercises, convert each percent to a decimal. \text{6%} 0.06 \text{23%} \text{128%} 1.28 4.9% In the following exercises, convert each percent to ⓐ a simplified fraction and ⓑ a decimal. In 2012,\text{13.5%} of the United States population was age 6565 or over. (Source: www.census.gov) ⓐ 27200\frac{27}{200} ⓑ 0.1350.135 In 2012,\text{6.5%} of the United States population was under 55 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 \text{50%}. ⓐ 12\frac{1}{2} ⓑ 0.50.5 A couple plans to have three children. The probability they will all be girls is \text{12.5%}. In the following exercises, convert each decimal to a percent. 0.040.04 4% 0.150.15 2.822.82 282% 33 0.0030.003 0.3% 1.3951.395 In the following exercises, convert each fraction to a percent. 34\frac{3}{4} 75% 115\frac{11}{5} 3583\frac{5}{8} 362.5% 29\frac{2}{9} According to the Centers for Disease Control, 25\frac{2}{5} 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\frac{3}{4} take a multivitamin. In the following exercises, translate and solve. What number is \text{46%} of 350?350? 161 \text{120%} of 5555 is what number? 8484 is \text{35%} of what number? 240 1515 is \text{8%} of what number? \text{200%}[/latex] of what number is [latex]50? 25 \text{7.9%}[/latex] of what number is [latex]\text{$4.74}? What percent of 120120 is 81.6?81.6? 68% What percent of 340340 is 595?595?

Solve General Applications of Percents

In the following exercises, solve. When Aurelio and his family ate dinner at a restaurant, the bill was \text{$83.50}. Aurelio wants to leave \text{20%} of the total bill as a tip. How much should the tip be? $16.70 One granola bar has 22 grams of fiber, which is \text{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 190190 calories, and 5454 calories are from fat. What percent of the total calories is from fat? 28.4% Elsa gets paid \text{$4,600} per month. Her car payment is \text{$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 \text{$19.00} to \text{$19.76}. Find the percent increase. 4% Last year Bernard bought a new car for \text{$30,000}. This year the car is worth \text{$24,000}. Find the percent decrease.

Solve Sales Tax, Commission, and Discount Applications

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

Solve Simple Interest Applications

In the following exercises, solve the simple interest problem. Find the simple interest earned after 44 years on \text{$2,250} invested at an interest rate of \text{5%}. $450 Find the simple interest earned after 77 years on \text{$12,000} invested at an interest rate of \text{8.5%}. Find the principal invested if \text{$660} interest was earned in 55 years at an interest rate of \text{3%}. $4400 Find the interest rate if \text{$2,898} interest was earned from a principal of \text{$23,000} invested for 33 years. Kazuo deposited \text{$10,000} in a bank account with interest rate \text{4.5%}. How much interest was earned in 22 years? $900 Brent invested \text{$23,000} in a friend’s business. In 55 years the friend paid him the \text{$23,000} plus \text{$9,200} interest. What was the rate of interest? Fresia lent her son \text{$5,000} for college expenses. Three years later he repaid her the \text{$5,000} plus \text{$375} interest. What was the rate of interest? 2.5% In 66 years, a bond that paid \text{5.5%} earned \text{$594} interest. What was the principal of the bond?

Solve Proportions and their Applications

In the following exercises, write each sentence as a proportion. 33 is to 88 as 1212 is to 3232. 38=1232\frac{3}{8}=\frac{12}{32} 9595 miles to 33 gallons is the same as 475475 miles to 1515 gallons. 11 teacher to 1818 students is the same as 2323 teachers to 414414 students. 118=23414\frac{1}{18}=\frac{23}{414} \text{$7.35} for 1515 ounces is the same as \text{$2.94} for 66 ounces. In the following exercises, determine whether each equation is a proportion. 513=3078\frac{5}{13}=\frac{30}{78} yes 167=4823\frac{16}{7}=\frac{48}{23} 1218=6.9910.99\frac{12}{18}=\frac{6.99}{10.99} no 11.69.2=37.1229.44\frac{11.6}{9.2}=\frac{37.12}{29.44} In the following exercises, solve each proportion. x36=59\frac{x}{36}=\frac{5}{9} 20 7a=−684\frac{7}{a}=\frac{-6}{84} 1.21.8=d6\frac{1.2}{1.8}=\frac{d}{6} 4 122=m20\frac{\frac{1}{2}}{2}=\frac{m}{20} In the following exercises, solve the proportion problem. The children’s dosage of acetaminophen is 55 milliliters (ml) for every 2525 pounds of a child’s weight. How many milliliters of acetaminophen will be prescribed for a 6060 pound child? 12 After a workout, Dennis takes his pulse for 1010 sec and counts 2121 beats. How many beats per minute is this? An 88 ounce serving of ice cream has 272272 calories. If Lavonne eats 1010 ounces of ice cream, how many calories does she get? 340 Alma is going to Europe and wants to exchange \text{$1,200} into Euros. If each dollar is 0.750.75 Euros, how many Euros will Alma get? Zack wants to drive from Omaha to Denver, a distance of 494494 miles. If his car gets 3838 miles to the gallon, how many gallons of gas will Zack need to get to Denver? 13 gallons Teresa is planning a party for 100100 people. Each gallon of punch will serve 1818 people. How many gallons of punch will she need? In the following exercises, translate to a proportion. What number is \text{62%} of 395?395? n395=62100\frac{n}{395}=\frac{62}{100} 4242 is \text{70%} of what number? What percent of 1,0001,000 is 15?15? 151000=p100\frac{15}{1000}=\frac{p}{100} What percent of 140140 is 210?210? In the following exercises, translate and solve using proportions. What number is \text{85%} of 900?900? 765 \text{6%}[/latex] of what number is [latex]\text{$24}? \text{$3.51} is \text{4.5%} of what number? $78 What percent of 3,1003,100 is 930?930? In the following exercises, convert each percent to ⓐ a decimal ⓑ a simplified fraction. \text{24%} 0.24,6250.24,\frac{6}{25} \text{5%} \text{350%} 3.5,3123.5,3\frac{1}{2} In the following exercises, convert each fraction to a percent. (Round to 33 decimal places if needed.) 78\frac{7}{8} 13\frac{1}{3} 33.333% 1112\frac{11}{12} In the following exercises, solve the percent problem. 65[/latex]iswhatpercentof[latex]260?65[/latex] is what percent of [latex]260? 25% What number is \text{27%} of 3,000?3,000? \text{150%}[/latex] of what number is [latex]60? 40 Yuki’s monthly paycheck is \text{$3,825}. She pays \text{$918} for rent. What percent of her paycheck goes to rent? The total number of vehicles on one freeway dropped from 84,000\text{84,000} to 74,000\text{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 \text{7.72%} of the purchase price. The purchase price of the bicycle was \text{$600}. What was the total cost? Mara received \text{$31.80} commission when she sold a \text{$795} suit. What was her rate of commission? 4% Kiyoshi bought a television set on sale for \text{$899}. The original price was \text{$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 \text{$20}. She refinished it, then added a \text{250%} markup before advertising it for sale. What price did she ask for the dresser? $50 Find the simple interest earned after 55 years on \text{$3000} invested at an interest rate of \text{4.2%}. Brenda borrowed \text{$400} from her brother. Two years later, she repaid the \text{$400} plus \text{$50} interest. What was the rate of interest? 6.2% Write as a proportion: 44 gallons to 144144 miles is the same as 1010 gallons to 360360 miles. Solve for a: 12a=−1565\frac{12}{a}=\frac{-15}{65} −52 Vin read 1010 pages of a book in 1212 minutes. At that rate, how long will it take him to read 3535 pages?

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