Problem Set: Percents

Writing Percents Using Words, Ratios, and Fractions

Use the Definition of Percents

1. In [latex]2014[/latex], the unemployment rate for those with only a high school degree was [latex]\text{6.0%}[/latex].

   Answer: [latex]\Large\frac{6}{100}[/latex]

2. In [latex]2015[/latex], among the unemployed, [latex]\text{29%}[/latex] were long-term unemployed.
3. The unemployment rate for those with Bachelor's degrees was [latex]\text{3.2%}[/latex] in [latex]2014[/latex].

   Answer: [latex]\Large\frac{32}{1000}[/latex]

4. The unemployment rate in Michigan in [latex]2014[/latex] was [latex]\text{7.3%}[/latex].

1. [latex]57[/latex] out of [latex]100[/latex] nursing candidates received their degree at a community college.

   Answer: ⓐ [latex]\Large\frac{57}{100}[/latex] ⓑ [latex]\text{57%}[/latex]

2. [latex]80[/latex] out of [latex]100[/latex] firefighters and law enforcement officers were educated at a community college.
3. [latex]42[/latex] out of [latex]100[/latex] first-time freshmen students attend a community college.

   Answer: ⓐ [latex]\Large\frac{42}{100}[/latex] ⓑ [latex]\text{42%}[/latex]

4. [latex]71[/latex] out of [latex]100[/latex] full-time community college faculty have a master's degree.

Convert Percents to Fractions and Decimals

1. [latex]\text{4%}[/latex]

   Answer: [latex]\Large\frac{1}{25}[/latex]

2. [latex]\text{8%}[/latex]
3. [latex]\text{17%}[/latex]

   Answer: [latex]\Large\frac{17}{100}[/latex]

4. [latex]\text{19%}[/latex]
5. [latex]\text{52%}[/latex]

   Answer: [latex]\Large\frac{13}{25}[/latex]

6. [latex]\text{78%}[/latex]
7. [latex]\text{125%}[/latex]

   Answer: [latex]\Large\frac{5}{4}[/latex]

8. [latex]\text{135%}[/latex]
9. [latex]\text{37.5%}[/latex]

   Answer: [latex]\Large\frac{3}{8}[/latex]

10. [latex]\text{42.5%}[/latex]
11. [latex]\text{18.4%}[/latex]

    Answer: [latex]\Large\frac{23}{125}[/latex]

12. [latex]\text{46.4%}[/latex]

1. [latex]\text{5%}[/latex]

   Answer: 0.05

2. [latex]\text{9%}[/latex]
3. [latex]\text{1%}[/latex]

   Answer: 0.01

4. [latex]\text{2%}[/latex]
5. [latex]\text{63%}[/latex]

   Answer: 0.63

6. [latex]\text{71%}[/latex]
7. [latex]\text{40%}[/latex]

   Answer: 0.4

8. [latex]\text{50%}[/latex]
9. [latex]\text{115%}[/latex]

   Answer: 1.15

10. [latex]\text{125%}[/latex]
11. [latex]\text{150%}[/latex]

    Answer: 1.5

12. [latex]\text{250%}[/latex]
13. [latex]\text{21.4%}[/latex]

    Answer: 0.214

14. [latex]\text{39.3%}[/latex]
15. [latex]\text{7.8%}[/latex]

    Answer: 0.078

16. [latex]\text{6.4%}[/latex]

1. In [latex]2010,\text{1.5%}[/latex] of home sales had owner financing. (Source: Bloomberg Businessweek, 5/23–29/2011)

   Answer: ⓐ [latex]\Large\frac{3}{200}[/latex] ⓑ [latex]0.015[/latex]

2. In [latex]2000,\text{4.2%}[/latex] of the United States population was of Asian descent. (Source: www.census.gov)
3. According to government data, in [latex]2013[/latex] the number of cell phones in India was [latex]\text{70.23%}[/latex] of the population.

   Answer: ⓐ [latex]\Large\frac{7023}{10,000}[/latex] ⓑ [latex]0.7023[/latex]

4. According to the U.S. Census Bureau, among Americans age [latex]25[/latex] or older who had doctorate degrees in [latex]2014,\text{37.1%}[/latex] are women.
5. A couple plans to have two children. The probability they will have two girls is [latex]\text{25%}[/latex].

   Answer: ⓐ [latex]\Large\frac{1}{4}[/latex] ⓑ [latex]0.25[/latex]

6. Javier will choose one digit at random from [latex]0[/latex] through [latex]9[/latex]. The probability he will choose [latex]3[/latex] is [latex]\text{10%}[/latex].
7. According to the local weather report, the probability of thunderstorms in New York City on July [latex]15[/latex] is [latex]\text{60%}[/latex].

   Answer: ⓐ [latex]\Large\frac{3}{5}[/latex] ⓑ [latex]0.6[/latex]

8. A club sells [latex]50[/latex] tickets to a raffle. Osbaldo bought one ticket. The probability he will win the raffle is [latex]\text{2%}[/latex].

Convert Decimals and Fractions to Percents

1. [latex]0.01[/latex]

   Answer: 1%

2. [latex]0.03[/latex]
3. [latex]0.18[/latex]

   Answer: 18%

4. [latex]0.15[/latex]
5. [latex]1.35[/latex]

   Answer: 135%

6. [latex]1.56[/latex]
7. [latex]3[/latex]

   Answer: 300%

8. [latex]4[/latex]
9. [latex]0.009[/latex]

   Answer: 0.9%

10. [latex]0.008[/latex]
11. [latex]0.0875[/latex]

    Answer: 8.75%

12. [latex]0.0625[/latex]
13. [latex]1.5[/latex]

    Answer: 150%

14. [latex]2.2[/latex]
15. [latex]2.254[/latex]

    Answer: 225.4%

16. [latex]2.317[/latex]

1. [latex]\Large\frac{1}{4}[/latex]

   Answer: 25%

2. [latex]\Large\frac{1}{5}[/latex]
3. [latex]\Large\frac{3}{8}[/latex]

   Answer: 37.5%

4. [latex]\Large\frac{5}{8}[/latex]
5. [latex]\Large\frac{7}{4}[/latex]

   Answer: 175%

6. [latex]\Large\frac{9}{8}[/latex]
7. [latex]6\Large\frac{4}{5}[/latex]

   Answer: 680%

8. [latex]5\Large\frac{1}{4}[/latex]
9. [latex]\Large\frac{5}{12}[/latex]

   Answer: 41.7%

10. [latex]\Large\frac{11}{12}[/latex]
11. [latex]2\Large\frac{2}{3}[/latex]

    Answer: [latex]266.\stackrel{-}{6}\text{%}[/latex]

12. [latex]1\Large\frac{2}{3}[/latex]
13. [latex]\Large\frac{3}{7}[/latex]

    Answer: 42.9%

14. [latex]\Large\frac{6}{7}[/latex]
15. [latex]\Large\frac{5}{9}[/latex]

    Answer: 55.6%

16. [latex]\Large\frac{4}{9}[/latex]

1. [latex]\Large\frac{1}{4}[/latex] of washing machines needed repair.

   Answer: 25%

2. [latex]\Large\frac{1}{5}[/latex] of dishwashers needed repair.

1. According to the National Center for Health Statistics, in [latex]2012,\Large\frac{7}{20}[/latex] of American adults were obese.

   Answer: 35%

2. The U.S. Census Bureau estimated that in [latex]2013,\text{85%}[/latex] of Americans lived in the same house as they did [latex]1[/latex] year before.

Solving General Applications of Percent

Translate and Solve Basic Percent Equations

1. What number is [latex]\text{45%}[/latex] of [latex]120?[/latex]

   Answer: 54

2. What number is [latex]\text{65%}[/latex] of [latex]100?[/latex]
3. What number is [latex]\text{24%}[/latex] of [latex]112?[/latex]

   Answer: 26.88

4. What number is [latex]\text{36%}[/latex] of [latex]124?[/latex]
5. [latex]\text{250%}[/latex] of [latex]65[/latex] is what number?

   Answer: 162.5

6. [latex]\text{150%}[/latex] of [latex]90[/latex] is what number?
7. [latex]\text{800%}[/latex] of [latex]2,250[/latex] is what number?

   Answer: 18,000

8. [latex]\text{600%}[/latex] of [latex]1,740[/latex] is what number?
9. [latex]28[/latex] is [latex]\text{25%}[/latex] of what number?

   Answer: 112

10. [latex]36[/latex] is [latex]\text{25%}[/latex] of what number?
11. [latex]81[/latex] is [latex]\text{75%}[/latex] of what number?

    Answer: 108

12. [latex]93[/latex] is [latex]\text{75%}[/latex] of what number?
13. [latex]\text{8.2%}[/latex] of what number is [latex]{$2.87}?[/latex]

    Answer: $35

14. [latex]\text{6.4%}[/latex] of what number is [latex]{$2.88}?[/latex]
15. [latex]\text{11.5%}[/latex] of what number is [latex]{$108.10}?[/latex]

    Answer: $940

16. [latex]\text{12.3%}[/latex] of what number is [latex]{$92.25}?[/latex]
17. What percent of [latex]260[/latex] is [latex]78?[/latex]

    Answer: 30%

18. What percent of [latex]215[/latex] is [latex]86?[/latex]
19. What percent of [latex]1,500[/latex] is [latex]540?[/latex]

    Answer: 36%

20. What percent of [latex]1,800[/latex] is [latex]846?[/latex]
21. [latex]30[/latex] is what percent of [latex]20?[/latex]

    Answer: 150%

22. [latex]50[/latex] is what percent of [latex]40?[/latex]
23. [latex]840[/latex] is what percent of [latex]480?[/latex]

    Answer: 175%

24. [latex]790[/latex] is what percent of [latex]395?[/latex]

Solve Applications of Percents

1. Geneva treated her parents to dinner at their favorite restaurant. The bill was [latex]{$74.25}[/latex]. She wants to leave [latex]\text{16%}[/latex] of the total bill as a tip. How much should the tip be?

   Answer: $11.88

2. When Hiro and his co-workers had lunch at a restaurant the bill was [latex]{$90.50}[/latex]. They want to leave [latex]\text{18%}[/latex] of the total bill as a tip. How much should the tip be?
3. Trong has [latex]\text{12%}[/latex] of each paycheck automatically deposited to his savings account. His last paycheck was [latex]{$2,165}[/latex]. How much money was deposited to Trong's savings account?

   Answer: $259.80

4. Cherise deposits [latex]\text{8%}[/latex] of each paycheck into her retirement account. Her last paycheck was [latex]{$1,485}[/latex]. How much did Cherise deposit into her retirement account?
5. One serving of oatmeal has [latex]8[/latex] grams of fiber, which is [latex]\text{33%}[/latex] of the recommended daily amount. What is the total recommended daily amount of fiber?

   Answer: 24.2 grams

6. One serving of trail mix has [latex]67[/latex] grams of carbohydrates, which is [latex]\text{22%}[/latex] of the recommended daily amount. What is the total recommended daily amount of carbohydrates?
7. A bacon cheeseburger at a popular fast food restaurant contains [latex]2,070[/latex] milligrams (mg) of sodium, which is [latex]\text{86%}[/latex] of the recommended daily amount. What is the total recommended daily amount of sodium?

   Answer: 2,407 grams

8. A grilled chicken salad at a popular fast food restaurant contains [latex]650[/latex] milligrams (mg) of sodium, which is [latex]\text{27%}[/latex] of the recommended daily amount. What is the total recommended daily amount of sodium?
9. The nutrition fact sheet at a fast food restaurant says the fish sandwich has [latex]380[/latex] calories, and [latex]171[/latex] calories are from fat. What percent of the total calories is from fat?

   Answer: 45%

10. The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has [latex]190[/latex] calories, and [latex]114[/latex] calories are from fat. What percent of the total calories is from fat?
11. Emma gets paid [latex]{$3,000}[/latex] per month. She pays [latex]{$750}[/latex] a month for rent. What percent of her monthly pay goes to rent?

    Answer: 25%

12. Dimple gets paid [latex]{$3,200}[/latex] per month. She pays [latex]{$960}[/latex] a month for rent. What percent of her monthly pay goes to rent?

Find Percent Increase and Percent Decrease

1. Tamanika got a raise in her hourly pay, from [latex]{$15.50}[/latex] to [latex]{$17.55}[/latex]. Find the percent increase.

   Answer: 13.2%

2. Ayodele got a raise in her hourly pay, from [latex]{$24.50}[/latex] to [latex]{$25.48}[/latex]. Find the percent increase.
3. Annual student fees at the University of California rose from about [latex]{$4,000}[/latex] in [latex]2000[/latex] to about [latex]{$9,000}[/latex] in [latex]2014[/latex]. Find the percent increase.

   Answer: 125%

4. The price of a share of one stock rose from [latex]{$12.50}[/latex] to [latex]{$50}[/latex]. Find the percent increase.
5. According to Time magazine [latex]\left(\text{7/19/2011}\right)[/latex] annual global seafood consumption rose from [latex]22[/latex] pounds per person in [latex]1960[/latex] to [latex]38[/latex] pounds per person today. Find the percent increase. (Round to the nearest tenth of a percent.)

   Answer: 72.7%

6. In one month, the median home price in the Northeast rose from [latex]{$225,400}[/latex] to [latex]{$241,500}[/latex]. Find the percent increase. (Round to the nearest tenth of a percent.)
7. A grocery store reduced the price of a loaf of bread from [latex]{$2.80}[/latex] to [latex]{$2.73}[/latex]. Find the percent decrease.

   Answer: 2.5%

8. The price of a share of one stock fell from [latex]{$8.75}[/latex] to [latex]{$8.54}[/latex]. Find the percent decrease.
9. Hernando's salary was [latex]{$49,500}[/latex] last year. This year his salary was cut to [latex]{$44,055}[/latex]. Find the percent decrease.

   Answer: 11%

10. From [latex]2000[/latex] to [latex]2010[/latex], the population of Detroit fell from about [latex]951,000[/latex] to about [latex]714,000[/latex]. Find the percent decrease. (Round to the nearest tenth of a percent.)
11. In one month, the median home price in the West fell from [latex]{$203,400}[/latex] to [latex]{$192,300}[/latex]. Find the percent decrease. (Round to the nearest tenth of a percent.)

    Answer: 5.5%

12. Sales of video games and consoles fell from [latex]{$1,150}[/latex] million to [latex]{$1,030}[/latex] million in one year. Find the percent decrease. (Round to the nearest tenth of a percent.)

Solving Sales Tax, Commission, and Discount Applications

1. The cost of a pair of boots was [latex]{$84}[/latex]. The sales tax rate is [latex]\text{5%}[/latex] of the purchase price.

   Answer: ⓐ $4.20 ⓑ $$88.20

2. The cost of a refrigerator was [latex]{$1,242}[/latex]. The sales tax rate is [latex]\text{8%}[/latex] of the purchase price.
3. The cost of a microwave oven was [latex]{$129}[/latex]. The sales tax rate is [latex]\text{7.5%}[/latex] of the purchase price.

   Answer: ⓐ $9.68 ⓑ $138.68

4. The cost of a tablet computer is [latex]{$350}[/latex]. The sales tax rate is [latex]\text{8.5%}[/latex] of the purchase price.
5. The cost of a file cabinet is [latex]{$250}[/latex]. The sales tax rate is [latex]\text{6.85%}[/latex] of the purchase price.

   Answer: ⓐ $17.13 ⓑ $267.13

6. The cost of a luggage set [latex]{$400}[/latex]. The sales tax rate is [latex]\text{5.75%}[/latex] of the purchase price.
7. The cost of a [latex]\text{6 -drawer}[/latex] dresser [latex]{$1,199}[/latex]. The sales tax rate is [latex]\text{5.125%}[/latex] of the purchase price.

   Answer: ⓐ $61.45 ⓑ $1,260.45

8. The cost of a sofa is [latex]{$1,350}[/latex]. The sales tax rate is [latex]\text{4.225%}[/latex] of the purchase price.

1. Shawna bought a mixer for [latex]{$300}[/latex]. The sales tax on the purchase was [latex]{$19.50}[/latex].

   Answer: 6.5%

2. Orphia bought a coffee table for [latex]{$400}[/latex]. The sales tax on the purchase was [latex]{$38}[/latex].
3. Bopha bought a bedroom set for [latex]{$3,600}[/latex]. The sales tax on the purchase was [latex]{$246.60}[/latex].

   Answer: 6.85%

4. Ruth bought a washer and dryer set for [latex]{$2,100}[/latex]. The sales tax on the purchase was [latex]{$152.25}[/latex].

Solve Commission Applications

1. Christopher sold his dinette set for [latex]{$225}[/latex] through an online site, which charged him [latex]\text{9%}[/latex] of the selling price as commission. How much was the commission?

   Answer: $20.25

2. Michele rented a booth at a craft fair, which charged her [latex]\text{8%}[/latex] commission on her sales. One day her total sales were [latex]{$193}[/latex]. How much was the commission?
3. Farrah works in a jewelry store and receives [latex]\text{12%}[/latex] commission when she makes a sale. How much commission will she receive for selling a [latex]{$8,125}[/latex] ring?

   Answer: $975

4. Jamal works at a car dealership and receives [latex]\text{9%}[/latex] commission when he sells a car. How much commission will he receive for selling a [latex]{$32,575}[/latex] car?
5. Hector receives [latex]\text{17.5%}[/latex] commission when he sells an insurance policy. How much commission will he receive for selling a policy for [latex]{$4,910}?[/latex]

   Answer: $859.25

6. Denise receives [latex]\text{10.5%}[/latex] commission when she books a tour at the travel agency. How much commission will she receive for booking a tour with total cost [latex]{$7,420}?[/latex]

1. Dontay is a realtor and earned [latex]{$11,250}[/latex] commission on the sale of a [latex]{$375,000}[/latex] house. What is his rate of commission?

   Answer: 3%

2. Nevaeh is a cruise specialist and earned [latex]{$364}[/latex] commission after booking a cruise that cost [latex]{$5,200}[/latex]. What is her rate of commission?
3. As a waitress, Emily earned [latex]{$420}[/latex] in tips on sales of [latex]{$2,625}[/latex] last Saturday night. What was her rate of commission?

   Answer: 16%

4. Alejandra earned [latex]{$1,393.74}[/latex] commission on weekly sales of [latex]{$15,486}[/latex] as a salesperson at the computer store. What is her rate of commission?
5. Maureen earned [latex]{$7,052.50}[/latex] commission when she sold a [latex]{$45,500}[/latex] car. What was the rate of commission?

   Answer: 15.5%

6. Lucas earned [latex]{$4,487.50}[/latex] commission when he brought a [latex]{$35,900}[/latex] job to his office. What was the rate of commission?

Solve Discount Applications

1. Perla bought a cellphone that was on sale for [latex]{$50}[/latex] off. The original price of the cellphone was [latex]{$189}[/latex].

   Answer: $139

2. Sophie saw a dress she liked on sale for [latex]{$15}[/latex] off. The original price of the dress was [latex]{$96}[/latex].

   Answer: $81

3. Rick wants to buy a tool set with original price [latex]{$165}[/latex]. Next week the tool set will be on sale for [latex]\text{40%}[/latex] off.

   Answer: $125

4. Angelo's store is having a sale on TV sets. One set, with an original price of [latex]{$859}[/latex], is selling for [latex]{$125}[/latex] off.

1. Janelle bought a beach chair on sale at [latex]\text{60%}[/latex] off. The original price was [latex]{$44.95}[/latex]

   Answer: ⓐ $26.97 ⓑ $17.98

2. Errol bought a skateboard helmet on sale at [latex]\text{40%}[/latex] off. The original price was [latex]{$49.95}[/latex].
3. Kathy wants to buy a camera that lists for [latex]{$389}[/latex]. The camera is on sale with a [latex]\text{33%}[/latex] discount.

   Answer: ⓐ $128.37 ⓑ $260.63

4. Colleen bought a suit that was discounted [latex]\text{25%}[/latex] from an original price of [latex]{$245}[/latex].
5. Erys bought a treadmill on sale at [latex]\text{35%}[/latex] off. The original price was [latex]{$949.95}[/latex].

   Answer: ⓐ $332.48 ⓑ $617.50

6. Jay bought a guitar on sale at [latex]\text{45%}[/latex] off. The original price was [latex]{$514.75}[/latex].

1. Larry and Donna bought a sofa at the sale price of [latex]{$1,344}[/latex]. The original price of the sofa was [latex]{$1,920}[/latex].

   Answer: ⓐ $576 ⓑ 30%

2. Hiroshi bought a lawnmower at the sale price of [latex]{$240}[/latex]. The original price of the lawnmower is [latex]{$300}[/latex].
3. Patty bought a baby stroller on sale for [latex]{$301.75}[/latex]. The original price of the stroller was [latex]{$355.}[/latex]

   Answer: ⓐ $53.25 ⓑ 15%

4. Bill found a book he wanted on sale for [latex]{$20.80}[/latex]. The original price of the book was [latex]{$32}[/latex].
5. Nikki bought a patio set on sale for [latex]{$480}[/latex]. The original price was [latex]{$850}[/latex].

   Answer: ⓐ $370 ⓑ 43.5%

6. Stella bought a dinette set on sale for [latex]{$725}[/latex]. The original price was [latex]{$1,299}[/latex].

Solve Mark-up Applications

1. Daria bought a bracelet at wholesale cost [latex]{$16}[/latex] to sell in her handicraft store. She marked the price up [latex]\text{45%}[/latex].

   Answer: ⓐ $7.20 ⓑ $23.20

2. Regina bought a handmade quilt at wholesale cost [latex]{$120}[/latex] to sell in her quilt store. She marked the price up [latex]\text{55%}[/latex].
3. Tom paid [latex]{$0.60}[/latex] a pound for tomatoes to sell at his produce store. He added a [latex]\text{33%}[/latex] mark-up.

   Answer: ⓐ $0.20 ⓑ $0.80

4. Flora paid her supplier [latex]{$0.74}[/latex] a stem for roses to sell at her flower shop. She added an [latex]\text{85%}[/latex] mark-up.
5. Alan bought a used bicycle for [latex]{$115}[/latex]. After re-conditioning it, he added [latex]\text{225%}[/latex] mark-up and then advertised it for sale.

   Answer: ⓐ $258.75 ⓑ $373.75

6. Michael bought a classic car for [latex]{$8,500}[/latex]. He restored it, then added [latex]\text{150%}[/latex] mark-up before advertising it for sale.

Solving Simple Interest Applications

Answer: $180

Answer: $14,000

Answer: 6.3%

1. Find the simple interest earned after [latex]5[/latex] years on [latex]{$600}[/latex] at an interest rate of [latex]\text{3%.}[/latex]

   Answer: $90

2. Find the simple interest earned after [latex]4[/latex] years on [latex]{$900}[/latex] at an interest rate of [latex]\text{6%.}[/latex]
3. Find the simple interest earned after [latex]2[/latex] years on [latex]{$8,950}[/latex] at an interest rate of [latex]\text{3.24%}[/latex].

   Answer: $579.96

4. Find the simple interest earned after [latex]3[/latex] years on [latex]{$6,510}[/latex] at an interest rate of [latex]\text{2.85%}[/latex].
5. Find the simple interest earned after [latex]8[/latex] years on [latex]{$15,500}[/latex] at an interest rate of [latex]\text{11.425%}[/latex].

   Answer: $14,167

6. Find the simple interest earned after [latex]6[/latex] years on [latex]{$23,900}[/latex] at an interest rate of [latex]\text{12.175%}[/latex].
7. Find the principal invested if [latex]{$656}[/latex] interest was earned in [latex]5[/latex] years at an interest rate of [latex]\text{4%}[/latex].

   Answer: $3,280

8. Find the principal invested if [latex]{$177}[/latex] interest was earned in [latex]2[/latex] years at an interest rate of [latex]\text{3%}[/latex].
9. Find the principal invested if [latex]{$70.95}[/latex] interest was earned in [latex]3[/latex] years at an interest rate of [latex]\text{2.75%.}[/latex]

   Answer: $860

10. Find the principal invested if [latex]{$636.84}[/latex] interest was earned in [latex]6[/latex] years at an interest rate of [latex]\text{4.35%.}[/latex]
11. Find the principal invested if [latex]{$15,222.57}[/latex] interest was earned in [latex]6[/latex] years at an interest rate of [latex]\text{10.28%}[/latex].

    Answer: $24,679.91

12. Find the principal invested if [latex]{$10,953.70}[/latex] interest was earned in [latex]5[/latex] years at an interest rate of [latex]\text{11.04%.}[/latex]
13. Find the rate if a principal of [latex]{$5,400}[/latex] earned [latex]{$432}[/latex] interest in [latex]2[/latex] years.

    Answer: 4%

14. Find the rate if a principal of [latex]{$2,600}[/latex] earned [latex]{$468}[/latex] interest in [latex]6[/latex] years.
15. Find the rate if a principal of [latex]{$11,000}[/latex] earned [latex]{$1,815}[/latex] interest in [latex]3[/latex] years.

    Answer: 5.5%

16. Find the rate if a principal of [latex]{$8,500}[/latex] earned [latex]{$3,230}[/latex] interest in [latex]4[/latex] years.

Solve Simple Interest Applications

1. Casey deposited [latex]{$1,450}[/latex] in a bank account with interest rate [latex]\text{4%.}[/latex] How much interest was earned in [latex]2[/latex] years?

   Answer: $116

2. Terrence deposited [latex]{$5,720}[/latex] in a bank account with interest rate [latex]\text{6%.}[/latex] How much interest was earned in [latex]4[/latex] years?
3. Robin deposited [latex]{$31,000}[/latex] in a bank account with interest rate [latex]\text{5.2%}[/latex]. How much interest was earned in [latex]3[/latex] years?

   Answer: $4,836

4. Carleen deposited [latex]{$16,400}[/latex] in a bank account with interest rate [latex]\text{3.9%}[/latex]. How much interest was earned in [latex]8[/latex] years?
5. Hilaria borrowed [latex]{$8,000}[/latex] from her grandfather to pay for college. Five years later, she paid him back the [latex]{$8,000}[/latex], plus [latex]{$1,200}[/latex] interest. What was the rate of interest?

   Answer: 3%

6. Kenneth lent his niece [latex]{$1,200}[/latex] to buy a computer. Two years later, she paid him back the [latex]{$1,200}[/latex], plus [latex]{$96}[/latex] interest. What was the rate of interest?
7. Lebron lent his daughter [latex]{$20,000}[/latex] to help her buy a condominium. When she sold the condominium four years later, she paid him the [latex]{$20,000}[/latex], plus [latex]{$3,000}[/latex] interest. What was the rate of interest?

   Answer: 3.75%

8. Pablo borrowed [latex]{$50,000}[/latex] to start a business. Three years later, he repaid the [latex]{$50,000}[/latex], plus [latex]{$9,375}[/latex] interest. What was the rate of interest?
9. In [latex]10[/latex] years, a bank account that paid [latex]\text{5.25%}[/latex] earned [latex]{$18,375}[/latex] interest. What was the principal of the account?

   Answer: $35,000

10. In [latex]25[/latex] years, a bond that paid [latex]\text{4.75%}[/latex] earned [latex]{$2,375}[/latex] interest. What was the principal of the bond?
11. Joshua's computer loan statement said he would pay [latex]{$1,244.34}[/latex] in interest for a [latex]3[/latex] year loan at [latex]\text{12.4%}[/latex]. How much did Joshua borrow to buy the computer?

    Answer: $3,345

12. Margaret's car loan statement said she would pay [latex]{$7,683.20}[/latex] in interest for a [latex]5[/latex] year loan at [latex]\text{9.8%.}[/latex] How much did Margaret borrow to buy the car?
13. Caitlin invested [latex]{$8,200}[/latex] in an [latex]\text{18-month}[/latex] certificate of deposit paying [latex]\text{2.7%}[/latex] interest. How much interest did she earn form this investment?

    Answer: $332.10

14. Diego invested [latex]{$6,100}[/latex] in a [latex]\text{9-month}[/latex] certificate of deposit paying [latex]\text{1.8%}[/latex] interest. How much interest did he earn from this investment?
15. Airin borrowed [latex]{$3,900}[/latex] from her parents for the down payment on a car and promised to pay them back in [latex]15[/latex] months at a [latex]\text{4%}[/latex] rate of interest. How much interest did she owe her parents?

    Answer: $195.00

16. Yuta borrowed [latex]{$840}[/latex] from his brother to pay for his textbooks and promised to pay him back in [latex]5[/latex] months at a [latex]\text{6%}[/latex] rate of interest. How much interest did Yuta owe his brother?

Solving Proportions and their Applications

1. [latex]4[/latex] is to [latex]15[/latex] as [latex]36[/latex] is to [latex]135[/latex].

   Answer: [latex]\Large\frac{4}{15}\normalsize =\Large\frac{36}{135}[/latex]

2. [latex]7[/latex] is to [latex]9[/latex] as [latex]35[/latex] is to [latex]45[/latex].
3. [latex]12[/latex] is to [latex]5[/latex] as [latex]96[/latex] is to [latex]40[/latex].

   Answer: [latex]\Large\frac{12}{5}\normalsize =\Large\frac{96}{40}[/latex]

4. [latex]15[/latex] is to [latex]8[/latex] as [latex]75[/latex] is to [latex]40[/latex].
5. [latex]5[/latex] wins in [latex]7[/latex] games is the same as [latex]115[/latex] wins in [latex]161[/latex] games.

   Answer: [latex]\Large\frac{5}{7}\normalsize =\Large\frac{115}{161}[/latex]

6. [latex]4[/latex] wins in [latex]9[/latex] games is the same as [latex]36[/latex] wins in [latex]81[/latex] games.
7. [latex]8[/latex] campers to [latex]1[/latex] counselor is the same as [latex]48[/latex] campers to [latex]6[/latex] counselors.

   Answer: [latex]\Large\frac{8}{1}\normalsize =\Large\frac{48}{6}[/latex]

8. [latex]6[/latex] campers to [latex]1[/latex] counselor is the same as [latex]48[/latex] campers to [latex]8[/latex] counselors.
9. [latex]{$9.36}[/latex] for [latex]18[/latex] ounces is the same as [latex]{$2.60}[/latex] for [latex]5[/latex] ounces.

   Answer: [latex]\Large\frac{9.36}{18}\normalsize =\Large\frac{2.60}{5}[/latex]

10. [latex]{$3.92}[/latex] for [latex]8[/latex] ounces is the same as [latex]{$1.47}[/latex] for [latex]3[/latex] ounces.
11. [latex]{$18.04}[/latex] for [latex]11[/latex] pounds is the same as [latex]{$4.92}[/latex] for [latex]3[/latex] pounds.

    Answer: [latex]\Large\frac{18.04}{11}\normalsize =\Large\frac{4.92}{3}[/latex]

12. [latex]{$12.42}[/latex] for [latex]27[/latex] pounds is the same as [latex]{$5.52}[/latex] for [latex]12[/latex] pounds.

1. [latex]\Large\frac{7}{15}\normalsize =\Large\frac{56}{120}[/latex]

   Answer: yes

2. [latex]\Large\frac{5}{12}\normalsize =\Large\frac{45}{108}[/latex]
3. [latex]\Large\frac{11}{6}\normalsize =\Large\frac{21}{16}[/latex]

   Answer: no

4. [latex]\Large\frac{9}{4}\normalsize =\Large\frac{39}{34}[/latex]
5. [latex]\Large\frac{12}{18}\normalsize =\Large\frac{4.99}{7.56}[/latex]

   Answer: no

6. [latex]\Large\frac{9}{16}\normalsize =\Large\frac{2.16}{3.89}[/latex]
7. [latex]\Large\frac{13.5}{8.5}\normalsize =\Large\frac{31.05}{19.55}[/latex]

   Answer: yes

8. [latex]\Large\frac{10.1}{8.4}\normalsize =\Large\frac{3.03}{2.52}[/latex]

Solve Proportions

1. [latex]\Large\frac{x}{56}\normalsize =\Large\frac{7}{8}[/latex]

   Answer: [latex]x=49[/latex]

2. [latex]\Large\frac{n}{91}\normalsize =\Large\frac{8}{13}[/latex]
3. [latex]\Large\frac{49}{63}\normalsize =\Large\frac{z}{9}[/latex]

   Answer: [latex]z=7[/latex]

4. [latex]\Large\frac{56}{72}\normalsize =\Large\frac{y}{9}[/latex]
5. [latex]\Large\frac{5}{a}\normalsize =\Large\frac{65}{117}[/latex]

   Answer: [latex]a=9[/latex]

6. [latex]\Large\frac{4}{b}\normalsize =\Large\frac{64}{144}[/latex]
7. [latex]\Large\frac{98}{154}\normalsize =\Large\frac{-7}{p}[/latex]

   Answer: [latex]p=−11[/latex]

8. [latex]\Large\frac{72}{156}\normalsize =\Large\frac{-6}{q}[/latex]
9. [latex]\Large\frac{a}{-8}\normalsize =\Large\frac{-42}{48}[/latex]

   Answer: [latex]a=7[/latex]

10. [latex]\Large\frac{b}{-7}\normalsize =\Large\frac{-30}{42}[/latex]
11. [latex]\Large\frac{2.6}{3.9}\normalsize =\Large\frac{c}{3}[/latex]

    Answer: [latex]c=2[/latex]

12. [latex]\Large\frac{2.7}{3.6}\normalsize =\Large\frac{d}{4}[/latex]
13. [latex]\Large\frac{2.7}{j}\normalsize =\Large\frac{0.9}{0.2}[/latex]

    Answer: [latex]j=0.6[/latex]

14. [latex]\Large\frac{2.8}{k}\normalsize =\Large\frac{2.1}{1.5}[/latex]
15. [latex]\Large\frac{\Large\frac{1}{2}}{1}\normalsize =\Large\frac{m}{8}[/latex]

    Answer: [latex]m=4[/latex]

16. [latex]\Large\frac{\Large\frac{1}{3}}{3}\normalsize =\Large\frac{9}{n}[/latex]

Solve Applications Using Proportions

1. Pediatricians prescribe [latex]5[/latex] milliliters (ml) of acetaminophen for every [latex]25[/latex] pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs [latex]45[/latex] pounds?

   Answer: 9 ml

2. Brianna, who weighs [latex]6[/latex] kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at [latex]15[/latex] milligrams (mg) for every [latex]1[/latex] kilogram (kg) of the child’s weight. How many milligrams will the doctor prescribe?
3. At the gym, Carol takes her pulse for [latex]10[/latex] sec and counts [latex]19[/latex] beats. How many beats per minute is this? Has Carol met her target heart rate of [latex]140[/latex] beats per minute?

   Answer: 114, no

4. Kevin wants to keep his heart rate at [latex]160[/latex] beats per minute while training. During his workout he counts [latex]27[/latex] beats in [latex]10[/latex] seconds. How many beats per minute is this? Has Kevin met his target heart rate?
5. A new energy drink advertises [latex]106[/latex] calories for [latex]8[/latex] ounces. How many calories are in [latex]12[/latex] ounces of the drink?

   Answer: 159 cal

6. One [latex]12[/latex] ounce can of soda has [latex]150[/latex] calories. If Josiah drinks the big [latex]32[/latex] ounce size from the local mini-mart, how many calories does he get?
7. Karen eats [latex]\Large\frac{1}{2}[/latex] cup of oatmeal that counts for [latex]2[/latex] points on her weight loss program. Her husband, Joe, can have [latex]3[/latex] points of oatmeal for breakfast. How much oatmeal can he have?

   Answer: [latex]\Large\frac{3}{4}\normalsize\text{cup}[/latex]

8. An oatmeal cookie recipe calls for [latex]\Large\frac{1}{2}[/latex] cup of butter to make [latex]4[/latex] dozen cookies. Hilda needs to make [latex]10[/latex] dozen cookies for the bake sale. How many cups of butter will she need?
9. Janice is traveling to Canada and will change [latex]{$250}[/latex] US dollars into Canadian dollars. At the current exchange rate, [latex]{$1}[/latex] US is equal to [latex]{$1.01}[/latex] Canadian. How many Canadian dollars will she get for her trip?

   Answer: $252.50

10. Todd is traveling to Mexico and needs to exchange [latex]{$450}[/latex] into Mexican pesos. If each dollar is worth [latex]12.29[/latex] pesos, how many pesos will he get for his trip?
11. Steve changed [latex]{$600}[/latex] into [latex]480[/latex] Euros. How many Euros did he receive per US dollar?

    Answer: 1.25

12. Martha changed [latex]{$350}[/latex] US into [latex]385[/latex] Australian dollars. How many Australian dollars did she receive per US dollar?
13. At the laundromat, Lucy changed [latex]{$12.00}[/latex] into quarters. How many quarters did she get?

    Answer: 48 quarters

14. When she arrived at a casino, Gerty changed [latex]{$20}[/latex] into nickels. How many nickels did she get?
15. Jesse’s car gets [latex]30[/latex] miles per gallon of gas. If Las Vegas is [latex]285[/latex] miles away, how many gallons of gas are needed to get there and then home? If gas is [latex]{$3.09}[/latex] per gallon, what is the total cost of the gas for the trip?

    Answer: 19, $58.71

16. Danny wants to drive to Phoenix to see his grandfather. Phoenix is [latex]370[/latex] miles from Danny’s home and his car gets [latex]18.5[/latex] miles per gallon. How many gallons of gas will Danny need to get to and from Phoenix? If gas is [latex]{$3.19}[/latex] per gallon, what is the total cost for the gas to drive to see his grandfather?
17. Hugh leaves early one morning to drive from his home in Chicago to go to Mount Rushmore, [latex]812[/latex] miles away. After [latex]3[/latex] hours, he has gone [latex]190[/latex] miles. At that rate, how long will the whole drive take?

    Answer: 12.8 hours

18. Kelly leaves her home in Seattle to drive to Spokane, a distance of [latex]280[/latex] miles. After [latex]2[/latex] hours, she has gone [latex]152[/latex] miles. At that rate, how long will the whole drive take?
19. Phil wants to fertilize his lawn. Each bag of fertilizer covers about [latex]4,000[/latex] square feet of lawn. Phil’s lawn is approximately [latex]13,500[/latex] square feet. How many bags of fertilizer will he have to buy?

    Answer: 4 bags

20. April wants to paint the exterior of her house. One gallon of paint covers about [latex]350[/latex] square feet, and the exterior of the house measures approximately [latex]2000[/latex] square feet. How many gallons of paint will she have to buy?

Write Percent Equations as Proportions

1. What number is [latex]\text{35%}[/latex] of [latex]250?[/latex]

   Answer: [latex]\Large\frac{n}{250}\normalsize =\Large\frac{35}{100}[/latex]

2. What number is [latex]\text{75%}[/latex] of [latex]920?[/latex]
3. What number is [latex]\text{110%}[/latex] of [latex]47?[/latex]

   Answer: [latex]\Large\frac{n}{47}\normalsize =\Large\frac{110}{100}[/latex]

4. What number is [latex]\text{150%}[/latex] of [latex]64?[/latex]
5. [latex]45[/latex] is [latex]\text{30%}[/latex] of what number?

   Answer: [latex]\Large\frac{45}{n}\normalsize =\Large\frac{30}{100}[/latex]

6. [latex]25[/latex] is [latex]\text{80%}[/latex] of what number?
7. [latex]90[/latex] is [latex]\text{150%}[/latex] of what number?

   Answer: [latex]\Large\frac{90}{n}\normalsize =\Large\frac{150}{100}[/latex]

8. [latex]77[/latex] is [latex]\text{110%}[/latex] of what number?
9. What percent of [latex]85[/latex] is [latex]17?[/latex]

   Answer: [latex]\Large\frac{17}{85}\normalsize =\Large\frac{p}{100}[/latex]

10. What percent of [latex]92[/latex] is [latex]46?[/latex]
11. What percent of [latex]260[/latex] is [latex]340?[/latex]

    Answer: [latex]\Large\frac{340}{260}\normalsize =\Large\frac{p}{100}[/latex]

12. What percent of [latex]180[/latex] is [latex]220?[/latex]

Translate and Solve Percent Proportions

1. What number is [latex]\text{65%}[/latex] of [latex]180?[/latex]

   Answer: 117

2. What number is [latex]\text{55%}[/latex] of [latex]300?[/latex]

   Answer: 165

3. [latex]\text{18%}[/latex] of [latex]92[/latex] is what number?

   Answer: 16.56

4. [latex]\text{22%}[/latex] of [latex]74[/latex] is what number?
5. [latex]\text{175%}[/latex] of [latex]26[/latex] is what number?

   Answer: 45.5

6. [latex]\text{250%}[/latex] of [latex]61[/latex] is what number?
7. What is [latex]\text{300%}[/latex] of [latex]488?[/latex]

   Answer: 1464

8. What is [latex]\text{500%}[/latex] of [latex]315?[/latex]
9. [latex]\text{17%}[/latex] of what number is [latex]{$7.65}?[/latex]

   Answer: $45

10. [latex]\text{19%}[/latex] of what number is [latex]{$6.46}?[/latex]
11. [latex]{$13.53}[/latex] is [latex]\text{8.25%}[/latex] of what number?

    Answer: $164

12. [latex]{$18.12}[/latex] is [latex]\text{7.55%}[/latex] of what number?
13. What percent of [latex]56[/latex] is [latex]14?[/latex]

    Answer: 25%

14. What percent of [latex]80[/latex] is [latex]28?[/latex]
15. What percent of [latex]96[/latex] is [latex]12?[/latex]

    Answer: 12.5%

16. What percent of [latex]120[/latex] is [latex]27?[/latex]

Chapter Review Exercises

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