Writing Percents Using Words, Ratios, and Fractions

Use the Definition of Percents

In the following exercises, write each percent as a ratio.

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

   [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].
   Show Solution

   [latex]\Large\frac{32}{1000}[/latex]
4. The unemployment rate in Michigan in [latex]2014[/latex] was [latex]\text{7.3%}[/latex].

In the following exercises, write as ⓐ a ratio and ⓑ a percent.

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

   ⓐ [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.
   Show Solution

   ⓐ [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

In the following exercises, convert each percent to a fraction and simplify all fractions.

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

   [latex]\Large\frac{1}{25}[/latex]
2. [latex]\text{8%}[/latex]
3. [latex]\text{17%}[/latex]
   Show Answer

   [latex]\Large\frac{17}{100}[/latex]
4. [latex]\text{19%}[/latex]
5. [latex]\text{52%}[/latex]
   Show Answer

   [latex]\Large\frac{13}{25}[/latex]
6. [latex]\text{78%}[/latex]
7. [latex]\text{125%}[/latex]
   Show Answer

   [latex]\Large\frac{5}{4}[/latex]
8. [latex]\text{135%}[/latex]
9. [latex]\text{37.5%}[/latex]
   Show Answer

   [latex]\Large\frac{3}{8}[/latex]
10. [latex]\text{42.5%}[/latex]
11. [latex]\text{18.4%}[/latex]
    Show Answer

    [latex]\Large\frac{23}{125}[/latex]
12. [latex]\text{46.4%}[/latex]

In the following exercises, convert each percent to a decimal.

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

   0.05
2. [latex]\text{9%}[/latex]
3. [latex]\text{1%}[/latex]
   Show Solution

   0.01
4. [latex]\text{2%}[/latex]
5. [latex]\text{63%}[/latex]
   Show Solution

   0.63
6. [latex]\text{71%}[/latex]
7. [latex]\text{40%}[/latex]
   Show Solution

   0.4
8. [latex]\text{50%}[/latex]
9. [latex]\text{115%}[/latex]
   Show Solution

   1.15
10. [latex]\text{125%}[/latex]
11. [latex]\text{150%}[/latex]
    Show Solution

    1.5
12. [latex]\text{250%}[/latex]
13. [latex]\text{21.4%}[/latex]
    Show Solution

    0.214
14. [latex]\text{39.3%}[/latex]
15. [latex]\text{7.8%}[/latex]
    Show Solution

    0.078
16. [latex]\text{6.4%}[/latex]

In the following exercises, convert each percent to ⓐ a simplified fraction and ⓑ a decimal.

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

   ⓐ [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.
   Show Solution

   ⓐ [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].
   Show Solution

   ⓐ [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].
   Show Solution

   ⓐ [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

In the following exercises, convert each decimal to a percent.

1. [latex]0.01[/latex]
   Show Solution

   1%
2. [latex]0.03[/latex]
3. [latex]0.18[/latex]
   Show Solution

   18%
4. [latex]0.15[/latex]
5. [latex]1.35[/latex]
   Show Solution

   135%
6. [latex]1.56[/latex]
7. [latex]3[/latex]
   Show Solution

   300%
8. [latex]4[/latex]
9. [latex]0.009[/latex]
   Show Solution

   0.9%
10. [latex]0.008[/latex]
11. [latex]0.0875[/latex]
    Show Solution

    8.75%
12. [latex]0.0625[/latex]
13. [latex]1.5[/latex]
    Show Solution

    150%
14. [latex]2.2[/latex]
15. [latex]2.254[/latex]
    Show Solution

    225.4%
16. [latex]2.317[/latex]

In the following exercises, convert each fraction to a percent.

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

   25%
2. [latex]\Large\frac{1}{5}[/latex]
3. [latex]\Large\frac{3}{8}[/latex]
   Show Solution

   37.5%
4. [latex]\Large\frac{5}{8}[/latex]
5. [latex]\Large\frac{7}{4}[/latex]
   Show Solution

   175%
6. [latex]\Large\frac{9}{8}[/latex]
7. [latex]6\Large\frac{4}{5}[/latex]
   Show Solution

   680%
8. [latex]5\Large\frac{1}{4}[/latex]
9. [latex]\Large\frac{5}{12}[/latex]
   Show Solution

   41.7%
10. [latex]\Large\frac{11}{12}[/latex]
11. [latex]2\Large\frac{2}{3}[/latex]
    Show Solution

    [latex]266.\stackrel{-}{6}\text{%}[/latex]
12. [latex]1\Large\frac{2}{3}[/latex]
13. [latex]\Large\frac{3}{7}[/latex]
    Show Solution

    42.9%
14. [latex]\Large\frac{6}{7}[/latex]
15. [latex]\Large\frac{5}{9}[/latex]
    Show Solution

    55.6%
16. [latex]\Large\frac{4}{9}[/latex]

In the following exercises, convert each fraction to a percent.

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

   25%
2. [latex]\Large\frac{1}{5}[/latex] of dishwashers needed repair.

In the following exercises, convert each fraction to a percent.

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

   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.

In the following exercises, complete the table.

Solving General Applications of Percent

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

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

   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]
   Show Solution

   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?
   Show Solution

   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?
   Show Solution

   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?
   Show Solution

   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?
    Show Solution

    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]
    Show Solution

    $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]
    Show Solution

    $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]
    Show Solution

    30%
18. What percent of [latex]215[/latex] is [latex]86?[/latex]
19. What percent of [latex]1,500[/latex] is [latex]540?[/latex]
    Show Solution

    36%
20. What percent of [latex]1,800[/latex] is [latex]846?[/latex]
21. [latex]30[/latex] is what percent of [latex]20?[/latex]
    Show Solution

    150%
22. [latex]50[/latex] is what percent of [latex]40?[/latex]
23. [latex]840[/latex] is what percent of [latex]480?[/latex]
    Show Solution

    175%
24. [latex]790[/latex] is what percent of [latex]395?[/latex]

Solve Applications of Percents

In the following exercises, solve the 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?
   Show Solution

   $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?
   Show Solution

   $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?
   Show Solution

   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?
   Show Solution

   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?
   Show Solution

   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?
    Show Solution

    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

In the following exercises, find the percent increase or 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.
   Show Solution

   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.
   Show Solution

   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.)
   Show Solution

   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.
   Show Solution

   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.
   Show Solution

   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.)
    Show Solution

    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

In the following exercises, find ⓐ the sales tax and ⓑ the total cost.

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.
   Show Solution

   ⓐ $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.
   Show Solution

   ⓐ $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.
   Show Solution

   ⓐ $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.
   Show Solution

   ⓐ $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.

In the following exercises, find the sales tax rate.

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

   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].
   Show Solution

   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

In the following exercises, find the commission.

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?
   Show Solution

   $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?
   Show Solution

   $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]
   Show Solution

   $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]

In the following exercises, find the rate of commission.

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?
   Show Solution

   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?
   Show Solution

   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?
   Show Solution

   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

In the following exercises, find the sale price.

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

   $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].
   Show Solution

   $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.
   Show Solution

   $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.

In the following exercises, find ⓐ the amount of discount and ⓑ the sale price.

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

   ⓐ $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.
   Show Solution

   ⓐ $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].
   Show Solution

   ⓐ $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].

In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.)

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].
   Show Solution

   ⓐ $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]
   Show Solution

   ⓐ $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].
   Show Solution

   ⓐ $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

In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.

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].
   Show Solution

   ⓐ $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.
   Show Solution

   ⓐ $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.
   Show Solution

   ⓐ $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

In the following exercises, use the simple interest formula to fill in the missing information.

In the following exercises, solve the problem using the simple interest formula.

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

   $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].
   Show Solution

   $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].
   Show Solution

   $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].
   Show Solution

   $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]
   Show Solution

   $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].
    Show Solution

    $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.
    Show Solution

    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.
    Show Solution

    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

In the following exercises, solve the problem using the simple interest formula.

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?
   Show Solution

   $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?
   Show Solution

   $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?
   Show Solution

   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?
   Show Solution

   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?
   Show Solution

   $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?
    Show Solution

    $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?
    Show Solution

    $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?
    Show Solution

    $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

In the following exercises, write each sentence as a proportion.

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

   [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].
   Show Solution

   [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.
   Show Solution

   [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.
   Show Solution

   [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.
   Show Solution

   [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.
    Show Solution

    [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.

In the following exercises, determine whether each equation is a proportion.

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

   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]
   Show Solution

   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]
   Show Solution

   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]
   Show Solution

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

Solve Proportions

In the following exercises, solve each proportion.

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

   [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]
   Show Solution

   [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]
   Show Solution

   [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]
   Show Solution

   [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]
   Show Solution

   [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]
    Show Solution

    [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]
    Show Solution

    [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]
    Show Solution

    [latex]m=4[/latex]
16. [latex]\Large\frac{\Large\frac{1}{3}}{3}\normalsize =\Large\frac{9}{n}[/latex]

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

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?
   Show Solution

   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?
   Show Solution

   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?
   Show Solution

   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?
   Show Solution

   [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?
   Show Solution

   $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?
    Show Solution

    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?
    Show Solution

    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?
    Show Solution

    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?
    Show Solution

    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?
    Show Solution

    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

In the following exercises, translate to a proportion.

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

   [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]
   Show Solution

   [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?
   Show Solution

   [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?
   Show Solution

   [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]
   Show Solution

   [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]
    Show Solution

    [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

In the following exercises, translate and solve using proportions.

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

   117
2. What number is [latex]\text{55%}[/latex] of [latex]300?[/latex]
   Show Solution

   165
3. [latex]\text{18%}[/latex] of [latex]92[/latex] is what number?
   Show Solution

   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?
   Show Solution

   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]
   Show Solution

   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]
   Show Solution

   $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?
    Show Solution

    $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]
    Show Solution

    25%
14. What percent of [latex]80[/latex] is [latex]28?[/latex]
15. What percent of [latex]96[/latex] is [latex]12?[/latex]
    Show Solution

    12.5%
16. What percent of [latex]120[/latex] is [latex]27?[/latex]

Chapter Review Exercises