# Problem Set: Percents

**Writing Percents Using Words, Ratios, and Fractions**

**Use the Definition of Percents**

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

- 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]

- In [latex]2015[/latex], among the unemployed, [latex]\text{29%}[/latex] were long-term unemployed.
- 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]

- 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.**

- [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]

- [latex]80[/latex] out of [latex]100[/latex] firefighters and law enforcement officers were educated at a community college.
- [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]

- [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.**

- [latex]\text{4%}[/latex]
Answer: [latex]\Large\frac{1}{25}[/latex]

- [latex]\text{8%}[/latex]
- [latex]\text{17%}[/latex]
Answer: [latex]\Large\frac{17}{100}[/latex]

- [latex]\text{19%}[/latex]
- [latex]\text{52%}[/latex]
Answer: [latex]\Large\frac{13}{25}[/latex]

- [latex]\text{78%}[/latex]
- [latex]\text{125%}[/latex]
Answer: [latex]\Large\frac{5}{4}[/latex]

- [latex]\text{135%}[/latex]
- [latex]\text{37.5%}[/latex]
Answer: [latex]\Large\frac{3}{8}[/latex]

- [latex]\text{42.5%}[/latex]
- [latex]\text{18.4%}[/latex]
Answer: [latex]\Large\frac{23}{125}[/latex]

- [latex]\text{46.4%}[/latex]

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

- [latex]\text{5%}[/latex]
Answer: 0.05

- [latex]\text{9%}[/latex]
- [latex]\text{1%}[/latex]
Answer: 0.01

- [latex]\text{2%}[/latex]
- [latex]\text{63%}[/latex]
Answer: 0.63

- [latex]\text{71%}[/latex]
- [latex]\text{40%}[/latex]
Answer: 0.4

- [latex]\text{50%}[/latex]
- [latex]\text{115%}[/latex]
Answer: 1.15

- [latex]\text{125%}[/latex]
- [latex]\text{150%}[/latex]
Answer: 1.5

- [latex]\text{250%}[/latex]
- [latex]\text{21.4%}[/latex]
Answer: 0.214

- [latex]\text{39.3%}[/latex]
- [latex]\text{7.8%}[/latex]
Answer: 0.078

- [latex]\text{6.4%}[/latex]

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

- 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]

- In [latex]2000,\text{4.2%}[/latex] of the United States population was of Asian descent. (
*Source:*www.census.gov) - 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]

- 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.
- 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]

- 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].
- 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]

- 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.**

- [latex]0.01[/latex]
Answer: 1%

- [latex]0.03[/latex]
- [latex]0.18[/latex]
Answer: 18%

- [latex]0.15[/latex]
- [latex]1.35[/latex]
Answer: 135%

- [latex]1.56[/latex]
- [latex]3[/latex]
Answer: 300%

- [latex]4[/latex]
- [latex]0.009[/latex]
Answer: 0.9%

- [latex]0.008[/latex]
- [latex]0.0875[/latex]
Answer: 8.75%

- [latex]0.0625[/latex]
- [latex]1.5[/latex]
Answer: 150%

- [latex]2.2[/latex]
- [latex]2.254[/latex]
Answer: 225.4%

- [latex]2.317[/latex]

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

- [latex]\Large\frac{1}{4}[/latex]
Answer: 25%

- [latex]\Large\frac{1}{5}[/latex]
- [latex]\Large\frac{3}{8}[/latex]
Answer: 37.5%

- [latex]\Large\frac{5}{8}[/latex]
- [latex]\Large\frac{7}{4}[/latex]
Answer: 175%

- [latex]\Large\frac{9}{8}[/latex]
- [latex]6\Large\frac{4}{5}[/latex]
Answer: 680%

- [latex]5\Large\frac{1}{4}[/latex]
- [latex]\Large\frac{5}{12}[/latex]
Answer: 41.7%

- [latex]\Large\frac{11}{12}[/latex]
- [latex]2\Large\frac{2}{3}[/latex]
Answer: [latex]266.\stackrel{-}{6}\text{%}[/latex]

- [latex]1\Large\frac{2}{3}[/latex]
- [latex]\Large\frac{3}{7}[/latex]
Answer: 42.9%

- [latex]\Large\frac{6}{7}[/latex]
- [latex]\Large\frac{5}{9}[/latex]
Answer: 55.6%

- [latex]\Large\frac{4}{9}[/latex]

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

- [latex]\Large\frac{1}{4}[/latex] of washing machines needed repair.
Answer: 25%

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

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

- According to the National Center for Health Statistics, in [latex]2012,\Large\frac{7}{20}[/latex] of American adults were obese.
Answer: 35%

- 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.**

Fraction | Decimal | Percent |
---|---|---|

[latex]\Large\frac{1}{2}[/latex] | ||

[latex]0.45[/latex] | ||

[latex]18%[/latex] | ||

[latex]\Large\frac{1}{3}[/latex] | ||

[latex]0.0008[/latex] | ||

[latex]2[/latex] |

Fraction | Decimal | Percent |
---|---|---|

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

[latex]0.65[/latex] | ||

[latex]22%[/latex] | ||

[latex]\Large\frac{2}{3}[/latex] | ||

[latex]0.0004[/latex] | ||

[latex]3[/latex] |

### 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 [latex]\text{9.05%}[/latex]. She knows this is a little less than [latex]\text{10%}[/latex].
ⓐ Convert [latex]\text{10%}[/latex] to a fraction.
ⓑ Use your answer from ⓐ to estimate the sales tax Felipa would pay on a [latex]{$95}[/latex] dress.
Answer: ⓐ [latex]\Large\frac{1}{10}[/latex] ⓑ [latex]\approx {$9.50}[/latex]

**Savings**

Ryan has [latex]\text{25%}[/latex] of each paycheck automatically deposited in his savings account.
ⓐ Write [latex]\text{25%}[/latex] as a fraction.
ⓑ Use your answer from ⓐ to find the amount that goes to savings from Ryan's [latex]{$2,400}[/latex] 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 |
---|---|

[latex]\text{A}[/latex] | [latex]\text{4/5}[/latex] |

[latex]\text{B}[/latex] | [latex]\text{3.5/4}[/latex] |

[latex]\text{C}[/latex] | [latex]\text{85%}[/latex] |

Answer: [latex]\Large\frac{17}{20}\normalsize ;0.85[/latex]

Write seller [latex]\text{B's}[/latex] rating as a percent and a decimal. Write seller [latex]\text{A's}[/latex] rating as a percent and a decimal.Answer: 80%; 0.8

Which seller should Amelio buy from and why?### Writing Exercises

- Convert [latex]\text{25%},\text{50%},\text{75%},\text{and}\text{100%}[/latex] to fractions. Do you notice a pattern? Explain what the pattern is.
Answer: [latex]\Large\frac{1}{4}\normalsize ,\Large\frac{1}{2}\normalsize ,\Large\frac{3}{4}\normalsize ,1[/latex].

- Convert [latex]\Large\frac{1}{10}\normalsize,\Large\frac{2}{10}\normalsize,\Large\frac{3}{10}\normalsize,\Large\frac{4}{10}\normalsize,\Large\frac{5}{10}\normalsize,\Large\frac{6}{10}\normalsize,\Large\frac{7}{10}\normalsize,\Large\frac{8}{10}[/latex], and [latex]\Large\frac{9}{10}[/latex] to percents. Do you notice a pattern? Explain what the pattern is.
- When the Szetos sold their home, the selling price was [latex]\text{500%}[/latex] of what they had paid for the house [latex]\text{30 years}[/latex] ago. Explain what [latex]\text{500%}[/latex] means in this context.
Answer: The Szetos sold their home for five times what they paid 30 years ago.

- According to cnn.com, cell phone use in [latex]2008[/latex] was [latex]\text{600%}[/latex] of what it had been in [latex]2001[/latex]. Explain what [latex]\text{600%}[/latex] means in this context.

## Solving General Applications of Percent

**Translate and Solve Basic Percent Equations**

**In the following exercises, translate and solve.**

- What number is [latex]\text{45%}[/latex] of [latex]120?[/latex]
Answer: 54

- What number is [latex]\text{65%}[/latex] of [latex]100?[/latex]
- What number is [latex]\text{24%}[/latex] of [latex]112?[/latex]
Answer: 26.88

- What number is [latex]\text{36%}[/latex] of [latex]124?[/latex]
- [latex]\text{250%}[/latex] of [latex]65[/latex] is what number?
Answer: 162.5

- [latex]\text{150%}[/latex] of [latex]90[/latex] is what number?
- [latex]\text{800%}[/latex] of [latex]2,250[/latex] is what number?
Answer: 18,000

- [latex]\text{600%}[/latex] of [latex]1,740[/latex] is what number?
- [latex]28[/latex] is [latex]\text{25%}[/latex] of what number?
Answer: 112

- [latex]36[/latex] is [latex]\text{25%}[/latex] of what number?
- [latex]81[/latex] is [latex]\text{75%}[/latex] of what number?
Answer: 108

- [latex]93[/latex] is [latex]\text{75%}[/latex] of what number?
- [latex]\text{8.2%}[/latex] of what number is [latex]{$2.87}?[/latex]
Answer: $35

- [latex]\text{6.4%}[/latex] of what number is [latex]{$2.88}?[/latex]
- [latex]\text{11.5%}[/latex] of what number is [latex]{$108.10}?[/latex]
Answer: $940

- [latex]\text{12.3%}[/latex] of what number is [latex]{$92.25}?[/latex]
- What percent of [latex]260[/latex] is [latex]78?[/latex]
Answer: 30%

- What percent of [latex]215[/latex] is [latex]86?[/latex]
- What percent of [latex]1,500[/latex] is [latex]540?[/latex]
Answer: 36%

- What percent of [latex]1,800[/latex] is [latex]846?[/latex]
- [latex]30[/latex] is what percent of [latex]20?[/latex]
Answer: 150%

- [latex]50[/latex] is what percent of [latex]40?[/latex]
- [latex]840[/latex] is what percent of [latex]480?[/latex]
Answer: 175%

- [latex]790[/latex] is what percent of [latex]395?[/latex]

**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 [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

- 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?
- 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

- 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?
- 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

- 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?
- 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

- 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?
- 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%

- 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?
- 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%

- 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.**

- 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%

- Ayodele got a raise in her hourly pay, from [latex]{$24.50}[/latex] to [latex]{$25.48}[/latex]. Find the percent increase.
- 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%

- The price of a share of one stock rose from [latex]{$12.50}[/latex] to [latex]{$50}[/latex]. Find the percent increase.
- 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%

- 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.)
- 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%

- The price of a share of one stock fell from [latex]{$8.75}[/latex] to [latex]{$8.54}[/latex]. Find the percent decrease.
- 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%

- 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.)
- 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%

- 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.)

### Everyday math

**Tipping**

At the campus coffee cart, a medium coffee costs [latex]{$1.65}[/latex]. MaryAnne brings [latex]{$2.00}[/latex] with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?
Answer: 21.2%

**Late Fees**

Alison was late paying her credit card bill of [latex]{$249}[/latex]. She was charged a [latex]\text{5%}[/latex] late fee. What was the amount of the late fee?
### writing exercises

Without solving the problem [latex]"44[/latex] is [latex]\text{80%}[/latex] of what number", think about what the solution might be. Should it be a number that is greater than [latex]44[/latex] or less than [latex]44?[/latex] Explain your reasoning.Answer: The original number should be greater than 44 because 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 [latex]\text{20%}[/latex] of [latex]300?"[/latex] think about what the solution might be. Should it be a number that is greater than [latex]300[/latex] or less than [latex]300?[/latex] Explain your reasoning. After returning from vacation, Alex said he should have packed [latex]\text{50%}[/latex] fewer shorts and [latex]\text{200%}[/latex] more shirts. Explain what Alex meant.Answer: 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 [latex]\text{150%}[/latex] of their usual commuting time. Explain what this means.### Solving Sales Tax, Commission, and Discount Applications

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

- 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

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

- The cost of a tablet computer is [latex]{$350}[/latex]. The sales tax rate is [latex]\text{8.5%}[/latex] of the purchase price.
- 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

- The cost of a luggage set [latex]{$400}[/latex]. The sales tax rate is [latex]\text{5.75%}[/latex] of the purchase price.
- 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

- 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.**

- Shawna bought a mixer for [latex]{$300}[/latex]. The sales tax on the purchase was [latex]{$19.50}[/latex].
Answer: 6.5%

- Orphia bought a coffee table for [latex]{$400}[/latex]. The sales tax on the purchase was [latex]{$38}[/latex].
- Bopha bought a bedroom set for [latex]{$3,600}[/latex]. The sales tax on the purchase was [latex]{$246.60}[/latex].
Answer: 6.85%

- 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.**

- 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

- 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?
- 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

- 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?
- 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

- 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**.

- 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%

- 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?
- 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%

- 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?
- 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%

- 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.**

- 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

- 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

- 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

- 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.**

- 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

- Errol bought a skateboard helmet on sale at [latex]\text{40%}[/latex] off. The original price was [latex]{$49.95}[/latex].
- 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

- Colleen bought a suit that was discounted [latex]\text{25%}[/latex] from an original price of [latex]{$245}[/latex].
- 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

- 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.)**

- 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%

- Hiroshi bought a lawnmower at the sale price of [latex]{$240}[/latex]. The original price of the lawnmower is [latex]{$300}[/latex].
- 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%

- Bill found a book he wanted on sale for [latex]{$20.80}[/latex]. The original price of the book was [latex]{$32}[/latex].
- Nikki bought a patio set on sale for [latex]{$480}[/latex]. The original price was [latex]{$850}[/latex].
Answer: ⓐ $370 ⓑ 43.5%

- 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.**

- 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

- 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].
- 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

- 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.
- 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

- 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.

### Everyday math

**Coupons**

Yvonne can use two coupons for the same purchase at her favorite department store. One coupon gives her [latex]{$20}[/latex] off and the other gives her [latex]\text{25%}[/latex] off. She wants to buy a bedspread that sells for [latex]{$195}[/latex].
ⓐ Calculate the discount price if Yvonne uses the [latex]{$20}[/latex] coupon first and then takes [latex]\text{25%}[/latex] off.
ⓑ Calculate the discount price if Yvonne uses the [latex]\text{25%}[/latex] off coupon first and then uses the [latex]\text{20%}[/latex] coupon.
ⓒ In which order should Yvonne use the coupons?
Answer: ⓐ $131.25 ⓑ $126.25 ⓒ 25% off first, then $20 off

**Cash Back**

Jason can buy a bag of dog food for [latex]{$35}[/latex] at two different stores. One store offers [latex]\text{6%}[/latex] cash back on the purchase plus [latex]{$5}[/latex] off his next purchase. The other store offers [latex]\text{20%}[/latex] 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 [latex]\text{40%}[/latex] off. The original price of the jacket was [latex]{$150}[/latex]. While the sales clerk figured the price by calculating the amount of discount and then subtracting that amount from [latex]{$150}[/latex], Priam found the price faster by calculating [latex]\text{60%}[/latex] of [latex]{$150}[/latex]. ⓐ Explain why Priam was correct. ⓑ Will Priam's method work for any original price?Answer: ⓐ 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 [latex]\text{50%}[/latex] off. The original price of the scarf was [latex]{$32.90}[/latex]. Roxy claimed that the price she paid for the scarf was the same as the amount she saved. Was Roxy correct? Explain.## Solving Simple Interest Applications

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

Interest | Principal | Rate | Time (years) |
---|---|---|---|

[latex]{$1200}[/latex] | [latex]\text{3%}[/latex] | [latex]5[/latex] |

Answer: $180

Interest | Principal | Rate | Time (years) |
---|---|---|---|

[latex]{$1500}[/latex] | [latex]\text{2%}[/latex] | [latex]\text{4}[/latex] |

Interest | Principal | Rate | Time (years) |
---|---|---|---|

[latex]$4410[/latex] | [latex]\text{4.5%}[/latex] | [latex]\text{7}[/latex] |

Answer: $14,000

Interest | Principal | Rate | Time (years) |
---|---|---|---|

[latex]$2212[/latex] | [latex]\text{3.2%}[/latex] | [latex]\text{6}[/latex] |

Interest | Principal | Rate | Time (years) |
---|---|---|---|

[latex]$577.08[/latex] | [latex]{$4580}[/latex] | [latex]\text{2}[/latex] |

Answer: 6.3%

Interest | Principal | Rate | Time (years) |
---|---|---|---|

[latex]$528.12[/latex] | [latex]{$3260}[/latex] | [latex]\text{3}[/latex] |

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

- 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

- Find the simple interest earned after [latex]4[/latex] years on [latex]{$900}[/latex] at an interest rate of [latex]\text{6%.}[/latex]
- 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

- 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].
- 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

- 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].
- 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

- 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].
- 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

- 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]
- 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

- 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]
- Find the rate if a principal of [latex]{$5,400}[/latex] earned [latex]{$432}[/latex] interest in [latex]2[/latex] years.
Answer: 4%

- Find the rate if a principal of [latex]{$2,600}[/latex] earned [latex]{$468}[/latex] interest in [latex]6[/latex] years.
- 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%

- 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.**

- 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

- 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?
- 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

- 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?
- 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%

- 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?
- 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%

- 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?
- 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

- 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?
- 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

- 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?
- 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

- 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?
- 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

- 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?

### 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 [latex]{$8,000}[/latex] for [latex]5[/latex] 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 [latex]{$8,000}[/latex] for [latex]5[/latex] 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?### Solving Proportions and their Applications

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

- [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]

- [latex]7[/latex] is to [latex]9[/latex] as [latex]35[/latex] is to [latex]45[/latex].
- [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]

- [latex]15[/latex] is to [latex]8[/latex] as [latex]75[/latex] is to [latex]40[/latex].
- [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]

- [latex]4[/latex] wins in [latex]9[/latex] games is the same as [latex]36[/latex] wins in [latex]81[/latex] games.
- [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]

- [latex]6[/latex] campers to [latex]1[/latex] counselor is the same as [latex]48[/latex] campers to [latex]8[/latex] counselors.
- [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]

- [latex]{$3.92}[/latex] for [latex]8[/latex] ounces is the same as [latex]{$1.47}[/latex] for [latex]3[/latex] ounces.
- [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]

- [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.**

- [latex]\Large\frac{7}{15}\normalsize =\Large\frac{56}{120}[/latex]
Answer: yes

- [latex]\Large\frac{5}{12}\normalsize =\Large\frac{45}{108}[/latex]
- [latex]\Large\frac{11}{6}\normalsize =\Large\frac{21}{16}[/latex]
Answer: no

- [latex]\Large\frac{9}{4}\normalsize =\Large\frac{39}{34}[/latex]
- [latex]\Large\frac{12}{18}\normalsize =\Large\frac{4.99}{7.56}[/latex]
Answer: no

- [latex]\Large\frac{9}{16}\normalsize =\Large\frac{2.16}{3.89}[/latex]
- [latex]\Large\frac{13.5}{8.5}\normalsize =\Large\frac{31.05}{19.55}[/latex]
Answer: yes

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

**Solve Proportions**

**In the following exercises, solve each proportion.**

- [latex]\Large\frac{x}{56}\normalsize =\Large\frac{7}{8}[/latex]
Answer: [latex]x=49[/latex]

- [latex]\Large\frac{n}{91}\normalsize =\Large\frac{8}{13}[/latex]
- [latex]\Large\frac{49}{63}\normalsize =\Large\frac{z}{9}[/latex]
Answer: [latex]z=7[/latex]

- [latex]\Large\frac{56}{72}\normalsize =\Large\frac{y}{9}[/latex]
- [latex]\Large\frac{5}{a}\normalsize =\Large\frac{65}{117}[/latex]
Answer: [latex]a=9[/latex]

- [latex]\Large\frac{4}{b}\normalsize =\Large\frac{64}{144}[/latex]
- [latex]\Large\frac{98}{154}\normalsize =\Large\frac{-7}{p}[/latex]
Answer: [latex]p=−11[/latex]

- [latex]\Large\frac{72}{156}\normalsize =\Large\frac{-6}{q}[/latex]
- [latex]\Large\frac{a}{-8}\normalsize =\Large\frac{-42}{48}[/latex]
Answer: [latex]a=7[/latex]

- [latex]\Large\frac{b}{-7}\normalsize =\Large\frac{-30}{42}[/latex]
- [latex]\Large\frac{2.6}{3.9}\normalsize =\Large\frac{c}{3}[/latex]
Answer: [latex]c=2[/latex]

- [latex]\Large\frac{2.7}{3.6}\normalsize =\Large\frac{d}{4}[/latex]
- [latex]\Large\frac{2.7}{j}\normalsize =\Large\frac{0.9}{0.2}[/latex]
Answer: [latex]j=0.6[/latex]

- [latex]\Large\frac{2.8}{k}\normalsize =\Large\frac{2.1}{1.5}[/latex]
- [latex]\Large\frac{\Large\frac{1}{2}}{1}\normalsize =\Large\frac{m}{8}[/latex]
Answer: [latex]m=4[/latex]

- [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.**

- 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

- 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?
- 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

- 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?
- 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

- 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?
- 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]

- 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?
- 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

- 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?
- Steve changed [latex]{$600}[/latex] into [latex]480[/latex] Euros. How many Euros did he receive per US dollar?
Answer: 1.25

- Martha changed [latex]{$350}[/latex] US into [latex]385[/latex] Australian dollars. How many Australian dollars did she receive per US dollar?
- At the laundromat, Lucy changed [latex]{$12.00}[/latex] into quarters. How many quarters did she get?
Answer: 48 quarters

- When she arrived at a casino, Gerty changed [latex]{$20}[/latex] into nickels. How many nickels did she get?
- 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

- 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?
- 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

- 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?
- 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

- 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.**

- What number is [latex]\text{35%}[/latex] of [latex]250?[/latex]
Answer: [latex]\Large\frac{n}{250}\normalsize =\Large\frac{35}{100}[/latex]

- What number is [latex]\text{75%}[/latex] of [latex]920?[/latex]
- What number is [latex]\text{110%}[/latex] of [latex]47?[/latex]
Answer: [latex]\Large\frac{n}{47}\normalsize =\Large\frac{110}{100}[/latex]

- What number is [latex]\text{150%}[/latex] of [latex]64?[/latex]
- [latex]45[/latex] is [latex]\text{30%}[/latex] of what number?
Answer: [latex]\Large\frac{45}{n}\normalsize =\Large\frac{30}{100}[/latex]

- [latex]25[/latex] is [latex]\text{80%}[/latex] of what number?
- [latex]90[/latex] is [latex]\text{150%}[/latex] of what number?
Answer: [latex]\Large\frac{90}{n}\normalsize =\Large\frac{150}{100}[/latex]

- [latex]77[/latex] is [latex]\text{110%}[/latex] of what number?
- What percent of [latex]85[/latex] is [latex]17?[/latex]
Answer: [latex]\Large\frac{17}{85}\normalsize =\Large\frac{p}{100}[/latex]

- What percent of [latex]92[/latex] is [latex]46?[/latex]
- What percent of [latex]260[/latex] is [latex]340?[/latex]
Answer: [latex]\Large\frac{340}{260}\normalsize =\Large\frac{p}{100}[/latex]

- What percent of [latex]180[/latex] is [latex]220?[/latex]

**Translate and Solve Percent Proportions**

**In the following exercises, translate and solve using proportions.**

- What number is [latex]\text{65%}[/latex] of [latex]180?[/latex]
Answer: 117

- What number is [latex]\text{55%}[/latex] of [latex]300?[/latex]
Answer: 165

- [latex]\text{18%}[/latex] of [latex]92[/latex] is what number?
Answer: 16.56

- [latex]\text{22%}[/latex] of [latex]74[/latex] is what number?
- [latex]\text{175%}[/latex] of [latex]26[/latex] is what number?
Answer: 45.5

- [latex]\text{250%}[/latex] of [latex]61[/latex] is what number?
- What is [latex]\text{300%}[/latex] of [latex]488?[/latex]
Answer: 1464

- What is [latex]\text{500%}[/latex] of [latex]315?[/latex]
- [latex]\text{17%}[/latex] of what number is [latex]{$7.65}?[/latex]
Answer: $45

- [latex]\text{19%}[/latex] of what number is [latex]{$6.46}?[/latex]
- [latex]{$13.53}[/latex] is [latex]\text{8.25%}[/latex] of what number?
Answer: $164

- [latex]{$18.12}[/latex] is [latex]\text{7.55%}[/latex] of what number?
- What percent of [latex]56[/latex] is [latex]14?[/latex]
Answer: 25%

- What percent of [latex]80[/latex] is [latex]28?[/latex]
- What percent of [latex]96[/latex] is [latex]12?[/latex]
Answer: 12.5%

- What percent of [latex]120[/latex] is [latex]27?[/latex]

### 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 [latex]3[/latex] ounces of concentrate with [latex]5[/latex] ounces of water. If he puts [latex]12[/latex] ounces of concentrate in a bucket, how many ounces of water should he add? How many ounces of the solution will he have altogether?
Answer: 20, 32

**Mixing a concentrate**

Travis is going to wash his car. The directions on the bottle of car wash concentrate say to mix [latex]2[/latex] ounces of concentrate with [latex]15[/latex] ounces of water. If Travis puts [latex]6[/latex] ounces of concentrate in a bucket, how much water must he mix with the concentrate?
### writing exercises

To solve "what number is [latex]\text{45%}[/latex] of [latex]350\text{"}[/latex] 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 [latex]125[/latex] is [latex]25\text{"}[/latex] 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.### Chapter Review Exercises

### UNDERSTANDING PERCENTS

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

- [latex]\text{32%}[/latex] admission rate for the university
Answer: [latex]\Large\frac{32}{100}[/latex]

- [latex]\text{53.3%}[/latex] rate of college students with student loans

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

- [latex]13[/latex] out of [latex]100[/latex] architects are women.
Answer: [latex]\Large\frac{13}{100}\normalsize ,\text{13%}[/latex]

- [latex]9[/latex] out of every [latex]100[/latex] nurses are men.

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

- [latex]\text{48%}[/latex]
Answer: [latex]\Large\frac{12}{25}[/latex]

- [latex]\text{175%}[/latex]
- [latex]\text{64.1%}[/latex]
Answer: [latex]\Large\frac{641}{1000}[/latex]

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

- [latex]\text{6%}[/latex]
Answer: 0.06

- [latex]\text{23%}[/latex]
- [latex]\text{128%}[/latex]
Answer: 1.28

- 4.9%

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

- In [latex]2012,\text{13.5%}[/latex] of the United States population was age [latex]65[/latex] or over. (Source: www.census.gov)
Answer: ⓐ [latex]\Large\frac{27}{200}[/latex] ⓑ [latex]0.135[/latex]

- In [latex]2012,\text{6.5%}[/latex] of the United States population was under [latex]5[/latex] 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 [latex]\text{50%}[/latex].
Answer: ⓐ [latex]\Large\frac{1}{2}[/latex] ⓑ [latex]0.5[/latex]

- A couple plans to have three children. The probability they will all be girls is [latex]\text{12.5%}[/latex].

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

- [latex]0.04[/latex]
Answer: 4%

- [latex]0.15[/latex]
- [latex]2.82[/latex]
Answer: 282%

- [latex]3[/latex]
- [latex]0.003[/latex]
Answer: 0.3%

- [latex]1.395[/latex]

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

- [latex]\Large\frac{3}{4}[/latex]
Answer: 75%

- [latex]\Large\frac{11}{5}[/latex]
- [latex]3\Large\frac{5}{8}[/latex]
Answer: 362.5%

- [latex]\Large\frac{2}{9}[/latex]
- According to the Centers for Disease Control, [latex]\Large\frac{2}{5}[/latex] of adults do not take a vitamin or supplement.
Answer: 40%

- According to the Centers for Disease Control, among adults who do take a vitamin or supplement, [latex]\Large\frac{3}{4}[/latex] take a multivitamin.

**In the following exercises, translate and solve.**

- What number is [latex]\text{46%}[/latex] of [latex]350?[/latex]
Answer: 161

- [latex]\text{120%}[/latex] of [latex]55[/latex] is what number?
- [latex]84[/latex] is [latex]\text{35%}[/latex] of what number?
Answer: 240

- [latex]15[/latex] is [latex]\text{8%}[/latex] of what number?
- [latex]\text{200%}[/latex] of what number is [latex]50?[/latex]
Answer: 25

- [latex]\text{7.9%}[/latex] of what number is [latex]{$4.74}?[/latex]
- What percent of [latex]120[/latex] is [latex]81.6?[/latex]
Answer: 68%

- What percent of [latex]340[/latex] is [latex]595?[/latex]

### sOLVE GENERAL APPLICATIONS OF PERCENTS

**In the following exercises, solve.**

- When Aurelio and his family ate dinner at a restaurant, the bill was [latex]{$83.50}[/latex]. Aurelio wants to leave [latex]\text{20%}[/latex] of the total bill as a tip. How much should the tip be?
Answer: $16.70

- One granola bar has [latex]2[/latex] grams of fiber, which is [latex]\text{8%}[/latex] 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 [latex]190[/latex] calories, and [latex]54[/latex] calories are from fat. What percent of the total calories is from fat?
Answer: 28.4%

- Elsa gets paid [latex]{$4,600}[/latex] per month. Her car payment is [latex]{$253}[/latex]. 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 [latex]{$19.00}[/latex] to [latex]{$19.76}[/latex]. Find the percent increase.
Answer: 4%

- Last year Bernard bought a new car for [latex]{$30,000}[/latex]. This year the car is worth [latex]{$24,000}[/latex]. 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 [latex]{$750}[/latex]. The sales tax rate is [latex]\text{6%}[/latex] of the purchase price.
Answer: ⓐ $45 ⓑ $795

- The cost of a water heater is [latex]{$577}[/latex]. The sales tax rate is [latex]\text{8.75%}[/latex] of the purchase price.

**In the following exercises, find the sales tax rate.**

- Andy bought a piano for [latex]{$4,600}[/latex]. The sales tax on the purchase was [latex]{$333.50}[/latex].
Answer: 7.25%

- Nahomi bought a purse for [latex]{$200}[/latex]. The sales tax on the purchase was [latex]{$16.75}[/latex].

**In the following exercises, find the commission.**

- Ginny is a realtor. She receives [latex]\text{3%}[/latex] commission when she sells a house. How much commission will she receive for selling a house for [latex]{$380,000}?[/latex]
Answer: $11,400

- Jackson receives [latex]\text{16.5%}[/latex] commission when he sells a dinette set. How much commission will he receive for selling a dinette set for [latex]{$895}?[/latex]

**In the following exercises, find the rate of commission.**

- Ruben received [latex]{$675}[/latex] commission when he sold a [latex]{$4,500}[/latex] painting at the art gallery where he works. What was the rate of commission?
Answer: 15%

- Tori received [latex]{$80.75}[/latex] for selling a [latex]{$950}[/latex] 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 [latex]{$30}[/latex] off. The original price of the shoes was [latex]{$75}[/latex].
Answer: $45

- Takwanna saw a cookware set she liked on sale for [latex]{$145}[/latex] off. The original price of the cookware was [latex]{$312}[/latex].

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

- Nga bought a microwave for her office. The microwave was discounted [latex]\text{30%}[/latex] from an original price of [latex]{$84.90}[/latex].
Answer: ⓐ $25.47 ⓑ $59.43

- Jarrett bought a tie that was discounted [latex]\text{65%}[/latex] from an original price of [latex]{$45}[/latex].

**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 [latex]{$37}[/latex]. The original price of the bedspread was [latex]{$50}[/latex].
Answer: ⓐ $13 ⓑ 26%

- Tyler bought a phone on sale for [latex]{$49.99}[/latex]. The original price of the phone was [latex]{$79.99}[/latex].

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

- Manny paid [latex]{$0.80}[/latex] a pound for apples. He added [latex]\text{60%}[/latex] mark-up before selling them at his produce stand. What price did he charge for the apples?
Answer: ⓐ $0.48 ⓑ $1.28

- It cost Noelle [latex]{$17.40}[/latex] for the materials she used to make a purse. She added a [latex]\text{325%}[/latex] 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 [latex]4[/latex] years on [latex]{$2,250}[/latex] invested at an interest rate of [latex]\text{5%}[/latex].
Answer: $450

- Find the simple interest earned after [latex]7[/latex] years on [latex]{$12,000}[/latex] invested at an interest rate of [latex]\text{8.5%}[/latex].
- Find the principal invested if [latex]{$660}[/latex] interest was earned in [latex]5[/latex] years at an interest rate of [latex]\text{3%}[/latex].
Answer: $4400

- Find the interest rate if [latex]{$2,898}[/latex] interest was earned from a principal of [latex]{$23,000}[/latex] invested for [latex]3[/latex] years.
- Kazuo deposited [latex]{$10,000}[/latex] in a bank account with interest rate [latex]\text{4.5%}[/latex]. How much interest was earned in [latex]2[/latex] years?
Answer: $900

- Brent invested [latex]{$23,000}[/latex] in a friend’s business. In [latex]5[/latex] years the friend paid him the [latex]{$23,000}[/latex] plus [latex]{$9,200}[/latex] interest. What was the rate of interest?
- Fresia lent her son [latex]{$5,000}[/latex] for college expenses. Three years later he repaid her the [latex]{$5,000}[/latex] plus [latex]{$375}[/latex] interest. What was the rate of interest?
Answer: 2.5%

- In [latex]6[/latex] years, a bond that paid [latex]\text{5.5%}[/latex] earned [latex]{$594}[/latex] interest. What was the principal of the bond?

### Solve Proportions and their Applications

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

- [latex]3[/latex] is to [latex]8[/latex] as [latex]12[/latex] is to [latex]32[/latex].
Answer: [latex]\Large\frac{3}{8}\normalsize =\Large\frac{12}{32}[/latex]

- [latex]95[/latex] miles to [latex]3[/latex] gallons is the same as [latex]475[/latex] miles to [latex]15[/latex] gallons.
- [latex]1[/latex] teacher to [latex]18[/latex] students is the same as [latex]23[/latex] teachers to [latex]414[/latex] students.
Answer: [latex]\Large\frac{1}{18}\normalsize =\Large\frac{23}{414}[/latex]

- [latex]{$7.35}[/latex] for [latex]15[/latex] ounces is the same as [latex]{$2.94}[/latex] for [latex]6[/latex] ounces.

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

- [latex]\Large\frac{5}{13}\normalsize =\Large\frac{30}{78}[/latex]
Answer: yes

- [latex]\Large\frac{16}{7}\normalsize =\Large\frac{48}{23}[/latex]
- [latex]\Large\frac{12}{18}\normalsize =\Large\frac{6.99}{10.99}[/latex]
Answer: no

- [latex]\Large\frac{11.6}{9.2}\normalsize =\Large\frac{37.12}{29.44}[/latex]

**In the following exercises, solve each proportion.**

- [latex]\Large\frac{x}{36}\normalsize =\Large\frac{5}{9}[/latex]
Answer: [latex]x=20[/latex]

- [latex]\Large\frac{7}{a}\normalsize =\Large\frac{-6}{84}[/latex]
- [latex]\Large\frac{1.2}{1.8}\normalsize =\Large\frac{d}{6}[/latex]
Answer: [latex]d=4[/latex]

- [latex]\Large\frac{\Large\frac{1}{2}}{2}\normalsize =\Large\frac{m}{20}[/latex]

**In the following exercises, solve the proportion problem.**

- The children’s dosage of acetaminophen is [latex]5[/latex] milliliters (ml) for every [latex]25[/latex] pounds of a child’s weight. How many milliliters of acetaminophen will be prescribed for a [latex]60[/latex] pound child?
Answer: 12

- After a workout, Dennis takes his pulse for [latex]10[/latex] sec and counts [latex]21[/latex] beats. How many beats per minute is this?
- An [latex]8[/latex] ounce serving of ice cream has [latex]272[/latex] calories. If Lavonne eats [latex]10[/latex] ounces of ice cream, how many calories does she get?
Answer: 340

- Alma is going to Europe and wants to exchange [latex]{$1,200}[/latex] into Euros. If each dollar is [latex]0.75[/latex] Euros, how many Euros will Alma get?
- Zack wants to drive from Omaha to Denver, a distance of [latex]494[/latex] miles. If his car gets [latex]38[/latex] miles to the gallon, how many gallons of gas will Zack need to get to Denver?
Answer: 13 gallons

- Teresa is planning a party for [latex]100[/latex] people. Each gallon of punch will serve [latex]18[/latex] people. How many gallons of punch will she need?

**In the following exercises, translate to a proportion.**

- What number is [latex]\text{62%}[/latex] of [latex]395?[/latex]
Answer: [latex]\Large\frac{n}{395}\normalsize =\Large\frac{62}{100}[/latex]

- [latex]42[/latex] is [latex]\text{70%}[/latex] of what number?
- What percent of [latex]1,000[/latex] is [latex]15?[/latex]
Answer: [latex]\Large\frac{15}{1000}\normalsize =\Large\frac{p}{100}[/latex]

- What percent of [latex]140[/latex] is [latex]210?[/latex]

**In the following exercises, translate and solve using proportions.**

- What number is [latex]\text{85%}[/latex] of [latex]900?[/latex]
Answer: 765

- [latex]\text{6%}[/latex] of what number is [latex]{$24}?[/latex]
- [latex]{$3.51}[/latex] is [latex]\text{4.5%}[/latex] of what number?
Answer: $78

- What percent of [latex]3,100[/latex] is [latex]930?[/latex]

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

- [latex]\text{24%}[/latex]
Answer: [latex]0.24,\Large\frac{6}{25}[/latex]

- [latex]\text{5%}[/latex]
- [latex]\text{350%}[/latex]
Answer: [latex]3.5,3\Large\frac{1}{2}[/latex]

In the following exercises, convert each fraction to a percent. (Round to [latex]3[/latex] decimal places if needed.) - [latex]\Large\frac{7}{8}[/latex]
- [latex]\Large\frac{1}{3}[/latex]
Answer: 33.333%

- [latex]\Large\frac{11}{12}[/latex]

**In the following exercises, solve the percent problem.**

- [latex]65[/latex] is what percent of [latex]260?[/latex]
Answer: 25%

- What number is [latex]\text{27%}[/latex] of [latex]3,000?[/latex]
- [latex]\text{150%}[/latex] of what number is [latex]60?[/latex]
Answer: 40

- Yuki’s monthly paycheck is [latex]{$3,825}[/latex]. She pays [latex]{$918}[/latex] for rent. What percent of her paycheck goes to rent?
- The total number of vehicles on one freeway dropped from [latex]{84,000}[/latex] to [latex]{74,000}[/latex]. Find the percent decrease (round to the nearest tenth of a percent).
Answer: 11.9%

- Kyle bought a bicycle in Denver where the sales tax was [latex]\text{7.72%}[/latex] of the purchase price. The purchase price of the bicycle was [latex]{$600}[/latex]. What was the total cost?
- Mara received [latex]{$31.80}[/latex] commission when she sold a [latex]{$795}[/latex] suit. What was her rate of commission?
Answer: 4%

Answer: $50

Find the simple interest earned after [latex]5[/latex] years on [latex]{$3000}[/latex] invested at an interest rate of [latex]\text{4.2%}[/latex]. Brenda borrowed [latex]{$400}[/latex] from her brother. Two years later, she repaid the [latex]{$400}[/latex] plus [latex]{$50}[/latex] interest. What was the rate of interest?Answer: 6.2%

Write as a proportion: [latex]4[/latex] gallons to [latex]144[/latex] miles is the same as [latex]10[/latex] gallons to [latex]360[/latex] miles. Solve for a: [latex]\Large\frac{12}{a}\normalsize =\Large\frac{-15}{65}[/latex]Answer: -52

Vin read [latex]10[/latex] pages of a book in [latex]12[/latex] minutes. At that rate, how long will it take him to read [latex]35[/latex] pages?## Contribute!

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