Content check — Prealgebra, Chapter 6: Percents

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 6: Percents

343 problems · 0 figures

Be Prepared 6.1 §6.1 source ↗

Translate “the ratio of

33

5”

into an algebraic expression.
If you missed this problem, review Table 2.7.

Table 2.7 in the book ↗

Operation	Phrase	Expression
Addition	$a$ plus $b$ the sum of $a$ and $b$ $a$ increased by $b$ $b$ more than $a$ the total of $a$ and $b$ $b$ added to $a$	$a + b$
Subtraction	$a$ minus $b$ the difference of $a$ and $b$ $b$ subtracted from $a$ $a$ decreased by $b$ $b$ less than $a$	$a - b$
Multiplication	$a$ times $b$ the product of $a$ and $b$	$a \cdot b$ , $a b$ , $a (b)$ , $(a) (b)$
Division	$a$ divided by $b$ the quotient of $a$ and $b$ the ratio of $a$ and $b$ $b$ divided into $a$	$a \div b$ , $a / b$ , $\frac{a}{b}$ , $b a$

Answer

\frac{33}{5}

Be Prepared 6.2 §6.1 source ↗

Write

\frac{3}{5}

as a decimal.
If you missed this problem, review Example 5.28.

Example 5.28 in the book ↗

Answer

0.6

Be Prepared 6.3 §6.1 source ↗

Write

0.62

as a fraction.
If you missed this problem, review Example 5.4.

Example 5.4 in the book ↗

Answer

\frac{31}{50}

Try It 6.1 §6.1 source ↗

Write the percent as a ratio.

According to a survey, $89%$ of college students have a smartphone.

Answer

\frac{89}{100}

Try It 6.2 §6.1 source ↗

Write the percent as a ratio.

A study found that $72%$ of U.S. teens send text messages regularly.

Answer

\frac{72}{100}

Try It 6.3 §6.1 source ↗

Write as a ratio and then as a percent: The American Association of Community Colleges reported that

62

out of

100

full-time community college students balance their studies with full-time or part time employment.

Answer

\frac{62}{100}, 62%

Try It 6.4 §6.1 source ↗

Write as a ratio and then as a percent: In response to a student survey,

41

out of

100

Santa Ana College students expressed a goal of earning an Associate's degree or transferring to a four-year college.

Answer

\frac{41}{100}, 41%

Try It 6.5 §6.1 source ↗

Convert each percent to a fraction:

ⓐ $48%$

ⓑ $110%$

Answer

ⓐ $\frac{12}{25}$

ⓑ $\frac{11}{10}$

Try It 6.6 §6.1 source ↗

Convert each percent to a fraction:

ⓐ $64%$

ⓑ $150%$

Answer

ⓐ $\frac{16}{25}$

ⓑ $\frac{3}{2}$

Try It 6.7 §6.1 source ↗

Convert each percent to a fraction:

ⓐ $64.4%$

ⓑ $66 \frac{2}{3} %$

Answer

ⓐ $\frac{161}{250}$

ⓑ $\frac{2}{3}$

Try It 6.8 §6.1 source ↗

Convert each percent to a fraction:

ⓐ $42.5%$

ⓑ $8 \frac{3}{4} %$

Answer

ⓐ $\frac{17}{40}$

ⓑ $\frac{7}{80}$

Try It 6.9 §6.1 source ↗

Convert each percent to a decimal:

ⓐ $9%$

ⓑ $87%$

Answer

ⓐ 0.09

ⓑ 0.87

Try It 6.10 §6.1 source ↗

Convert each percent to a decimal:

ⓐ $3%$

ⓑ $91%$

Answer

ⓐ 0.03

ⓑ 0.91

Try It 6.11 §6.1 source ↗

Convert each percent to a decimal:

ⓐ $115%$

ⓑ $23.5%$

Answer

ⓐ 1.15

ⓑ 0.235

Try It 6.12 §6.1 source ↗

Convert each percent to a decimal:

ⓐ $123%$

ⓑ $16.8%$

Answer

ⓐ 1.23

ⓑ 0.168

Try It 6.13 §6.1 source ↗

Convert the percent to: ⓐ a fraction and ⓑ a decimal

Twitter's share of web traffic jumped $24%$ when one celebrity tweeted live on air.

Answer

ⓐ $\frac{6}{25}$

ⓑ $0.24$

Try It 6.14 §6.1 source ↗

Convert the percent to: ⓐ a fraction and ⓑ a decimal

The U.S. Census estimated that in $2013, 44%$ of the population of Boston age $25$ or older have a bachelor's or higher degrees.

Answer

ⓐ $\frac{11}{25}$

ⓑ $0.44$

Try It 6.15 §6.1 source ↗

Convert the percent to: ⓐ a fraction, and ⓑ a decimal

The probability that it will rain Monday is $30% .$

Answer

ⓐ $\frac{3}{10}$

ⓑ $0.3$

Try It 6.16 §6.1 source ↗

Convert the percent to: ⓐ a fraction, and ⓑ a decimal

The probability of getting heads three times when tossing a coin three times is $12.5% .$

Answer

ⓐ $\frac{1}{8}$

ⓑ $0.125$

Try It 6.17 §6.1 source ↗

Convert each decimal to a percent: ⓐ

0.01

ⓑ

0.17 .

Answer

ⓐ 1%

ⓑ 17%

Try It 6.18 §6.1 source ↗

Convert each decimal to a percent: ⓐ

0.04

ⓑ

0.41

Answer

ⓐ 4%

ⓑ 41%

Try It 6.19 §6.1 source ↗

Convert each decimal to a percent: ⓐ

1.75

ⓑ

0.0825

Answer

ⓐ 175%

ⓑ 8.25%

Try It 6.20 §6.1 source ↗

Convert each decimal to a percent: ⓐ

2.25

ⓑ

0.0925

Answer

ⓐ 225%

ⓑ 9.25%

Try It 6.21 §6.1 source ↗

Convert each fraction or mixed number to a percent: ⓐ

\frac{5}{8}

ⓑ

\frac{11}{4}

ⓒ

3 \frac{2}{5}

Answer

ⓐ 62.5%

ⓑ 275%

Try It 6.22 §6.1 source ↗

Convert each fraction or mixed number to a percent: ⓐ

\frac{7}{8}

ⓑ

\frac{9}{4}

ⓒ

1 \frac{3}{5}

Answer

ⓐ 87.5%

ⓑ 225%

Try It 6.23 §6.1 source ↗

Convert the fraction to a percent:

\frac{3}{7}

Answer

42.9%

Try It 6.24 §6.1 source ↗

Convert the fraction to a percent:

\frac{4}{7}

Answer

57.1%

Try It 6.25 §6.1 source ↗

Convert the fraction to a percent:

According to the U.S. Census Bureau, about $\frac{1}{9}$ of United States housing units have just $1$ bedroom.

Answer

11. \bar{1} %, or 11 \frac{1}{9} %

Try It 6.26 §6.1 source ↗

Convert the fraction to a percent:

According to the U.S. Census Bureau, about $\frac{1}{6}$ of Colorado residents speak a language other than English at home.

Answer

16 . \bar{6} %, or 16 \frac{2}{3} %

6.1-1 §6.1 source ↗

Use the Definition of Percents

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

In $2014,$ the unemployment rate for those with only a high school degree was $6.0% .$

Answer

\frac{6}{100}

6.1-3 §6.1 source ↗

Use the Definition of Percents

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

The unemployment rate for those with Bachelor's degrees was $3.2%$ in $2014 .$

Answer

\frac{32}{1000}

6.1-5 §6.1 source ↗

In the following exercises, write as

$57$ out of $100$ nursing candidates received their degree at a community college.

Answer

ⓐ $\frac{57}{100}$

ⓑ $57%$

6.1-7 §6.1 source ↗

In the following exercises, write as

$42$ out of $100$ first-time freshmen students attend a community college.

Answer

ⓐ $\frac{42}{100}$

ⓑ $42%$

6.1-9 §6.1 source ↗

Convert Percents to Fractions and Decimals

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

$4%$

Answer

\frac{1}{25}

6.1-11 §6.1 source ↗

Convert Percents to Fractions and Decimals

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

$17%$

Answer

\frac{17}{100}

6.1-13 §6.1 source ↗

Convert Percents to Fractions and Decimals

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

$52%$

Answer

\frac{13}{25}

6.1-15 §6.1 source ↗

Convert Percents to Fractions and Decimals

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

$125%$

Answer

\frac{5}{4}

6.1-17 §6.1 source ↗

Convert Percents to Fractions and Decimals

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

$37.5%$

Answer

\frac{3}{8}

6.1-19 §6.1 source ↗

Convert Percents to Fractions and Decimals

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

$18.4%$

Answer

\frac{23}{125}

6.1-21 §6.1 source ↗

Convert Percents to Fractions and Decimals

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

$9 \frac{1}{2} %$

Answer

\frac{19}{200}

6.1-23 §6.1 source ↗

Convert Percents to Fractions and Decimals

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

$5 \frac{1}{3} %$

Answer

\frac{4}{75}

6.1-25 §6.1 source ↗

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

$5%$

Answer

0.05

6.1-27 §6.1 source ↗

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

$1%$

Answer

0.01

6.1-29 §6.1 source ↗

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

$63%$

Answer

0.63

6.1-31 §6.1 source ↗

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

$40%$

Answer

0.4

6.1-33 §6.1 source ↗

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

$115%$

Answer

1.15

6.1-35 §6.1 source ↗

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

$150%$

Answer

1.5

6.1-37 §6.1 source ↗

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

$21.4%$

Answer

0.214

6.1-39 §6.1 source ↗

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

$7.8%$

Answer

0.078

6.1-41 §6.1 source ↗

In the following exercises, convert each percent to

In $2010, 1.5%$ of home sales had owner financing. (Source: Bloomberg Businessweek, 5/23–29/2011)

Answer

ⓐ $\frac{3}{200}$

ⓑ $0.015$

6.1-43 §6.1 source ↗

In the following exercises, convert each percent to

According to government data, in $2013$ the number of cell phones in India was $70.23%$ of the population.

Answer

ⓐ $\frac{7023}{10,000}$

ⓑ $0.7023$

6.1-45 §6.1 source ↗

In the following exercises, convert each percent to

A couple plans to have two children. The probability they will have two girls is $25% .$

Answer

ⓐ $\frac{1}{4}$

ⓑ $0.25$

6.1-47 §6.1 source ↗

In the following exercises, convert each percent to

According to the local weather report, the probability of thunderstorms in New York City on July $15$ is $60% .$

Answer

ⓐ $\frac{3}{5}$

ⓑ $0.6$

6.1-49 §6.1 source ↗

Convert Decimals and Fractions to Percents

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

$0.01$

Answer

6.1-51 §6.1 source ↗

Convert Decimals and Fractions to Percents

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

$0.18$

Answer

18%

6.1-53 §6.1 source ↗

Convert Decimals and Fractions to Percents

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

$1.35$

Answer

135%

6.1-55 §6.1 source ↗

Convert Decimals and Fractions to Percents

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

$3$

Answer

300%

6.1-57 §6.1 source ↗

Convert Decimals and Fractions to Percents

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

$0.009$

Answer

0.9%

6.1-59 §6.1 source ↗

Convert Decimals and Fractions to Percents

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

$0.0875$

Answer

8.75%

6.1-61 §6.1 source ↗

Convert Decimals and Fractions to Percents

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

$1.5$

Answer

150%

6.1-63 §6.1 source ↗

Convert Decimals and Fractions to Percents

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

$2.254$

Answer

225.4%

6.1-65 §6.1 source ↗

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

$\frac{1}{4}$

Answer

25%

6.1-67 §6.1 source ↗

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

$\frac{3}{8}$

Answer

37.5%

6.1-69 §6.1 source ↗

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

$\frac{7}{4}$

Answer

175%

6.1-71 §6.1 source ↗

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

$6 \frac{4}{5}$

Answer

680%

6.1-73 §6.1 source ↗

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

$\frac{5}{12}$

Answer

41 \frac{2}{3} % o r 41. \bar{6} %

6.1-75 §6.1 source ↗

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

$2 \frac{2}{3}$

Answer

266 . \bar{6} %

6.1-77 §6.1 source ↗

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

$\frac{3}{7}$

Answer

42.9%

6.1-79 §6.1 source ↗

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

$\frac{5}{9}$

Answer

55. \bar{5} %

6.1-81 §6.1 source ↗

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

$\frac{1}{4}$ of washing machines needed repair.

Answer

25%

6.1-83 §6.1 source ↗

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

According to the National Center for Health Statistics, in $2012, \frac{7}{20}$ of American adults were obese.

Answer

35%

6.1-85 §6.1 source ↗

In the following exercises, complete the table.

Table 6.3 in the book ↗

Fraction	Decimal	Percent
$\frac{1}{2}$
	$0.45$
		$18 %$
$\frac{1}{3}$
	$0.008$
$2$

Answer

Fraction	Decimal	Percent
$\frac{1}{2}$	$0.5$	$50 %$
$\frac{9}{20}$	$0.45$	$45 %$
$\frac{9}{50}$	$0.18$	$18 %$
$\frac{1}{3}$	$0.3$	$33.3 %$
$\frac{1}{125}$	$0.008$	$0.8 %$
$2$	$2.0$	$200 %$

6.1-87 §6.1 source ↗

In the following exercises, complete the table.

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 $9.05% .$ She knows this is a little less than $10% .$

ⓐ Convert $10%$ to a fraction.

ⓑ Use your answer from ⓐ to estimate the sales tax Felipa would pay on a $$95$ dress.

Answer

ⓐ $\frac{1}{10}$

ⓑ $approximately $9.50$

6.1-89 §6.1 source ↗

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.

Use the chart to answer the following questions

Seller	Rating
$A$	$4/5$
$B$	$3.5/4$
$C$	$85%$

Write seller $C’s$ rating as a fraction and a decimal.

Answer

\frac{17}{20}; 0.85

6.1-91 §6.1 source ↗

Use the chart to answer the following questions

Seller	Rating
$A$	$4/5$
$B$	$3.5/4$
$C$	$85%$

Write seller $A’s$ rating as a percent and a decimal.

Answer

80%; 0.8

6.1-93 §6.1 source ↗

Use the chart to answer the following questions

Seller	Rating
$A$	$4/5$
$B$	$3.5/4$
$C$	$85%$

Convert $25%,$ $50%,$ $75%,$ $and 100%$ to fractions. Do you notice a pattern? Explain what the pattern is.

Answer

\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1 .

6.1-95 §6.1 source ↗

Use the chart to answer the following questions

Seller	Rating
$A$	$4/5$
$B$	$3.5/4$
$C$	$85%$

When the Szetos sold their home, the selling price was $500%$ of what they had paid for the house $30 years$ ago. Explain what $500%$ means in this context.

Answer

The Szetos sold their home for five times what they paid 30 years ago.

Be Prepared 6.4 §6.2 source ↗

Translate and solve:

\frac{3}{4}

x

24 .

If you missed this problem, review Example 4.105.

Example 4.105 in the book ↗

Answer

32

Be Prepared 6.5 §6.2 source ↗

Simplify:

(4.5) (2.38) .

If you missed this problem, review Example 5.15.

Example 5.15 in the book ↗

Answer

10.71

Be Prepared 6.6 §6.2 source ↗

Solve:

3.5 = 0.7 n .

If you missed this problem, review Example 5.43.

Example 5.43 in the book ↗

Answer

5

Try It 6.27 §6.2 source ↗

What number is

45%

80 ?

Answer

Try It 6.28 §6.2 source ↗

What number is

55%

60 ?

Answer

Try It 6.29 §6.2 source ↗

150%

78

is what number?

Answer

117

Try It 6.30 §6.2 source ↗

175%

72

is what number?

Answer

126

Try It 6.31 §6.2 source ↗

17

25%

of what number?

Answer

Try It 6.32 §6.2 source ↗

40

62.5%

of what number?

Answer

Try It 6.33 §6.2 source ↗

7.5%

of what number is

$1.95 ?

Answer

$26

Try It 6.34 §6.2 source ↗

8.5%

of what number is

$3.06 ?

Answer

$36

Try It 6.35 §6.2 source ↗

What percent of

76

57 ?

Answer

75%

Try It 6.36 §6.2 source ↗

What percent of

120

96 ?

Answer

80%

Try It 6.37 §6.2 source ↗

110

is what percent of

88 ?

Answer

125%

Try It 6.38 §6.2 source ↗

126

is what percent of

72 ?

Answer

175%

Try It 6.39 §6.2 source ↗

Cierra and her sister enjoyed a special dinner in a restaurant, and the bill was

$81.50 .

If she wants to leave

18%

of the total bill as her tip, how much should she leave?

Answer

$14.67

Try It 6.40 §6.2 source ↗

Kimngoc had lunch at her favorite restaurant. She wants to leave

15%

of the total bill as her tip. If her bill was

$14.40,

how much will she leave for the tip?

Answer

$2.16

Try It 6.41 §6.2 source ↗

One serving of wheat square cereal has

7

grams of fiber, which is

29%

of the recommended daily amount. What is the total recommended daily amount of fiber?

Answer

24.1 grams

Try It 6.42 §6.2 source ↗

One serving of rice cereal has

190

mg of sodium, which is

8%

of the recommended daily amount. What is the total recommended daily amount of sodium?

Answer

2,375 mg

Try It 6.43 §6.2 source ↗

Veronica is planning to make muffins from a mix. The package says each muffin will be

230

calories and

60

calories will be from fat. What percent of the total calories is from fat? (Round to the nearest whole percent.)

Answer

26%

Try It 6.44 §6.2 source ↗

The brownie mix Ricardo plans to use says that each brownie will be

190

calories, and

70

calories are from fat. What percent of the total calories are from fat?

Answer

37%

Try It 6.45 §6.2 source ↗

2011,

the IRS increased the deductible mileage cost to

55.5

cents from

51

cents. Find the percent increase. (Round to the nearest tenth of a percent.)

Answer

8.8%

Try It 6.46 §6.2 source ↗

1995,

the standard bus fare in Chicago was

$1.50 .

2008,

the standard bus fare was

$2.25 .

Find the percent increase. (Round to the nearest tenth of a percent.)

Answer

50%

Try It 6.47 §6.2 source ↗

The population of one city was about

672,000

2010 .

The population of the city is projected to be about

630,000

2020 .

Find the percent decrease. (Round to the nearest tenth of a percent.)

Answer

6.3%

Try It 6.48 §6.2 source ↗

Last year Sheila's salary was

$42,000 .

Because of furlough days, this year her salary was

$37,800 .

Find the percent decrease. (Round to the nearest tenth of a percent.)

Answer

10%

6.2-97 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What number is $45%$ of $120 ?$

Answer

6.2-99 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What number is $24%$ of $112 ?$

Answer

26.88

6.2-101 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

$250%$ of $65$ is what number?

Answer

162.5

6.2-103 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

$800%$ of $2,250$ is what number?

Answer

18,000

6.2-105 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

$28$ is $25%$ of what number?

Answer

112

6.2-107 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

$81$ is $75%$ of what number?

Answer

108

6.2-109 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

$8.2%$ of what number is $$2.87 ?$

Answer

$35

6.2-111 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

$11.5%$ of what number is $$108.10 ?$

Answer

$940

6.2-113 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What percent of $260$ is $78 ?$

Answer

30%

6.2-115 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What percent of $1,500$ is $540 ?$

Answer

36%

6.2-117 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

$30$ is what percent of $20 ?$

Answer

150%

6.2-119 §6.2 source ↗

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

$840$ is what percent of $480 ?$

Answer

175%

6.2-121 §6.2 source ↗

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 $$74.25 .$ She wants to leave $16%$ of the total bill as a tip. How much should the tip be?

Answer

$11.88

6.2-123 §6.2 source ↗

Solve Applications of Percents

In the following exercises, solve the applications of percents.

Trong has $12%$ of each paycheck automatically deposited to his savings account. His last paycheck was $$2,165 .$ How much money was deposited to Trong's savings account?

Answer

$259.80

6.2-125 §6.2 source ↗

Solve Applications of Percents

In the following exercises, solve the applications of percents.

One serving of oatmeal has $8$ grams of fiber, which is $33%$ of the recommended daily amount. What is the total recommended daily amount of fiber?

Answer

24.2 grams

6.2-127 §6.2 source ↗

Solve Applications of Percents

In the following exercises, solve the applications of percents.

A bacon cheeseburger at a popular fast food restaurant contains $2,070$ milligrams (mg) of sodium, which is $86%$ of the recommended daily amount. What is the total recommended daily amount of sodium?

Answer

2,407 mg

6.2-129 §6.2 source ↗

Solve Applications of Percents

In the following exercises, solve the applications of percents.

The nutrition fact sheet at a fast food restaurant says the fish sandwich has $380$ calories, and $171$ calories are from fat. What percent of the total calories is from fat?

Answer

45%

6.2-131 §6.2 source ↗

Solve Applications of Percents

In the following exercises, solve the applications of percents.

Emma gets paid $$3,000$ per month. She pays $$750$ a month for rent. What percent of her monthly pay goes to rent?

Answer

25%

6.2-133 §6.2 source ↗

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 $$15.50$ to $$17.55 .$ Find the percent increase.

Answer

13.2%

6.2-135 §6.2 source ↗

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

Annual student fees at the University of California rose from about $$4,000$ in $2000$ to about $$9,000$ in $2014 .$ Find the percent increase.

Answer

125%

6.2-137 §6.2 source ↗

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

According to Time magazine $(7/19/2011)$ annual global seafood consumption rose from $22$ pounds per person in $1960$ to $38$ pounds per person today. Find the percent increase. (Round to the nearest tenth of a percent.)

Answer

72.7%

6.2-139 §6.2 source ↗

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

A grocery store reduced the price of a loaf of bread from $$2.80$ to $$2.73 .$ Find the percent decrease.

Answer

2.5%

6.2-141 §6.2 source ↗

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

Hernando's salary was $$49,500$ last year. This year his salary was cut to $$44,055 .$ Find the percent decrease.

Answer

11%

6.2-143 §6.2 source ↗

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

In one month, the median home price in the West fell from $$203,400$ to $$192,300 .$ Find the percent decrease. (Round to the nearest tenth of a percent.)

Answer

5.5%

6.2-145 §6.2 source ↗

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

Tipping At the campus coffee cart, a medium coffee costs $$1.65 .$ MaryAnne brings $$2.00$ 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%

6.2-147 §6.2 source ↗

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

Without solving the problem $“ 44$ is $80%$ of what number”, think about what the solution might be. Should it be a number that is greater than $44$ or less than $44 ?$ Explain your reasoning.

Answer

The original number should be greater than 44.80% is less than 100%, so when 80% is converted to a decimal and multiplied to the base in the percent equation, the resulting amount of 44 is less. 44 is only the larger number in cases where the percent is greater than 100%.

6.2-149 §6.2 source ↗

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

After returning from vacation, Alex said he should have packed $50%$ fewer shorts and $200%$ more shirts. Explain what Alex meant.

Answer

Alex should have packed half as many shorts and twice as many shirts.

Be Prepared 6.7 §6.3 source ↗

Solve

0.0875 (720)

through multiplication.
If you missed this problem, review Example 5.17.

Example 5.17 in the book ↗

Answer

63

Be Prepared 6.8 §6.3 source ↗

Solve

12.96 \div 0.04

through division.
If you missed this problem, review Example 5.22.

Example 5.22 in the book ↗

Answer

324

Try It 6.49 §6.3 source ↗

Find ⓐ the sales tax and ⓑ the total cost: Alexandra bought a television set for

$724

in Boston, where the sales tax rate was

6.25%

of the purchase price.

Answer

ⓐ $45.25

ⓑ $769.25

Try It 6.50 §6.3 source ↗

Find ⓐ the sales tax and ⓑ the total cost: Kim bought a winter coat for

$250

in St. Louis, where the sales tax rate was

8.2%

of the purchase price.

Answer

ⓐ $20.50

ⓑ $270.50

Try It 6.51 §6.3 source ↗

Diego bought a new car for

$26,525 .

He was surprised that the dealer then added

$2,387.25 .

What was the sales tax rate for this purchase?

Answer

Try It 6.52 §6.3 source ↗

What is the sales tax rate if a

$7,594

purchase will have

$569.55

of sales tax added to it?

Answer

7.5%

Try It 6.53 §6.3 source ↗

Bob is a travel agent. He receives

7%

commission when he books a cruise for a customer. How much commission will he receive for booking a

$3,900

cruise?

Answer

$273

Try It 6.54 §6.3 source ↗

Fernando receives

18%

commission when he makes a computer sale. How much commission will he receive for selling a computer for

$2,190 ?

Answer

$394.20

Try It 6.55 §6.3 source ↗

Homer received

$1,140

commission when he sold a car for

$28,500 .

What rate of commission did he get?

Answer

Try It 6.56 §6.3 source ↗

Bernice earned

$451

commission when she sold an

$8,200

living room set. What rate of commission did she get?

Answer

5.5%

Try It 6.57 §6.3 source ↗

Marta bought a dishwasher that was on sale for

$75

off. The original price of the dishwasher was

$525 .

What was the sale price of the dishwasher?

Answer

$450

Try It 6.58 §6.3 source ↗

Orlando bought a pair of shoes that was on sale for

$30

off. The original price of the shoes was

$112 .

What was the sale price of the shoes?

Answer

$82

Try It 6.59 §6.3 source ↗

Find ⓐ the amount of discount and ⓑ the sale price: Sergio bought a belt that was discounted

40%

from an original price of

$29 .

Answer

ⓐ $11.60

ⓑ $17.40

Try It 6.60 §6.3 source ↗

Find ⓐ the amount of discount and ⓑ the sale price: Oscar bought a barbecue grill that was discounted

65%

from an original price of

$395 .

Answer

ⓐ $256.75

ⓑ $138.25

Try It 6.61 §6.3 source ↗

Find ⓐ the amount of discount and ⓑ the discount rate: Lena bought a kitchen table at the sale price of

$375.20 .

The original price of the table was

$560 .

Answer

ⓐ $184.80

ⓑ 33%

Try It 6.62 §6.3 source ↗

Find ⓐ the amount of discount and ⓑ the discount rate: Nick bought a multi-room air conditioner at a sale price of

$340 .

The original price of the air conditioner was

$400 .

Answer

ⓐ $60

ⓑ 15%

Try It 6.63 §6.3 source ↗

Jim's music store bought a guitar at wholesale price

$1,200 .

Jim marked the price up

50% .

Find the ⓐ amount of mark-up and ⓑ the list price.

Answer

ⓐ $600

ⓑ $1,800

Try It 6.64 §6.3 source ↗

The Auto Resale Store bought Pablo's Toyota for

$8,500 .

They marked the price up

35% .

Find the ⓐ amount of mark-up and ⓑ the list price.

Answer

ⓐ $2,975

ⓑ $11,475

6.3-151 §6.3 source ↗

Solve Sales Tax Applications

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

The cost of a pair of boots was $$84 .$ The sales tax rate is $5%$ of the purchase price.

Answer

ⓐ $4.20

ⓑ $88.20

6.3-153 §6.3 source ↗

Solve Sales Tax Applications

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

The cost of a microwave oven was $$129 .$ The sales tax rate is $7.5%$ of the purchase price.

Answer

ⓐ $9.68

ⓑ $138.68

6.3-155 §6.3 source ↗

Solve Sales Tax Applications

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

The cost of a file cabinet is $$250 .$ The sales tax rate is $6.85%$ of the purchase price.

Answer

ⓐ $17.13

ⓑ $267.13

6.3-157 §6.3 source ↗

Solve Sales Tax Applications

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

The cost of a $6-drawer$ dresser $$1,199 .$ The sales tax rate is $5.125%$ of the purchase price.

Answer

ⓐ $61.45

ⓑ $1,260.45

6.3-159 §6.3 source ↗

In the following exercises, find the sales tax rate.

Shawna bought a mixer for $$300 .$ The sales tax on the purchase was $$19.50 .$

Answer

6.5%

6.3-161 §6.3 source ↗

In the following exercises, find the sales tax rate.

Bopha bought a bedroom set for $$3,600 .$ The sales tax on the purchase was $$246.60 .$

Answer

6.85%

6.3-163 §6.3 source ↗

Solve Commission Applications

In the following exercises, find the commission.

Christopher sold his dinette set for $$225$ through an online site, which charged him $9%$ of the selling price as commission. How much was the commission?

Answer

$20.25

6.3-165 §6.3 source ↗

Solve Commission Applications

In the following exercises, find the commission.

Farrah works in a jewelry store and receives $12%$ commission when she makes a sale. How much commission will she receive for selling a $$8,125$ ring?

Answer

$975

6.3-167 §6.3 source ↗

Solve Commission Applications

In the following exercises, find the commission.

Hector receives $17.5%$ commission when he sells an insurance policy. How much commission will he receive for selling a policy for $$4,910 ?$

Answer

$859.25

6.3-169 §6.3 source ↗

In the following exercises, find the rate of commission.

Dontay is a realtor and earned $$11,250$ commission on the sale of a $$375,000$ house. What is his rate of commission?

Answer

6.3-171 §6.3 source ↗

In the following exercises, find the rate of commission.

As a waitress, Emily earned $$420$ in tips on sales of $$2,625$ last Saturday night. What was her rate of commission?

Answer

16%

6.3-173 §6.3 source ↗

In the following exercises, find the rate of commission.

Maureen earned $$7,052.50$ commission when she sold a $$45,500$ car. What was the rate of commission?

Answer

15.5%

6.3-175 §6.3 source ↗

Solve Discount Applications

In the following exercises, find the sale price.

Perla bought a cellphone that was on sale for $$50$ off. The original price of the cellphone was $$189 .$

Answer

$139

6.3-176 §6.3 source ↗

Solve Discount Applications

In the following exercises, find the sale price.

Sophie saw a dress she liked on sale for $$15$ off. The original price of the dress was $$96 .$

Answer

$81

6.3-177 §6.3 source ↗

Solve Discount Applications

In the following exercises, find the sale price.

Rick wants to buy a tool set with original price $$165 .$ Next week the tool set will be on sale for $$40$ off.

Answer

$125

6.3-179 §6.3 source ↗

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

Janelle bought a beach chair on sale at $60%$ off. The original price was $$44.95$

Answer

ⓐ $26.97

ⓑ $17.98

6.3-181 §6.3 source ↗

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

Kathy wants to buy a camera that lists for $$389 .$ The camera is on sale with a $33%$ discount.

Answer

ⓐ $128.37

ⓑ $260.63

6.3-183 §6.3 source ↗

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

Erys bought a treadmill on sale at $35%$ off. The original price was $$949.95 .$

Answer

ⓐ $332.48

ⓑ $617.47

6.3-185 §6.3 source ↗

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 $$1,344 .$ The original price of the sofa was $$1,920 .$

Answer

ⓐ $576

ⓑ 30%

6.3-187 §6.3 source ↗

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

Patty bought a baby stroller on sale for $$301.75 .$ The original price of the stroller was $$355.$

Answer

ⓐ $53.25

ⓑ 15%

6.3-189 §6.3 source ↗

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

Nikki bought a patio set on sale for $$480 .$ The original price was $$850 .$

Answer

ⓐ $370

ⓑ 43.5%

6.3-191 §6.3 source ↗

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 $$16$ to sell in her handicraft store. She marked the price up $45% .$

Answer

ⓐ $7.20

ⓑ $23.20

6.3-193 §6.3 source ↗

Solve Mark-up Applications

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

Tom paid $$0.60$ a pound for tomatoes to sell at his produce store. He added a $33%$ mark-up.

Answer

ⓐ $0.20

ⓑ $0.80

6.3-195 §6.3 source ↗

Solve Mark-up Applications

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

Alan bought a used bicycle for $$115 .$ After re-conditioning it, he added $225%$ mark-up and then advertised it for sale.

Answer

ⓐ $258.75

ⓑ $373.75

6.3-197 §6.3 source ↗

Solve Mark-up Applications

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

Coupons Yvonne can use two coupons for the same purchase at her favorite department store. One coupon gives her $$20$ off and the other gives her $25%$ off. She wants to buy a bedspread that sells for $$195 .$

ⓐ Calculate the discount price if Yvonne uses the $$20$ coupon first and then takes $25%$ off.

ⓑ Calculate the discount price if Yvonne uses the $25%$ off coupon first and then uses the $$20$ coupon.

Answer

ⓐ $131.25

ⓑ $126.25

6.3-199 §6.3 source ↗

Solve Mark-up Applications

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

Priam bought a jacket that was on sale for $40%$ off. The original price of the jacket was $$150 .$ While the sales clerk figured the price by calculating the amount of discount and then subtracting that amount from $$150,$ Priam found the price faster by calculating $60%$ of $$150 .$

ⓐ 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.

Be Prepared 6.9 §6.4 source ↗

Solve

0.6 y = 45 .

If you missed this problem, review Example 5.43.

Example 5.43 in the book ↗

Answer

75

Be Prepared 6.10 §6.4 source ↗

Solve

\frac{n}{1.45} = 4.6 .

If you missed this problem, review Example 5.44.

Example 5.44 in the book ↗

Answer

6.67

Try It 6.65 §6.4 source ↗

Find the simple interest earned after

4

years on

$800

at an interest rate of

5%.

Answer

$160

Try It 6.66 §6.4 source ↗

Find the simple interest earned after

2

years on

$700

at an interest rate of

4%.

Answer

$56

Try It 6.67 §6.4 source ↗

Find the principal invested if

$495

interest was earned in

3

years at an interest rate of

6%.

Answer

$2,750

Try It 6.68 §6.4 source ↗

Find the principal invested if

$1,246

interest was earned in

5

years at an interest rate of

7% .

Answer

$3,560

Try It 6.69 §6.4 source ↗

Find the rate if a principal of

$5,000

earned

$1,350

interest in

6

years.

Answer

4.5%

Try It 6.70 §6.4 source ↗

Find the rate if a principal of

$9,000

earned

$1,755

interest in

3

years.

Answer

6.5%

Try It 6.71 §6.4 source ↗

Areli invested a principal of

$950

in her bank account with interest rate

3%.

How much interest did she earn in

5

years?

Answer

$142.50

Try It 6.72 §6.4 source ↗

Susana invested a principal of

$36,000

in her bank account with interest rate

6.5% .

How much interest did she earn in

3

years?

Answer

$7,020

Try It 6.73 §6.4 source ↗

Jim lent his sister

$5,000

to help her buy a house. In

3

years, she paid him the

$5,000,

plus

$900

interest. What was the rate of interest?

Answer

Try It 6.74 §6.4 source ↗

Hang borrowed

$7,500

from her parents to pay her tuition. In

5

years, she paid them

$1,500

interest in addition to the

$7,500

she borrowed. What was the rate of interest?

Answer

Try It 6.75 §6.4 source ↗

Sean's new car loan statement said he would pay

$4,866.25

in interest from an interest rate of

8.5%

over

5

years. How much did he borrow to buy his new car?

Answer

$11,450

Try It 6.76 §6.4 source ↗

5

years, Gloria's bank account earned

$2,400

interest at

5%.

How much had she deposited in the account?

Answer

$9,600

Try It 6.77 §6.4 source ↗

Adriana invested

$4,500

for

8

months in an account that paid

1.9%

interest. How much interest did she earn?

Answer

$57.00

Try It 6.78 §6.4 source ↗

Milton invested

$2,460

for

20

months in an account that paid

3.5%

interest How much interest did he earn?

Answer

$143.50

6.4-201 §6.4 source ↗

Use the Simple Interest Formula

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

Table 6.5 in the book ↗

Interest	Principal	Rate	Time (years)
	$$1200$	$3%$	$5$

Answer

$180

6.4-203 §6.4 source ↗

Use the Simple Interest Formula

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

Table 6.7 in the book ↗

Interest	Principal	Rate	Time (years)
$$4410$		$4.5%$	$7$

Answer

$14,000

6.4-205 §6.4 source ↗

Use the Simple Interest Formula

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

Table 6.9 in the book ↗

Interest	Principal	Rate	Time (years)
$$577.08$	$$4580$		$2$

Answer

6.3%

6.4-207 §6.4 source ↗

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

Find the simple interest earned after $5$ years on $$600$ at an interest rate of $3%.$

Answer

$90

6.4-209 §6.4 source ↗

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

Find the simple interest earned after $2$ years on $$8,950$ at an interest rate of $3.24% .$

Answer

$579.96

6.4-211 §6.4 source ↗

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

Find the simple interest earned after $8$ years on $$15,500$ at an interest rate of $11.425% .$

Answer

$14,167

6.4-213 §6.4 source ↗

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

Find the principal invested if $$656$ interest was earned in $5$ years at an interest rate of $4% .$

Answer

$3,280

6.4-215 §6.4 source ↗

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

Find the principal invested if $$70.95$ interest was earned in $3$ years at an interest rate of $2.75%.$

Answer

$860

6.4-217 §6.4 source ↗

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

Find the principal invested if $$15,222.57$ interest was earned in $6$ years at an interest rate of $10.28% .$

Answer

$24,679.91

6.4-219 §6.4 source ↗

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

Find the rate if a principal of $$5,400$ earned $$432$ interest in $2$ years.

Answer

6.4-221 §6.4 source ↗

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

Find the rate if a principal of $$11,000$ earned $$1,815$ interest in $3$ years.

Answer

5.5%

6.4-223 §6.4 source ↗

Solve Simple Interest Applications

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

Casey deposited $$1,450$ in a bank account with interest rate $4%.$ How much interest was earned in $2$ years?

Answer

$116

6.4-225 §6.4 source ↗

Solve Simple Interest Applications

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

Robin deposited $$31,000$ in a bank account with interest rate $5.2% .$ How much interest was earned in $3$ years?

Answer

$4,836

6.4-227 §6.4 source ↗

Solve Simple Interest Applications

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

Hilaria borrowed $$8,000$ from her grandfather to pay for college. Five years later, she paid him back the $$8,000,$ plus $$1,200$ interest. What was the rate of interest?

Answer

6.4-229 §6.4 source ↗

Solve Simple Interest Applications

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

Lebron lent his daughter $$20,000$ to help her buy a condominium. When she sold the condominium four years later, she paid him the $$20,000,$ plus $$3,000$ interest. What was the rate of interest?

Answer

3.75%

6.4-231 §6.4 source ↗

Solve Simple Interest Applications

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

In $10$ years, a bank account that paid $5.25%$ earned $$18,375$ interest. What was the principal of the account?

Answer

$35,000

6.4-233 §6.4 source ↗

Solve Simple Interest Applications

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

Joshua's computer loan statement said he would pay $$1,244.34$ in interest for a $3$ year loan at $12.4% .$ How much did Joshua borrow to buy the computer?

Answer

$3,345

6.4-235 §6.4 source ↗

Solve Simple Interest Applications

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

Caitlin invested $$8,200$ in an $18-month$ certificate of deposit paying $2.7%$ interest. How much interest did she earn form this investment?

Answer

$332.10

6.4-237 §6.4 source ↗

Solve Simple Interest Applications

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

Airin borrowed $$3,900$ from her parents for the down payment on a car and promised to pay them back in $15$ months at a $4%$ rate of interest. How much interest did she owe her parents?

Answer

$195.00

6.4-239 §6.4 source ↗

Solve Simple Interest Applications

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

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 $$8,000$ for $5$ years.

Answer

Answers will vary.

6.4-241 §6.4 source ↗

Solve Simple Interest Applications

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

Why do banks pay interest on money deposited in savings accounts?

Answer

Answers will vary.

Be Prepared 6.11 §6.5 source ↗

Simplify:

\frac{\frac{1}{3}}{4} .

If you missed this problem, review Example 4.44.

Example 4.44 in the book ↗

Answer

\frac{1}{12}

Be Prepared 6.12 §6.5 source ↗

Solve:

\frac{x}{4} = 20 .

If you missed this problem, review Example 4.99.

Example 4.99 in the book ↗

Answer

80

Be Prepared 6.13 §6.5 source ↗

Write as a rate: Sale rode his bike

24

miles in

2

hours.
If you missed this problem, review Example 5.63.

Example 5.63 in the book ↗

Answer

\frac{24 miles}{2 hours}

Try It 6.79 §6.5 source ↗

Write each sentence as a proportion:

ⓐ $5$ is to $9$ as $20$ is to $36 .$

ⓑ $7$ hits in $11$ at-bats is the same as $28$ hits in $44$ at-bats.

Answer

ⓐ $\frac{5}{9} = \frac{20}{36}$

ⓑ $\frac{7}{11} = \frac{28}{44}$

Try It 6.80 §6.5 source ↗

Write each sentence as a proportion:

ⓐ $6$ is to $7$ as $36$ is to $42 .$

ⓑ $8$ adults for $36$ children is the same as $12$ adults for $54$ children.

Answer

ⓐ $\frac{6}{7} = \frac{36}{42}$

ⓑ $\frac{8}{36} = \frac{12}{54}$

Try It 6.81 §6.5 source ↗

Determine whether each equation is a proportion:

ⓐ $\frac{7}{9} = \frac{54}{72}$

ⓑ $\frac{24.5}{45.5} =$ $\frac{7}{13}$

Answer

ⓐ no

ⓑ yes

Try It 6.82 §6.5 source ↗

Determine whether each equation is a proportion:

ⓐ $\frac{8}{9} = \frac{56}{73}$

ⓑ $\frac{28.5}{52.5} =$ $\frac{8}{15}$

Answer

ⓐ no

ⓑ no

Try It 6.83 §6.5 source ↗

Solve the proportion:

\frac{n}{84} = \frac{11}{12} .

Answer

Try It 6.84 §6.5 source ↗

Solve the proportion:

\frac{y}{96} = \frac{13}{12} .

Answer

104

Try It 6.85 §6.5 source ↗

Solve the proportion:

\frac{91}{b} = \frac{7}{5} .

Answer

Try It 6.86 §6.5 source ↗

Solve the proportion:

\frac{39}{c} = \frac{13}{8} .

Answer

Try It 6.87 §6.5 source ↗

Solve the proportion:

\frac{84}{98} = \frac{−6}{x} .

Answer

−7

Try It 6.88 §6.5 source ↗

Solve the proportion:

\frac{−7}{y} = \frac{105}{135} .

Answer

−9

Try It 6.89 §6.5 source ↗

Pediatricians prescribe

5

milliliters (ml) of acetaminophen for every

25

pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Emilia, who weighs

60

pounds?

Answer

12 ml

Try It 6.90 §6.5 source ↗

For every

1

kilogram (kg) of a child’s weight, pediatricians prescribe

15

milligrams (mg) of a fever reducer. If Isabella weighs

12

kg, how many milligrams of the fever reducer will the pediatrician prescribe?

Answer

180 mg

Try It 6.91 §6.5 source ↗

Marissa loves the Caramel Macchiato at the coffee shop. The

16

oz. medium size has

240

calories. How many calories will she get if she drinks the large

20

oz. size?

Answer

300

Try It 6.92 §6.5 source ↗

Yaneli loves Starburst candies, but wants to keep her snacks to

100

calories. If the candies have

160

calories for

8

pieces, how many pieces can she have in her snack?

Answer

5 pieces

Try It 6.93 §6.5 source ↗

Yurianna is going to Europe and wants to change

$800

dollars into Euros. At the current exchange rate,

$1

US is equal to

0.738

Euro. How many Euros will she have for her trip?

Answer

590 Euros

Try It 6.94 §6.5 source ↗

Corey and Nicole are traveling to Japan and need to exchange

$600

into Japanese yen. If each dollar is

94.1

yen, how many yen will they get?

Answer

56,460 yen

Try It 6.95 §6.5 source ↗

Translate to a proportion: What number is

60%

105 ?

Answer

\frac{n}{105} = \frac{60}{100}

Try It 6.96 §6.5 source ↗

Translate to a proportion: What number is

40%

85 ?

Answer

\frac{n}{85} = \frac{40}{100}

Try It 6.97 §6.5 source ↗

Translate to a proportion:

36

25%

of what number?

Answer

\frac{36}{n} = \frac{25}{100}

Try It 6.98 §6.5 source ↗

Translate to a proportion:

27

36%

of what number?

Answer

\frac{27}{n} = \frac{36}{100}

Try It 6.99 §6.5 source ↗

Translate to a proportion: What percent of

52

39 ?

Answer

\frac{n}{100} = \frac{39}{52}

Try It 6.100 §6.5 source ↗

Translate to a proportion: What percent of

92

23 ?

Answer

\frac{n}{100} = \frac{23}{92}

Try It 6.101 §6.5 source ↗

Translate and solve using proportions: What number is

65%

40 ?

Answer

\frac{n}{40} =

\frac{65}{100};

n =

26

Try It 6.102 §6.5 source ↗

Translate and solve using proportions: What number is

85%

40 ?

Answer

\frac{n}{40} =

\frac{85}{100};

n =

34

Try It 6.103 §6.5 source ↗

Translate and solve using proportions:

125%

64

is what number?

Answer

\frac{n}{64} =

\frac{125}{100};

n =

80

Try It 6.104 §6.5 source ↗

Translate and solve using proportions:

175%

84

is what number?

Answer

\frac{n}{84} =

\frac{175}{100};

n =

147

Try It 6.105 §6.5 source ↗

Translate and solve using proportions:

8.5%

of what number is

$3.23 ?

Answer

\frac{3.23}{n} =

\frac{8.5}{100};

n =

38

Try It 6.106 §6.5 source ↗

Translate and solve using proportions:

7.25%

of what number is

$4.64 ?

Answer

\frac{4.64}{n} =

\frac{7.25}{100};

n =

64

Try It 6.107 §6.5 source ↗

Translate and solve using proportions: What percent of

72

27 ?

Answer

\frac{27}{72} =

\frac{n}{100};

n =

37.5%

Try It 6.108 §6.5 source ↗

Translate and solve using proportions: What percent of

92

23 ?

Answer

\frac{23}{92} =

\frac{n}{100};

n =

25%

6.5-243 §6.5 source ↗

Use the Definition of Proportion

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

$4$ is to $15$ as $36$ is to $135 .$

Answer

\frac{4}{15} = \frac{36}{135}

6.5-245 §6.5 source ↗

Use the Definition of Proportion

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

$12$ is to $5$ as $96$ is to $40 .$

Answer

\frac{12}{5} = \frac{96}{40}

6.5-247 §6.5 source ↗

Use the Definition of Proportion

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

$5$ wins in $7$ games is the same as $115$ wins in $161$ games.

Answer

\frac{5}{7} = \frac{115}{161}

6.5-249 §6.5 source ↗

Use the Definition of Proportion

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

$8$ campers to $1$ counselor is the same as $48$ campers to $6$ counselors.

Answer

\frac{8}{1} = \frac{48}{6}

6.5-251 §6.5 source ↗

Use the Definition of Proportion

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

$$9.36$ for $18$ ounces is the same as $$2.60$ for $5$ ounces.

Answer

\frac{9.36}{18} =

\frac{2.60}{5}

6.5-253 §6.5 source ↗

Use the Definition of Proportion

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

$$18.04$ for $11$ pounds is the same as $$4.92$ for $3$ pounds.

Answer

\frac{18.04}{11} =

\frac{4.92}{3}

6.5-255 §6.5 source ↗

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

$\frac{7}{15} = \frac{56}{120}$

Answer

yes

6.5-257 §6.5 source ↗

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

$\frac{11}{6} = \frac{21}{16}$

Answer

6.5-259 §6.5 source ↗

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

$\frac{12}{18} =$ $\frac{4.99}{7.56}$

Answer

6.5-261 §6.5 source ↗

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

$\frac{13.5}{8.5} =$ $\frac{31.05}{19.55}$

Answer

yes

6.5-263 §6.5 source ↗

Solve Proportions

In the following exercises, solve each proportion.

$\frac{x}{56} = \frac{7}{8}$

Answer

x = 49

6.5-265 §6.5 source ↗

Solve Proportions

In the following exercises, solve each proportion.

$\frac{49}{63} = \frac{z}{9}$

Answer

z = 7

6.5-267 §6.5 source ↗

Solve Proportions

In the following exercises, solve each proportion.

$\frac{5}{a} = \frac{65}{117}$

Answer

a = 9

6.5-269 §6.5 source ↗

Solve Proportions

In the following exercises, solve each proportion.

$\frac{98}{154} = \frac{−7}{p}$

Answer

p = −11

6.5-271 §6.5 source ↗

Solve Proportions

In the following exercises, solve each proportion.

$\frac{a}{−8} = \frac{−42}{48}$

Answer

a = 7

6.5-273 §6.5 source ↗

Solve Proportions

In the following exercises, solve each proportion.

$\frac{2.6}{3.9} = \frac{c}{3}$

Answer

c = 2

6.5-275 §6.5 source ↗

Solve Proportions

In the following exercises, solve each proportion.

$\frac{2.7}{j} = \frac{0.9}{0.2}$

Answer

j = 0.6

6.5-277 §6.5 source ↗

Solve Proportions

In the following exercises, solve each proportion.

$\frac{\frac{1}{2}}{1} = \frac{m}{8}$

Answer

m = 4

6.5-279 §6.5 source ↗

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

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

Answer

9 ml

6.5-281 §6.5 source ↗

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

At the gym, Carol takes her pulse for $10$ sec and counts $19$ beats. How many beats per minute is this? Has Carol met her target heart rate of $140$ beats per minute?

Answer

114 beats/minute. Carol has not met her target heart rate.

6.5-283 §6.5 source ↗

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

A new energy drink advertises $106$ calories for $8$ ounces. How many calories are in $12$ ounces of the drink?

Answer

159 cal

6.5-285 §6.5 source ↗

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

Karen eats $\frac{1}{2}$ cup of oatmeal that counts for $2$ points on her weight loss program. Her husband, Joe, can have $3$ points of oatmeal for breakfast. How much oatmeal can he have?

Answer

\frac{3}{4} cup

6.5-287 §6.5 source ↗

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

Janice is traveling to Canada and will change $$250$ US dollars into Canadian dollars. At the current exchange rate, $$1$ US is equal to $$1.01$ Canadian. How many Canadian dollars will she get for her trip?

Answer

$252.50

6.5-289 §6.5 source ↗

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

Steve changed $$600$ into $480$ Euros. How many Euros did he receive per US dollar?

Answer

0.8 Euros

6.5-291 §6.5 source ↗

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

At the laundromat, Lucy changed $$12.00$ into quarters. How many quarters did she get?

Answer

48 quarters

6.5-293 §6.5 source ↗

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

Jesse’s car gets $30$ miles per gallon of gas. If Las Vegas is $285$ miles away, how many gallons of gas are needed to get there and then home? If gas is $$3.09$ per gallon, what is the total cost of the gas for the trip?

Answer

19 gallons, $58.71

6.5-295 §6.5 source ↗

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

Hugh leaves early one morning to drive from his home in Chicago to go to Mount Rushmore, $812$ miles away. After $3$ hours, he has gone $190$ miles. At that rate, how long will the whole drive take?

Answer

12.8 hours

6.5-297 §6.5 source ↗

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

Phil wants to fertilize his lawn. Each bag of fertilizer covers about $4,000$ square feet of lawn. Phil’s lawn is approximately $13,500$ square feet. How many bags of fertilizer will he have to buy?

Answer

4 bags

6.5-299 §6.5 source ↗

Write Percent Equations as Proportions

In the following exercises, translate to a proportion.

What number is $35%$ of $250 ?$

Answer

\frac{n}{250} = \frac{35}{100}

6.5-301 §6.5 source ↗

Write Percent Equations as Proportions

In the following exercises, translate to a proportion.

What number is $110%$ of $47 ?$

Answer

\frac{n}{47} = \frac{110}{100}

6.5-303 §6.5 source ↗

Write Percent Equations as Proportions

In the following exercises, translate to a proportion.

$45$ is $30%$ of what number?

Answer

\frac{45}{n} = \frac{30}{100}

6.5-305 §6.5 source ↗

Write Percent Equations as Proportions

In the following exercises, translate to a proportion.

$90$ is $150%$ of what number?

Answer

\frac{90}{n} = \frac{150}{100}

6.5-307 §6.5 source ↗

Write Percent Equations as Proportions

In the following exercises, translate to a proportion.

What percent of $85$ is $17 ?$

Answer

\frac{17}{85} = \frac{p}{100}

6.5-309 §6.5 source ↗

Write Percent Equations as Proportions

In the following exercises, translate to a proportion.

What percent of $260$ is $340 ?$

Answer

\frac{340}{260} = \frac{p}{100}

6.5-311 §6.5 source ↗

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

What number is $65%$ of $180 ?$

Answer

\frac{n}{180} = \frac{65}{100}

;

117

6.5-313 §6.5 source ↗

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

$18%$ of $92$ is what number?

Answer

\frac{n}{92} = \frac{18}{100}

;

16.56

6.5-315 §6.5 source ↗

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

$175%$ of $26$ is what number?

Answer

\frac{n}{26} = \frac{175}{100}

;

45.5

6.5-317 §6.5 source ↗

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

What is $300%$ of $488 ?$

Answer

\frac{n}{488} = \frac{300}{100}

;

1464

6.5-319 §6.5 source ↗

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

$17%$ of what number is $$7.65 ?$

Answer

\frac{7.65}{n} = \frac{17}{100}

;

45

6.5-321 §6.5 source ↗

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

$$13.53$ is $8.25%$ of what number?

Answer

\frac{13.53}{n} =

\frac{8.25}{100}

;

164

6.5-323 §6.5 source ↗

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

What percent of $56$ is $14 ?$

Answer

\frac{14}{56} = \frac{p}{100}

;

25 %

6.5-325 §6.5 source ↗

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

What percent of $96$ is $12 ?$

Answer

\frac{12}{96} = \frac{p}{100}

;

12.5 %

6.5-327 §6.5 source ↗

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

Mixing a concentrate Sam bought a large bottle of concentrated cleaning solution at the warehouse store. He must mix the concentrate with water to make a solution for washing his windows. The directions tell him to mix $3$ ounces of concentrate with $5$ ounces of water. If he puts $12$ ounces of concentrate in a bucket, how many ounces of water should he add? How many ounces of the solution will he have altogether?

Answer

He must add 20 oz of water to obtain a final solution of 32 oz.

6.5-329 §6.5 source ↗

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

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

Answer

Answers will vary.

6.R-331 §6.R source ↗

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

$32%$ admission rate for the university

Answer

\frac{32}{100}

6.R-333 §6.R source ↗

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

$13$ out of $100$ architects are women.

Answer

\frac{13}{100}, 13%

6.R-335 §6.R source ↗

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

$48%$

Answer

\frac{12}{25}

6.R-337 §6.R source ↗

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

$64.1%$

Answer

\frac{641}{1000}

6.R-339 §6.R source ↗

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

$6%$

Answer

0.06

6.R-341 §6.R source ↗

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

$128%$

Answer

1.28

6.R-343 §6.R source ↗

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

In $2012, 13.5%$ of the United States population was age $65$ or over. (Source: www.census.gov)

Answer

ⓐ $\frac{27}{200}$

ⓑ $0.135$

6.R-345 §6.R source ↗

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

When a die is tossed, the probability it will land with an even number of dots on the top side is $50% .$

Answer

ⓐ $\frac{1}{2}$

ⓑ $0.5$

6.R-347 §6.R source ↗

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

$0.04$

Answer

6.R-349 §6.R source ↗

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

$2.82$

Answer

282%

6.R-351 §6.R source ↗

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

$0.003$

Answer

0.3%

6.R-353 §6.R source ↗

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

$\frac{3}{4}$

Answer

75%

6.R-355 §6.R source ↗

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

$3 \frac{5}{8}$

Answer

362.5%

6.R-357 §6.R source ↗

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

According to the Centers for Disease Control, $\frac{2}{5}$ of adults do not take a vitamin or supplement.

Answer

40%

6.R-359 §6.R source ↗

In the following exercises, translate and solve.

What number is $46%$ of $350 ?$

Answer

161

6.R-361 §6.R source ↗

In the following exercises, translate and solve.

$84$ is $35%$ of what number?

Answer

240

6.R-363 §6.R source ↗

In the following exercises, translate and solve.

$200%$ of what number is $50 ?$

Answer

6.R-365 §6.R source ↗

In the following exercises, translate and solve.

What percent of $120$ is $81.6 ?$

Answer

68%

6.R-367 §6.R source ↗

In the following exercises, solve.

When Aurelio and his family ate dinner at a restaurant, the bill was $$83.50 .$ Aurelio wants to leave $20%$ of the total bill as a tip. How much should the tip be?

Answer

$16.70

6.R-369 §6.R source ↗

In the following exercises, solve.

The nutrition label on a package of granola bars says that each granola bar has $190$ calories, and $54$ calories are from fat. What percent of the total calories is from fat?

Answer

28.4%

6.R-371 §6.R source ↗

In the following exercises, solve.

Jorge got a raise in his hourly pay, from $$19.00$ to $$19.76 .$ Find the percent increase.

Answer

6.R-373 §6.R source ↗

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

The cost of a lawn mower was $$750 .$ The sales tax rate is $6%$ of the purchase price.

Answer

ⓐ $45

ⓑ $795

6.R-375 §6.R source ↗

In the following exercises, find the sales tax rate.

Andy bought a piano for $$4,600 .$ The sales tax on the purchase was $$333.50 .$

Answer

7.25%

6.R-377 §6.R source ↗

In the following exercises, find the commission.

Ginny is a realtor. She receives $3%$ commission when she sells a house. How much commission will she receive for selling a house for $$380,000 ?$

Answer

$11,400

6.R-379 §6.R source ↗

In the following exercises, find the rate of commission.

Ruben received $$675$ commission when he sold a $$4,500$ painting at the art gallery where he works. What was the rate of commission?

Answer

15%

6.R-381 §6.R source ↗

In the following exercises, find the sale price.

Aya bought a pair of shoes that was on sale for $$30$ off. The original price of the shoes was $$75 .$

Answer

$45

6.R-383 §6.R source ↗

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

Nga bought a microwave for her office. The microwave was discounted $30%$ from an original price of $$84.90 .$

Answer

ⓐ $25.47

ⓑ $59.43

6.R-385 §6.R source ↗

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

Hilda bought a bedspread on sale for $$37 .$ The original price of the bedspread was $$50 .$

Answer

ⓐ $13

ⓑ 26%

6.R-387 §6.R source ↗

In the following exercises, find

Manny paid $$0.80$ a pound for apples. He added $60%$ mark-up before selling them at his produce stand. What price did he charge for the apples?

Answer

ⓐ $0.48

ⓑ $1.28

6.R-389 §6.R source ↗

In the following exercises, solve the simple interest problem.

Find the simple interest earned after $4$ years on $$2,250$ invested at an interest rate of $5% .$

Answer

$450

6.R-391 §6.R source ↗

In the following exercises, solve the simple interest problem.

Find the principal invested if $$660$ interest was earned in $5$ years at an interest rate of $3% .$

Answer

$4400

6.R-393 §6.R source ↗

In the following exercises, solve the simple interest problem.

Kazuo deposited $$10,000$ in a bank account with interest rate $4.5% .$ How much interest was earned in $2$ years?

Answer

$900

6.R-395 §6.R source ↗

In the following exercises, solve the simple interest problem.

Fresia lent her son $$5,000$ for college expenses. Three years later he repaid her the $$5,000$ plus $$375$ interest. What was the rate of interest?

Answer

2.5%

6.R-397 §6.R source ↗

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

$3$ is to $8$ as $12$ is to $32 .$

Answer

\frac{3}{8} = \frac{12}{32}

6.R-399 §6.R source ↗

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

$1$ teacher to $18$ students is the same as $23$ teachers to $414$ students.

Answer

\frac{1}{18} = \frac{23}{414}

6.R-401 §6.R source ↗

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

$\frac{5}{13} = \frac{30}{78}$

Answer

yes

6.R-403 §6.R source ↗

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

$\frac{12}{18} =$ $\frac{6.99}{10.99}$

Answer

6.R-405 §6.R source ↗

In the following exercises, solve each proportion.

$\frac{x}{36} = \frac{5}{9}$

Answer

6.R-407 §6.R source ↗

In the following exercises, solve each proportion.

$\frac{1.2}{1.8} = \frac{d}{6}$

Answer

6.R-409 §6.R source ↗

In the following exercises, solve the proportion problem.

The children’s dosage of acetaminophen is $5$ milliliters (ml) for every $25$ pounds of a child’s weight. How many milliliters of acetaminophen will be prescribed for a $60$ pound child?

Answer

12 ml

6.R-411 §6.R source ↗

In the following exercises, solve the proportion problem.

An $8$ ounce serving of ice cream has $272$ calories. If Lavonne eats $10$ ounces of ice cream, how many calories does she get?

Answer

340 calories

6.R-413 §6.R source ↗

In the following exercises, solve the proportion problem.

Zack wants to drive from Omaha to Denver, a distance of $494$ miles. If his car gets $38$ miles to the gallon, how many gallons of gas will Zack need to get to Denver?

Answer

13 gallons

6.R-415 §6.R source ↗

In the following exercises, translate to a proportion.

What number is $62%$ of $395 ?$

Answer

\frac{n}{395} = \frac{62}{100}

6.R-417 §6.R source ↗

In the following exercises, translate to a proportion.

What percent of $1,000$ is $15 ?$

Answer

\frac{15}{1000} = \frac{p}{100}

6.R-419 §6.R source ↗

In the following exercises, translate and solve using proportions.

What number is $85%$ of $900 ?$

Answer

\frac{n}{900} =

\frac{85}{100},

765

6.R-421 §6.R source ↗

In the following exercises, translate and solve using proportions.

$$3.51$ is $4.5%$ of what number?

Answer

\frac{3.51}{n} =

\frac{4.5}{100},

$78

6.T-423 §6.T source ↗

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

$24%$

Answer

0.24, \frac{6}{25}

6.T-425 §6.T source ↗

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

$350%$

Answer

3.5, \frac{7}{2}

6.T-427 §6.T source ↗

In the following exercises, convert each fraction to a percent. (Round to $3$ decimal places if needed.)

$\frac{1}{3}$

Answer

33. \bar{3} % o r 33 \frac{1}{3} %

6.T-429 §6.T source ↗

In the following exercises, solve the percent problem.

$65$ is what percent of $260 ?$

Answer

25%

6.T-431 §6.T source ↗

In the following exercises, solve the percent problem.

$150%$ of what number is $60 ?$

Answer

6.T-433 §6.T source ↗

In the following exercises, solve the percent problem.

The total number of vehicles on one freeway dropped from $84,000$ to $74,000 .$ Find the percent decrease (round to the nearest tenth of a percent).

Answer

11.9%

6.T-435 §6.T source ↗

In the following exercises, solve the percent problem.

Mara received $$31.80$ commission when she sold a $$795$ suit. What was her rate of commission?

Answer

6.T-437 §6.T source ↗

In the following exercises, solve the percent problem.

Oxana bought a dresser at a garage sale for $$20 .$ She refinished it, then added a $250%$ markup before advertising it for sale. What price did she ask for the dresser?

Answer

$70

6.T-439 §6.T source ↗

In the following exercises, solve the percent problem.

Brenda borrowed $$400$ from her brother. Two years later, she repaid the $$400$ plus $$50$ interest. What was the rate of interest?

Answer

6.25%

6.T-441 §6.T source ↗

In the following exercises, solve the percent problem.

Solve for a: $\frac{12}{a} = \frac{−15}{65}$

Answer

−52

Loading chapter 7…

Problems and answers are adapted from Prealgebra 2e by Lynn Marecek, MaryAnne Anthony-Smith and Andrea Honeycutt Mathis, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.