Skip to content Skip to navigation

Connexions

You are here: Home » Content » Ratios and Rates: Applications of Percents

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • CCQ display tagshide tags

    This module is included in aLens by: Community College of QatarAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Used as supplemental materials for developmental math courses."

    Click the "CCQ" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

  • College Open Textbooks display tagshide tags

    This module is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook CollaborativeAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Reviewer's Comments: 'I would recommend this text for a basic math course for students moving on to elementary algebra. The information in most chapters is useful, very clear, and easily […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Fundamentals of Mathematics is a work text that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • UniqU content

    This module is included inLens: UniqU's lens
    By: UniqU, LLCAs a part of collection: "Fundamentals of Mathematics"

    Click the "UniqU content" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Ratios and Rates: Applications of Percents

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses applications of percents. By the end of the module students should be able to distinguish between base, percent, and percentage and be able to find the percentage, the percent, and the base.

Section Overview

  • Base, Percent, and Percentage
  • Finding the Percentage
  • Finding the Percent
  • Finding the Base

Base, Percent, and Percentage

There are three basic types of percent problems. Each type involves a base, a percent, and a percentage, and when they are translated from words to mathemati­cal symbols each becomes a multiplication statement. Examples of these types of problems are the following:

  1. What number is 30% of 50? (Missing product statement.)
  2. 15 is what percent of 50? (Missing factor statement.)
  3. 15 is 30% of what number? (Missing factor statement.)

In problem 1, the product is missing. To solve the problem, we represent the missing product with PP size 12{P} {}.

P = 30% ⋅ 50 P = 30% ⋅ 50 size 12{"P "=" 30% " cdot "50"} {}

Percentage

The missing product PP size 12{P} {} is called the percentage. Percentage means part, or por­tion. In P = 30% ⋅50P = 30% ⋅50 size 12{"P "=" 30% " cdot "50"} {}, PP size 12{P} {} represents a particular part of 50.

In problem 2, one of the factors is missing. Here we represent the missing factor with QQ size 12{Q} {}.

15 = Q ⋅ 50 15 = Q ⋅ 50 size 12{"15 "=" Q " cdot "50"} {}

Percent

The missing factor is the percent. Percent, we know, means per 100, or part of 100. In 15 = Q ⋅5015 = Q ⋅50 size 12{"15 "=" Q " cdot "50"} {}, QQ size 12{Q} {} indicates what part of 50 is being taken or considered. Specifi­cally, 15 = Q ⋅5015 = Q ⋅50 size 12{"15 "=" Q " cdot "50"} {} means that if 50 was to be divided into 100 equal parts, then QQ indicates 15 are being considered.

In problem 3, one of the factors is missing. Represent the missing factor with B B.

15 = 30% ⋅ B 15 = 30% ⋅ B size 12{"15 "=" 30% " cdot B} {}

Base

The missing factor is the base. Some meanings of base are a source of supply, or a starting place. In 15 = 30% ⋅B15 = 30% ⋅B size 12{"15 "=" 30% " cdot B} {}, BB size 12{B} {} indicates the amount of supply. Specifically, 15 = 30% ⋅B15 = 30% ⋅B size 12{"15 "=" 30% " cdot B} {} indicates that 15 represents 30% of the total supply.

Each of these three types of problems is of the form

( percentage ) = ( percent ) ⋅ ( base ) ( percentage ) = ( percent ) ⋅ ( base ) size 12{ \( "percentage" \) = \( "percent" \) cdot \( "base" \) } {}

We can determine any one of the three values given the other two using the methods discussed in (Reference).

Finding the Percentage

Sample Set A

Example 1

What number ︸ is ↓ 30% ↓ of ↓ 50 ↓ ? Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 30% ⋅ 50 Convert 30% to a decimal. P = .30 ⋅ 50 Multiply. P = 15 What number ︸ is ↓ 30% ↓ of ↓ 50 ↓ ? Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 30% ⋅ 50 Convert 30% to a decimal. P = .30 ⋅ 50 Multiply. P = 15

Thus, 15 is 30% of 50.

Do Section 5, Exercise 1.

Example 2

What number ︸ is ↓ 36% ↓ of ↓ 95 ↓ ? Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 36% ⋅ 95 Convert 36% to a decimal. P = .36 ⋅ 95 Multiply P = 34.2 What number ︸ is ↓ 36% ↓ of ↓ 95 ↓ ? Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 36% ⋅ 95 Convert 36% to a decimal. P = .36 ⋅ 95 Multiply P = 34.2

Thus, 34.2 is 36% of 95.

Do Section 5, Exercise 1.

Example 3

A salesperson, who gets a commission of 12% of each sale she makes, makes a sale of $8,400.00. How much is her commission?

We need to determine what part of $8,400.00 is to be taken. What part indicates percentage.

What number ︸ is ↓ 12% ↓ of ↓ 8,400.00 ↓ ? Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 12% ⋅ 8,400.00 Convert to decimals. P = .12 ⋅ 8,400.00 Multiply. P = 1008.00 What number ︸ is ↓ 12% ↓ of ↓ 8,400.00 ↓ ? Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 12% ⋅ 8,400.00 Convert to decimals. P = .12 ⋅ 8,400.00 Multiply. P = 1008.00

Thus, the salesperson's commission is $1,008.00.

Do Section 5, Exercise 2.

Example 4

A girl, by practicing typing on her home computer, has been able to increase her typing speed by 110%. If she originally typed 16 words per minute, by how many words per minute was she able to increase her speed?

We need to determine what part of 16 has been taken. What part indicates percentage.

What number ︸ is ↓ 110% ↓ of ↓ 16 ↓ ? Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 110% ⋅ 16 Convert to decimals. P = 1.10 ⋅ 16 Multiply. P = 17.6 What number ︸ is ↓ 110% ↓ of ↓ 16 ↓ ? Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 110% ⋅ 16 Convert to decimals. P = 1.10 ⋅ 16 Multiply. P = 17.6

Thus, the girl has increased her typing speed by 17.6 words per minute. Her new speed is 16 + 17.6 = 33.616 + 17.6 = 33.6 size 12{"16 "+" 17" "." "6 "=" 33" "." 6} {} words per minute.

Do Section 5, Exercise 3.

Example 5

A student who makes $125 a month working part-time receives a 4% salary raise. What is the student's new monthly salary?

With a 4% raise, this student will make 100% of the original salary + 4% of the original salary. This means the new salary will be 104% of the original salary. We need to determine what part of $125 is to be taken. What part indicates percentage.

What number ︸ is ↓ 104% ↓ of ↓ 125 ↓ Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 104% ⋅ 125 Convert to decimals. P = 1.04 ⋅ 125 Multiply. P = 130 What number ︸ is ↓ 104% ↓ of ↓ 125 ↓ Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 104% ⋅ 125 Convert to decimals. P = 1.04 ⋅ 125 Multiply. P = 130

Thus, this student's new monthly salary is $130.

Do Section 5, Exercise 4.

Example 6

An article of clothing is on sale at 15% off the marked price. If the marked price is $24.95, what is the sale price?

Since the item is discounted 15%, the new price will be 100% - 15% = 85%100% - 15% = 85% size 12{"100% - 15% "=" 85%"} {} of the marked price. We need to determine what part of 24.95 is to be taken. What part indicates percentage.

What number ︸ is ↓ 85% ↓ of ↓ $ 24.95 ↓ . Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 85% ⋅ 24.95 Convert to decimals. P = .85 ⋅ 24.95 Multiply. P = 21.2075 Since this number represents money, we'll round to 2 decimal places P = 21.21 What number ︸ is ↓ 85% ↓ of ↓ $ 24.95 ↓ . Missing product statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ P = 85% ⋅ 24.95 Convert to decimals. P = .85 ⋅ 24.95 Multiply. P = 21.2075 Since this number represents money, we'll round to 2 decimal places P = 21.21

Thus, the sale price of the item is $21.21.

Practice Set A

Exercise 1

What number is 42% of 85?

Solution

35.7

Exercise 2

A sales person makes a commission of 16% on each sale he makes. How much is his commission if he makes a sale of $8,500?

Solution

$1,360

Exercise 3

An assembly line worker can assemble 14 parts of a product in one hour. If he can increase his assembly speed by 35%, by how many parts per hour would he increase his assembly of products?

Solution

4.9

Exercise 4

A computer scientist in the Silicon Valley makes $42,000 annually. What would this scientist's new annual salary be if she were to receive an 8% raise?

Solution

$45,360

Finding the Percent

Sample Set B

Example 7

15 ↓ is ↓ what percent ︸ of ↓ 50 ↓ ? Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ [(product) = (factor) ⋅ (factor)] 15 = Q ⋅ 50 15 ↓ is ↓ what percent ︸ of ↓ 50 ↓ ? Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ [(product) = (factor) ⋅ (factor)] 15 = Q ⋅ 50

Recall that (missing factor) = (product) ÷ (known factor).

Q = 15÷50 Divide. Q = 0.3 Convert to a percent. Q = 30% Q = 15÷50 Divide. Q = 0.3 Convert to a percent. Q = 30%

Thus, 15 is 30% of 50.

Do Section 8, Exercise 5.

Example 8

4.32 ↓ is ↓ what percent ︸ of ↓ 72 ↓ ? Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ [(product) = (factor) ⋅ (factor)] 4.32 = Q ⋅ 72 4.32 ↓ is ↓ what percent ︸ of ↓ 72 ↓ ? Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ [(product) = (factor) ⋅ (factor)] 4.32 = Q ⋅ 72

Q = 4.32÷72 Divide. Q = 0.06 Convert to a percent. Q = 6% Q = 4.32÷72 Divide. Q = 0.06 Convert to a percent. Q = 6%

Thus, 4.32 is 6% of 72.

Do Section 8, Exercise 5.

Example 9

On a 160 question exam, a student got 125 correct answers. What percent is this? Round the result to two decimal places.

We need to determine the percent.

125 ↓ is ↓ what percent ︸ of ↓ 160 ↓ ? Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ [(product) = (factor) ⋅ (factor)] 125 = Q ⋅ 160 125 ↓ is ↓ what percent ︸ of ↓ 160 ↓ ? Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ [(product) = (factor) ⋅ (factor)] 125 = Q ⋅ 160

Q = 125÷160 Divide. Q = 0.78125 Round to two decimal places. Q = .78 Q = 125÷160 Divide. Q = 0.78125 Round to two decimal places. Q = .78

Thus, this student received a 78% on the exam.

Do Section 8, Exercise 6.

Example 10

A bottle contains 80 milliliters of hydrochloric acid (HCl) and 30 milliliters of water. What percent of HCl does the bottle contain? Round the result to two decimal places.

We need to determine the percent. The total amount of liquid in the bottle is

80 milliliters + 30 milliliters = 110 milliliters 80 milliliters+30 milliliters=110 milliliters.

80 ↓ is ↓ what percent ︸ of ↓ 110 ↓ ? Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ [(product) = (factor) ⋅ (factor)] 80 = Q ⋅ 110 80 ↓ is ↓ what percent ︸ of ↓ 110 ↓ ? Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ [(product) = (factor) ⋅ (factor)] 80 = Q ⋅ 110

Q = 80÷110 Divide. Q = 0.727272. . . Round to two decimal places. Q ≈ 73% The symbol "≈" is read as "approximately." Q = 80÷110 Divide. Q = 0.727272. . . Round to two decimal places. Q ≈ 73% The symbol "≈" is read as "approximately."

Thus, this bottle contains approximately 73% HCl.

Do Section 8, Exercise 7.

Example 11

Five years ago a woman had an annual income of $19,200. She presently earns $42,000 annually. By what percent has her salary increased? Round the result to two decimal places.

We need to determine the percent.

42,000 ↓ is ↓ what percent ︸ of ↓ 19,200 ↓ ? Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ 42,000 = Q ⋅ 19,200 42,000 ↓ is ↓ what percent ︸ of ↓ 19,200 ↓ ? Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ 42,000 = Q ⋅ 19,200

Q = 42,000÷19,200 Divide. Q = 2.1875 Round to two decimal places. Q = 2.19 Convert to a percent. Q = 219% Convert to a percent. Q = 42,000÷19,200 Divide. Q = 2.1875 Round to two decimal places. Q = 2.19 Convert to a percent. Q = 219% Convert to a percent.

Thus, this woman's annual salary has increased 219%.

Practice Set B

Exercise 5

99.13 is what percent of 431?

Solution

23%

Exercise 6

On an 80 question exam, a student got 72 correct answers. What percent did the student get on the exam?

Solution

90%

Exercise 7

A bottle contains 45 milliliters of sugar and 67 milliliters of water. What fraction of sugar does the bottle contain? Round the result to two decimal places (then express as a percent).

Solution

40%

Finding the Base

Sample Set C

Example 12

15 ↓ is ↓ 30% ↓ of ↓ what number? ︸ Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ [(percentage) = (factor) ⋅ (factor)] 15 = 30% ⋅ B Convert to decimals. 15 = .30 ⋅ B [(missing factor) = (product) ÷ (known factor)] 15 ↓ is ↓ 30% ↓ of ↓ what number? ︸ Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ [(percentage) = (factor) ⋅ (factor)] 15 = 30% ⋅ B Convert to decimals. 15 = .30 ⋅ B [(missing factor) = (product) ÷ (known factor)]

B = 15÷.30 B = 50 B = 15÷.30 B = 50

Thus, 15 is 30% of 50.

Try Exercise 8 in Section 11.

Example 13

56.43 ↓ is ↓ 33% ↓ of ↓ what number? ︸ Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ 56.43 = 33% ⋅ B Convert to decimals. 56.43 = .33 ⋅ B Divide. 56.43 ↓ is ↓ 33% ↓ of ↓ what number? ︸ Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ 56.43 = 33% ⋅ B Convert to decimals. 56.43 = .33 ⋅ B Divide.

B = 56.43÷.33 B = 171 B = 56.43÷.33 B = 171

Thus, 56.43 is 33% of 171.

Try Exercise 8 in Section 11.

Example 14

Fifteen milliliters of water represents 2% of a hydrochloric acid (HCl) solution. How many milliliters of solution are there?

We need to determine the total supply. The word supply indicates base.

15 ↓ is ↓ 2% ↓ of ↓ what number? ︸ Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ 15 = 2% ⋅ B Convert to decimals. 15 = .02 ⋅ B Divide. 15 ↓ is ↓ 2% ↓ of ↓ what number? ︸ Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ 15 = 2% ⋅ B Convert to decimals. 15 = .02 ⋅ B Divide.

B = 15÷.02 B = 750 B = 15÷.02 B = 750

Thus, there are 750 milliliters of solution in the bottle.

Try Exercise 9 in Section 11.

Example 15

In a particular city, a sales tax of 612612 size 12{6 { {1} over {2} } } {}% is charged on items purchased in local stores. If the tax on an item is $2.99, what is the price of the item?

We need to determine the price of the item. We can think of price as the starting place. Starting place indicates base. We need to determine the base.

2.99 ↓ is ↓ 612% ↓ of ↓ what number? ︸ Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ 2.99 = 612% ⋅ B Convert to decimals. 2.99 = 6.5% ⋅ B 2.99 = .065 ⋅ B [(missing factor) = (product) ÷ (known factor)] 2.99 ↓ is ↓ 612% ↓ of ↓ what number? ︸ Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ 2.99 = 612% ⋅ B Convert to decimals. 2.99 = 6.5% ⋅ B 2.99 = .065 ⋅ B [(missing factor) = (product) ÷ (known factor)]

B = 2.99÷.065 Divide. B = 46 B = 2.99÷.065 Divide. B = 46

Thus, the price of the item is $46.00.

Try Exercise 10 in Section 11.

Example 16

A clothing item is priced at $20.40. This marked price includes a 15% discount. What is the original price?

We need to determine the original price. We can think of the original price as the starting place. Starting place indicates base. We need to determine the base. The new price, $20.40, represents 100%- 15% = 85%100%- 15% = 85% size 12{"100% - 15% "=" 85%"} {} of the original price.

20.40 ↓ is ↓ 85% ↓ of ↓ what number? ︸ Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ 20.40 = 85% ⋅ B Convert to decimals. 20.40 = .85 ⋅ B [(missing factor) = (product) ÷ (known factor)] 20.40 ↓ is ↓ 85% ↓ of ↓ what number? ︸ Missing factor statement. (percentage) ↓ = ↓ (percent) ↓ ⋅ ↓ (base) ↓ 20.40 = 85% ⋅ B Convert to decimals. 20.40 = .85 ⋅ B [(missing factor) = (product) ÷ (known factor)]

B = 20.40÷.85 Divide. B = 24 B = 20.40÷.85 Divide. B = 24

Thus, the original price of the item is $24.00.

Try Exercise 11 in Section 11.

Practice Set C

Exercise 8

1.98 is 2% of what number?

Solution

99

Exercise 9

3.3 milliliters of HCl represents 25% of an HCl solution. How many milliliters of solution are there?

Solution

13.2ml

Exercise 10

A salesman, who makes a commission of 18141814 size 12{"18" { {1} over {4} } } {}% on each sale, makes a commission of $152.39 on a particular sale. Rounded to the nearest dollar, what is the amount of the sale?

Solution

$835

Exercise 11

At "super-long play," 212212 size 12{2 { {1} over {2} } } {}hours of play of a video cassette recorder represents 31.25% of the total playing time. What is the total playing time?

Solution

8 hours

Exercises

For the following 25 problems, find each indicated quantity.

Exercise 12

What is 21% of 104?

Solution

21.84

Exercise 13

What is 8% of 36?

Exercise 14

What is 98% of 545?

Solution

534.1

Exercise 15

What is 143% of 33?

Exercise 16

What is 10121012 size 12{"10" { {1} over {2} } } {}% of 20?

Solution

2.1

Exercise 17

3.25 is what percent of 88?

Exercise 18

22.44 is what percent of 44?

Solution

51

Exercise 19

0.0036 is what percent of 0.03?

Exercise 20

31.2 is what percent of 26?

Solution

120

Exercise 21

266.4 is what percent of 74?

Exercise 22

0.0101 is what percent of 0.0505?

Solution

20

Exercise 23

2.4 is 24% of what number?

Exercise 24

24.19 is 41% of what number?

Solution

59

Exercise 25

61.12 is 16% of what number?

Exercise 26

82.81 is 91% of what number?

Solution

91

Exercise 27

115.5 is 20% of what number?

Exercise 28

43.92 is 480% of what number?

Solution

9.15

Exercise 29

What is 85% of 62?

Exercise 30

29.14 is what percent of 5.13?

Solution

568

Exercise 31

0.6156 is what percent of 5.13?

Exercise 32

What is 0.41% of 291.1?

Solution

1.19351

Exercise 33

26.136 is 121% of what number?

Exercise 34

1,937.5 is what percent of 775?

Solution

250

Exercise 35

1 is what percent of 2,000?

Exercise 36

0 is what percent of 59?

Solution

0

Exercise 37

An item of clothing is on sale for 10% off the marked price. If the marked price is $14.95, what is the sale price? (Round to two decimal places.)

Exercise 38

A grocery clerk, who makes $365 per month, re­ceives a 7% raise. How much is her new monthly salary?

Solution

390.55

Exercise 39

An item of clothing which originally sells for $55.00 is marked down to $46.75. What percent has it been marked down?

Exercise 40

On a 25 question exam, a student gets 21 correct. What percent is this?

Solution

84

Exercise 41

On a 45 question exam, a student gets 40%. How many questions did this student get correct?

Exercise 42

A vitamin tablet, which weighs 250 milligrams, contains 35 milligrams of vitamin C. What per­cent of the weight of this tablet is vitamin C?

Solution

14

Exercise 43

Five years ago a secretary made $11,200 an­nually. The secretary now makes $17,920 an­nually. By what percent has this secretary's sal­ary been increased?

Exercise 44

A baseball team wins 48344834 size 12{"48" { {3} over {4} } } {}% of all their games. If they won 78 games, how many games did they play?

Solution

160

Exercise 45

A typist was able to increase his speed by 120% to 42 words per minute. What was his original typ­ing speed?

Exercise 46

A salesperson makes a commission of 12% on the total amount of each sale. If, in one month, she makes a total of $8,520 in sales, how much has she made in commission?

Solution

$1,022.40

Exercise 47

A salesperson receives a salary of $850 per month plus a commission of 812812 size 12{8 { {1} over {2} } } {}% of her sales. If, in a particular month, she sells $22,800 worth of merchandise, what will be her monthly earn­ings?

Exercise 48

A man borrows $1150.00 from a loan company. If he makes 12 equal monthly payments of $130.60, what percent of the loan is he paying in interest?

Solution

36.28%

Exercise 49

The distance from the sun to the earth is approx­imately 93,000,000 miles. The distance from the sun to Pluto is approximately 860.2% of the dis­tance from the sun to the Earth. Approximately, how many miles is Pluto from the sun?

Exercise 50

The number of people on food stamps in Maine in 1975 was 151,000. By 1980, the number had decreased to 59,200. By what percent did the number of people on food stamps decrease? (Round the result to the nearest percent.)

Solution

61

Exercise 51

In Nebraska, in 1960, there were 734,000 motor-vehicle registrations. By 1979, the total had in­creased by about 165.6%. About how many motor-vehicle registrations were there in Ne­braska in 1979?

Exercise 52

From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?

Solution

19,500

Exercise 53

In 1950, in the United States, there were 1,894 daily newspapers. That number decreased to 1,747 by 1981. What percent did the number of daily newspapers decrease?

Exercise 54

A particular alloy is 27% copper. How many pounds of copper are there in 55 pounds of the alloy?

Solution

14.85

Exercise 55

A bottle containing a solution of hydrochloric acid (HCl) is marked 15% (meaning that 15% of the HCl solution is acid). If a bottle contains 65 milliliters of solution, how many milliliters of water does it contain?

Exercise 56

A bottle containing a solution of HCl is marked 45%. A test shows that 36 of the 80 milliliters contained in the bottle are hydrochloric acid. Is the bottle marked correctly? If not, how should it be remarked?

Solution

Marked correctly

Exercises For Review

Exercise 57

((Reference)) Use the numbers 4 and 7 to illustrate the commutative property of multiplication.

Exercise 58

((Reference)) Convert 145145 size 12{ { {"14"} over {5} } } {} to a mixed number.

Solution

2 4 5 2 4 5 size 12{2 { {4} over {5} } } {}

Exercise 59

((Reference)) Arrange the numbers 712712 size 12{ { {7} over {"12"} } } {}, 5959 size 12{ { {5} over {9} } } {} and 4747 size 12{ { {4} over {7} } } {} in increasing order.

Exercise 60

((Reference)) Convert 4.006 to a mixed number.

Solution

4 3 500 4 3 500 size 12{4 { {3} over {"500"} } } {}

Exercise 61

((Reference)) Convert 7878 size 12{ { {7} over {8} } } {} % to a fraction.

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks