Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

6.5

Applications of Percent

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 22

Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

The freshman class of 450 students is 36% of all students at State College. How many students go to State College?

State the problem in words, then translate to an equation.

Method 1Method 1

In words:In words: 450 is 36% of what number?

Translate:Translate: 450 36% • x

Solving Applications Involving Percent

Continued

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33

Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

1250 students go to State College.

Solve: 450 0.36x

450 0.36x450 0.36x0.36 0.36

Divide both sides by 0.36.

1250 = x

Continued

Solving Applications Involving Percent

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44

Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

The freshman class of 450 students is 36% of all students at State College. How many students go to State College?

State the problem in words, then translate to a proportion. the problem in words, then translate to a proportion.

Method 2

In words: 450 is 36% of what number?

Translate:

amount basepercent

450 36=

100b

Solving Applications Involving Percent

Continued

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55

Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Solving Applications Involving Percent

Continued

1250 students go to State College.

b = 1250

Solve: 450 36

=100b

450 • 100 = b • 36

450b = 36

100

45000 = 36b45000 = 36b

3636

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66

Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Percent Increase and Percent Decrease

percent increasepercent increase

percent decreasepercent decrease

In each case write the quotient as a percent.In each case write the quotient as a percent.

amount of increase

original amount

amount of decrease

original amount

Helpful HintHelpful HintMake sure that this number in the denominator is the original number and not the new number.Make sure that this number in the denominator is the original number and not the new number.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77

Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Percent Increase

Example: Nancy’s salary increased from $16,000 last year to $17,280 this year. What was the percent increase in her salary?

Procedure: First, find the amount of increase. Then compare that amount to the previous amount, last year’s salary.

Amount of increase = original amount – new amount

Nancy’s salary increased by 8%.

= 17,280 – 16,000 = 1280

amount of increasePercent of increase = original amount

1280= 16000

= 0.08

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 88

Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Percent Decrease

Example: Mark weighed 285 pounds two years ago. After dieting, he reduced his weight to 171 pounds. What was the percent decrease in his weight?

Procedure: First, find the amount of decrease. Then compare that amount to Mark’s previous weight.

Amount of decrease = original amount – new amount

Mark’s weight decreased by 40%.

= 285 – 171 = 114amount of decreasePercent of decrease =

original amount114= 285

= 0.4