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 1 In words: In words: 450 is 36% of what number? 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 students go to State College. Solve: 450  0.36x 450  0.36x 450  0.36x 0.36 Divide both sides by  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? the problem in words, then translate to a proportion. State the problem in words, then translate to a proportion. Method 2 In words: 450 is 36% of what number? Translate: amountbasepercent 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: = b b = = 36b 36

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Percent Increase and Percent Decrease percent increase percent increase  percent decrease percent decrease  In each case write the quotient as a percent. Helpful Hint 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

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 = 114