1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 4.5 Solving Percent Problems by Using the Proportion:

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Understand the proportion o Use the proportion to solve percent problems.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. For the Proportion P% = percent (written as the ratio ) B = base (number that we are finding the percent of) A = amount (a part of the base) The Proportion

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Three Basic Types of Percent Problems using Type 1:Find the amount given the base and the percent. What is 65% of 500? Type 2:Find the base given the percent and the amount. 57% of what number is 51.3? Problem Solving with the Proportion

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Three Basic Types of Percent Problems using (cont.) Type 3:Find the percent given the base and the amount. What percent of 170 is 204? Problem Solving with the Proportion (cont.)

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Finding the Amount What is 65% of 500? Solution P% = 65% and B = 500. We want to find the amount A. So 65% of 500 is 325.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Finding the Base 57% of ________ is 51.3? Solution P% = 57% and A = 51.3. We want to find the base B. So 57% of 90 is 51.3.

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Finding the Percent What percent of 170 is 204? Solution B = 170 and A = 204. We want to find the percent P. So 120% of 170 is 204.

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Finding the Amount Many food product labels now list total calories and number of calories from fat. Dietary experts believe that a healthy diet has at most 30% of its calories derived from fat. Following this guideline, if an adult consumes 2500 calories per day, how many calories should be from fat?

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Finding the Amount (cont.) Solution In this problem, P% = 30% and B = 2500. We want to find the value of A. Substitution in the proportion

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Finding the Amount (cont.) So in a healthy diet of 2500 calories, no more than 750 calories should be derived from fat.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Solve for the unknown quantities. 1.What is 85% of 60? 2.What percent of 14 is 4.2? 3.63% of __________ is 504. 4.In one tennis match Andy served an “ace” on 15% of his serves. If he served 180 times, how many aces did he serve?

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.51 2.30% 3.800 4.27