1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 4.6 Solving Percent Problems by Using the Equation: R  B = A

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

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. The Equation R  B = A Terms Related to the Basic Equation R  B = A R = rate or percent (as a decimal number or fraction) B = base (number we are finding the percent of) A = amount (a part of the base) “of” means to multiply (the raised dot, , is used in the equation). “is” means equals ( = ).

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Problem Solving with the Equation R  B = A Notes The basic equation can be written in the form A = R  B. This form is convenient when solving for the amount, A.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Problem Solving with the Equation R  B = A Three Basic Types of Percent Problems Using R  B = A Type 1:Find the amount given the base and the percent. What is 65% of 800? A = 0.65  800 Type 2:Find the base given the percent and the amount. 42% of what number is 157.5? 0.42  B = 157.5

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Problem Solving with the Equation R  B = A Three Basic Types of Percent Problems Using R  B = A (cont.) Type 3:Find the percent given the base and the amount. What percent of 92 is 115? R  92 = 115

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. What is 65% of 800? Solution In this case, R = 65% = 0.65 and B = 800. We want to find the amount A. So 65% of 800 is 520. Example 1: Finding the Amount

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Notes The operations in these examples can be performed with a calculator or by hand, as shown in Example 1. In either case, the equations should be written so that the “=” signs are aligned one under the other. Also, writing the equations and the calculated values will help you remember whether you are multiplying or dividing. Problem Solving with the Equation R  B = A

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. 42% of what number is 157.5? Solution Here, R = 42% = 0.42 and A = 157.5. We want to find the base B. So 42% of 375 is 157.5. Example 2: Finding the Base

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. ________% of 92 is 115. Solution For this problem, B = 92 and A = 115. We want to find the percent R. So 125% of 92 is 115. Example 3: Finding the Percent

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Find 75% of 56. Solution Here, and B = 56. We want to find the amount A. So 75% of 56 is 42. Example 4: Finding the Amount

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. 250 is 62.5% of ________. Solution For this problem, and A = 250. We want to find the base B. Example 5: Finding the Base

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Finding the Base (cont.) Thus the amount 250 is 62.5% of 400.

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Use the basic equation R  B = A (or A = R  B ) to answer the following problems. 1.What is 40% of 73? 2.What percent of 88 is 55? 3.87.5% of what number is 21? 4._____ % of 4 is 7? 5.12% of _____ is 15? 6.150% of 12.6 is _____.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.29.2 2.62.5% 3.24 4.175% 5.125 6.18.9