5 3 A Solving Percent Problems Using Equations

Percent Problems into Equations To solve a percent problem, we express it as an equation with an unknown quantity. The following table is helpful when translating from a percent problem to an equation. Word of is what Mathematical Symbol Multiplication symbol: or ( ) or · = Any letter, for example, n find n= Tobey & Slater, Basic College Mathematics, 6 e 2

Percent Problems into Equations Example: Translate into an equation. What is 9% of 65? n = 9% 65 Example: Translate into an equation. 24 is what percent of 144? 24 = n 144 Tobey & Slater, Basic College Mathematics, 6 e 3

Solving a Percent Problem A percent problem has three different parts. amount = percent base Any one of the three quantities may be unknown. 1. When we do not know the amount: n = 10% 500 2. When we do not know the base: 50 = 10% n 3. When we do not know the percent: 50 = n 500 Tobey & Slater, Basic College Mathematics, 6 e 4

Solving a Percent Problem: Amount Unknown amount = percent base Example: What is 9% of 65? n = 9% 65 n = (0. 09) (65) n = 5. 85 is 9% of 65. Tobey & Slater, Basic College Mathematics, 6 e 5

Solving a Percent Problem: Base Unknown amount = percent base Example: 36 is 6% of what? 36 = 6% n 36 = 0. 06 n 36 is 6% of 600. Tobey & Slater, Basic College Mathematics, 6 e 6

Solving a Percent Problem: Percent Unknown amount = percent base Example: 24 is what percent of 144? 24 = n 144 Tobey & Slater, Basic College Mathematics, 6 e 7

§ 5. 3 B Solving Percent Problems Using Proportions © 2010 Pearson Prentice Hall.

The Parts of a Percent Proportions are another way to solve a percent problem. To use this proportion, we need to find the amount, base, and percent number in a word problem. Tobey & Slater, Basic College Mathematics, 6 e 9

The Parts of a Percent Proportion 10% of 500 is 50. p is the percent number. The amount, a, is the part compared to the whole. The base, b, is the entire quantity. Tobey & Slater, Basic College Mathematics, 6 e 10

The Parts of a Percent Proportion Example: Identify the amount, base, and percent number. What is 9% of 65? The amount, a, is unknown. a = the amount (unknown) The base usually follows the word of. b = 65 The value of p is 9. p=9 24 is what percent of 144? The amount is 24. a = 24 The base usually follows the word of. b = 144 The value of p is unknown. p = the percent (unknown) Tobey & Slater, Basic College Mathematics, 6 e 11

Solving a Percent Problem: Amount Unknown Example: p=9 What is 9% of 65? a = unknown b = 65 Cross multiply. Divide both sides by 100. Simplify. 5. 85 is 9% of 65. Tobey & Slater, Basic College Mathematics, 6 e 12

Solving a Percent Problem: Base Unknown Example: p=6 36 is 6% of what? a = 36 b = unknown Cross multiply. Divide both sides by 6. Simplify. 36 is 6% of 600. Tobey & Slater, Basic College Mathematics, 6 e 13

Solving a Percent Problem: Percent Unknown Example: p = unknown 24 is what percent of 144? a = 24 b = 144 Cross multiply. Divide both sides by 144. Simplify. Tobey & Slater, Basic College Mathematics, 6 e 14