314 CHAPTER 6 Algebra, Graphs, and Functions This general procedure for solving word problems is illustrated in Examples 1 through 4. In these examples, the equations we obtain are mathematical models of the given situations. Our first example, like many applications of algebra, involve percents. The word percent means “per hundred.” For example, 15% means 15 per hundred, or 15/100. When 15/100 is converted to a decimal number, we obtain 0.15. Thus, 15% 0.15. = See Section 10.1 for more discussion involving percents. Learning Catalytics Keyword: Angel-SOM-6.3 (See Preface for additional details.) Example 1 Salary Plus Commission Imogen works as a copier salesperson. Her total weekly compensation includes a salary of $525 plus a commission of 15% of her weekly sales amount. For one week, Imogen’s compensation was $2370 which included her salary and her commission. Determine her sales amount for the week. Solution The unknown quantity is Imogen’s sales amount for the week. We will let x represent the sales amount. Next, Imogen’s commission is 15% of her sales amount. Thus, her commission is 15% times x, or x 0.15 . We will use this expression, x 0.15 , along with the given information to construct an equation that will allow us to solve for x. Let x x Imogen’s sales amount 0.15 Imogen’s commission = = Then, x Salary Commission Total Compensation 525 0.15 2370 + = + = Now, solve the equation. + = + − = − = = = x x x x x 525 0.15 2370 525 0.15 525 2370 525 0.15 1845 0.15 0.15 1845 0.15 12,300 Therefore, Imogen’s sales amount for the week was $12,300. CHECK: The check is made with the information given in the original problem. = + = + = + = Total compensation Salary Commission 525 (0.15)(12,300) 525 1845 2370 Therefore, the answer checks. 7 Now try Exercise 31 Example 2 Party Punch Casey needs to make 2 gallons, or 256 ounces, of fruit punch for a birthday party. Her recipe requires mixing pineapple juice, ginger ale, and orange juice. The amount of ginger ale required is twice the amount of pineapple juice, and the amount of orange juice required is five times the amount of pineapple juice. How many ounces of pineapple juice, ginger ale, and orange juice should Casey mix together to make the punch? Solution The amount of ginger ale and the amount of orange juice are both described in terms of the amount of pineapple juice. The amount of ginger ale is twice the amount of pineapple juice. The amount of orange juice is five times the amount of pineapple juice. Therefore, we will let x represent the number of ounces Lopolo/Shutterstock
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