SAT Math Multiple Choice Question 823: Answer and Explanation
13. A construction company prepares an estimate to install a new pool for a homeowner.The estimate includes h hours of labor, where h > 80. The company's goal is for the estimate to be within 8 hours of the actual numberof hours of labor. If the company meets the goal and it takes a hours of actual labor, which inequality represents the relationship between the estimatednumber of hours of labor and the actual number of hours of labor?
Correct Answer: D
Category: Heart of Algebra / Inequalities
Strategic Advice: You can use an absolute value to represent an unknown difference that is described as "within" a certain amount-you don't know whether the end result is more or less, but you do know it is within a certain range.
Getting to the Answer: The difference between the actual number of hours of labor, a, and the number of hours the company estimated, h, is |a - h|. If the company meets their goal, the difference is less than 8, which can be represented as |a - h| ≤ 8 or -8 ≤ a - h ≤ 8. This means (D) is correct.