SAT Math Multiple Choice Question 823: Answer and Explanation

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Question: 823

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?

  • A.
  • B.
  • C.
  • D.

Correct Answer: D

Explanation:

D

Difficulty: Medium

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.

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