SAT Math Multiple Choice Question 427: Answer and Explanation

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Question: 427

7. When a homeowner hires a contractor to renovate a bathroom, the homeowner is charged for both labor and materials. By law, the contractor can charge sales tax on the materials, but not on the labor. If the contractor quotes the homeowner $3,000 for materials and $40 per hour for labor, and sales tax in the homeowner's state is 5.5%, which equation represents the total cost for the bathroom renovation if it takes the contractor h hours to complete the job?

  • A. c = (40h + 3,000)(1.055)
  • B. c = 1.055(40 + 3,000)h
  • C. c = 40h(1.055) + 3,000
  • D. c = 40h + 1.055(3,000)

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: Organize information as you read the question; the total cost includes the labor cost, the cost of the materials, and the 5.5% tax on the materials only.

Getting to the Answer: If the contractor works h hours, the labor cost of the renovation is the per-hour rate ($40) multiplied by the number of hours (h) or 40h. To this amount, add the $3,000 for materials, which are taxed at a rate of 5.5% and should therefore be multiplied by 1.055. The total cost is given by the equation c = 40h + 1.055(3,000), which is (D).

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