SAT Math Multiple Choice Question 428: Answer and Explanation

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Question: 428

8. A picture-framing shop sells ready-made frames and also does custom framing using different kinds and widths of wood or metal. The shop has a three-day sale. During the sale, for an 11-inch × 14-inch frame, a ready-made frame costs $12 and a custom frame costs $30. Over the course of the three days, the shop sells ninety-two 11 × 14 frames and collects $1,788. Solving which system of equations would yield the number of 11 × 14 ready-made frames r and the number of 11 × 14 custom frames c that the shop sold during the three-day sale?

  • A.
  • B.
  • C.
  • D.

Correct Answer: D



Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Strategic Advice: One equation should represent the total number of frames, while the other equation should represent the revenue from the frames.

Getting to the Answer: The number of custom frames c plus the number of ready-made frames r equals the total number of frames sold, 92. Therefore, one equation is c + r = 92. This means you can eliminate B and C. Now write the revenue equation: Revenue per custom frame (30c) plus revenue per ready-made frame (12r) equals the total amount collected (1,788). The revenue equation is 30c + 12r = 1,788. Don't let A fool you. The question says nothing about the revenue per day of the sale, so there is no reason to divide by 3. Choice (D) is correct.

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