SAT Math Multiple Choice Question 580: Answer and Explanation

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Question: 580

10. A movie rental kiosk dispenses DVDs and Blu-rays. DVDs cost $2.00 per night and Blu-rays cost $3.50 per night. Between 5 PM and 9 PM on Saturday, the kiosk dispensed 209 movies and collected $562.00. Solving which system of equations would yield the number of DVDs, d, and the number of Blu-rays, b, that the kiosk dispensed during the 4-hour period?

  • 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 rentals, while the other equation represents the cost of the rentals.

Getting to the Answer: The number of DVDs plus the number of Blu-rays equals the total number of rentals, 209. Therefore, one equation is d + b = 209. This means you can eliminate choices B and C. Now write the cost equation: cost per DVD times number of DVDs (2d) plus cost per Blu-ray times number of Blu-rays (3.5b) equals the total amount collected (562). The cost equation is 2d + 3.5b = 562. Don't let A fool you. The question says nothing about the cost per hour so there is no reason to divide the cost by 4. Choice (D) is correct.

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