PSAT Math Multiple-Choice Question 229: Answer and Explanation

Question: 229

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 p.m. and 9 p.m. 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

Explanation:

D

Difficulty: Medium

Category: Heart of Algebra/Systems of Linear Equations

Getting to the Answer: One equation should represent the total number of rentals, while the other equation represents the cost of the rentals. 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 (2 d) plus cost per Blu-ray times number of Blu-rays (3.5 b) equals the total amount collected (562). The cost equation is 2 d + 3.5 b = 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.