SAT Math Multiple Choice Question 471: Answer and Explanation

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Question: 471

6. A DVD rental kiosk dispenses movies for $1 for a 24-hour rental. After the initial rental period has expired, customers are charged a $0.50 late fee for every 24 hours that the movie is returned late. If a customer rents four movies at one time, which of the following graphs represents the total possible charges in late fees, assuming he returns all the movies together?

  • A.
  • B.
  • C.
  • D.

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: Be very careful that you understand what the question is asking. The question wants to know about total late fees, not the total charges and not the late fees per movie.

Getting to the Answer: Think about the question conceptually before you examine the graphs. The question asks about late fees only, not total charges. If the movies are returned on time, or 0 days late, the late fees will be $0, so the graph must start at the origin. Eliminate B and D. Next, the question asks about total late fees for all four movies. The late fee is $0.50 per movie per day, so the late fee for all four movies is 4 × $0.5 = $2 per day. This means (C) must be correct because the points increase at a rate of $2 per day. (Note that A shows the possible late fees for returning one movie late.)

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