SAT Math Multiple Choice Question 474: Answer and Explanation
9. A cable company offers movie rental packages. If you join the Movie Fan club, you get 10 movies for $20 and each movie after that costs $2.50. If you join the Movie Super Fan club, you get unlimited movies for a year for $75. How many movies would a person need to rent for each package to cost the same amount over a one-year period?
- A. 22
- B. 30
- C. 32
- D. 57
Correct Answer: C
Category: Heart of Algebra / Linear Equations
Strategic Advice: When a question asks for a number that results in the same amount of something, it usually means writing an equation with one expression set equal to the other.
Getting to the Answer: Let m represent the number of movie rentals. The Movie Super Fan package costs $75 for unlimited rentals, so write 75 on one side of the equal sign. The other package costs $2.50 per rental (not including the first 10 rentals), or 2.5(m – 10), plus a flat $20 fee for those first 10 rentals, so write 2.5(m – 10) + 20 on the other side of the equal sign. Simplify the right-hand side of the equation and then use inverse operations to solve for m.
Renting 32 movies would result in equal package costs, so (C) is correct. Note that this is one of those rare occasions when you could work backward from the answer choices (even though it may use up valuable time). Try 32 in the scenario: The first 10 movies are free, so you must pay for 22 at a cost of $2.50 each, making the total cost of the Movie Fan package $20 + 22($2.50) = $75.