PSAT Math Multiple-Choice Question 497: Answer and Explanation

Question: 497

James joins a local billiards club. The club charges a monthly membership fee of $15 and each hour of play costs $1.50. Which of the expressions below shows James’s monthly cost at the billiards club when he plays for h hours?

• A. (15 + h)1.50
• B. (15 + h)0.50
• C. 0.50h + 15
• D. 1.50h + 15

Correct Answer: D

Explanation:

D

The question asks for an equation that models a specific situation. There are variables in the answer choices, so plug in. Make h = 2. According to the question, each hour of play costs $1.50, which means that for 2 hours of play, James will pay $1.50(2) = $3. There is a monthly membership fee of $15, which will need to be added to his charge for 2 hours of play to get $3 + $15 = $18. This is the target value; circle it. Now plug h = 2 into the answer choices to see which one matches the target value. Choice (A) becomes (15 + 2)(1.50) = (17)(1.50) = 25.50. This does not match the target value, so eliminate (A). Choice (B) becomes (15 + 2)(0.50) = (17)(0.50) = 8.50. Eliminate (B). Choice (C) becomes (0.50) (2) + 15 = 1 + 15 = 16. Eliminate (C). Choice (D) becomes (1.50)(2) + 15 = 3 + 15 = 18. This matches the target value. The correct answer is (D).