PSAT Math Multiple-Choice Question 160: Answer and Explanation

Question: 160

A piano player charges a flat fee for an appearance plus an hourly rate based on the length of the performance. The equation C = 100t + 50 will relate the total charge C, in dollars, for a performance to the time t, in hours, of a performance. Based on this equation, how many additional hours will the length of the performance need to be for the piano player to charge an additional dollar?

• A.
• B.
• C. 50
• D. 100

Correct Answer: A

Explanation:

A

The question asks how many additional hours a performance will need to be for the piano player to charge an additional dollar. Although there are numbers in the answer choices, plugging in the answers is not the ideal approach here because they represent the difference rather than a value in the equation. Instead, since there is a relationship between the two variables, this can be solved using Plugging In. Let t = 2. If t = 2, then C = 100(2) + 50 = 250. The question asks about the piano player charging an additional dollar. Since the amount charged is C, let C = 250 + 1 = 251. Plug C = 251 into the equation to get 251 = 100t + 50. Solve for t. Subtract 50 from both sides to get 201 =100t. Divide both sides by 100 to get 2.01 = t. The question asks for the additional hours, so subtract the two values of t to get 2.01 - 2 = 0.01. This is equivalent to , so the correct answer is (A).