PSAT Math Multiple-Choice Question 53: Answer and Explanation

Question: 53

The number of bonus points, B(p), that a credit card holder receives is given by the function B(p) = ap + 7, where p represents the number of purchases made and a is a constant. If the number of purchases is increased by 4, the number of bonus points increases by 25. What is the value of a?

• A. 4
• B. 4.5
• C. 6.25
• D. 11

Correct Answer: C

Explanation:

C

The question asks for the value of the constant a. The question states that the number of bonus points increases by 25 when the number of purchases (p) increases by 4. To avoid working with multiple variables, pick a starting number for p. If p = 0, then the number of bonus points is: B(p) = a(0) + 7, or 7. When the number of purchases is increased by 4, the number of bonus points increases by 25. So if p = 0 + 4 = 4, then B(p) = 7 + 25 = 32. To find the value of a, plug B(p) = 32 and p = 4 into the equation and solve for a. The equation becomes 32 = a(4) + 7, or 32 = 4a + 7. This simplifies to 25 = 4a, or a = 6.25. The correct answer is (C).