PSAT Math Multiple-Choice Question 312: Answer and Explanation

Question: 312

Juan is on his school's archery team. In a match, he gets 12 arrows to shoot at a target. He gets 8 points if the arrow hits the inner circle of the target and 4 points if it hits the outer circle. Which of the following equations represents Juan's total score if a of his arrows hit the inner circle and the rest hit the outer circle?

• A. p = 8a
• B. p = 8a + 4
• C. p = 48 + 4a
• D. p = 96 - 4a

Correct Answer: C

Explanation:

C

Difficulty: Hard

Getting to the Answer: The key to answering this question is to determine how many arrows hit each circle. If there are 12 arrows total and a hit the inner circle, the rest, or 12 - a, must hit the outer circle. Now, write the expression in words: points per inner circle, 8, times number of arrows in inner circle, a, plus points per outer circle, 4, times number of arrows in outer circle, 12 - a. Next, translate the words into numbers, variables, and operations: 8a + 4(12 - a). This is not one of the answer choices, so simplify the expression by -distributing the 4 and then combining like terms: 8a + 4(12 - a) = 8a + 48 - 4a = 4a + 48, so the equation is p = 4a + 48. Rearrange the order of the terms on the right side to arrive at (C).