PSAT Math Multiple-Choice Question 232: Answer and Explanation

Question: 232

Annalisa has 10 beanbags to throw in a game. She gets 7 points if a beanbag lands in the smaller basket and 3 points if it lands in the larger basket. If she gets b beanbags into the larger basket and the rest into the smaller basket, which expression represents her total score?

• A. 3b
• B. 3b + 7
• C. 30 + 4b
• D. 70 - 4b

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Heart of Algebra/Linear Equations

Getting to the Answer: Write the expression in words first: points per large basket (3) times number of beanbags in large basket (b), plus points per small basket (7) times number of beanbags in small basket. If there are 10 beanbags total and b go into the larger basket, the rest, or 10 - b, must go into the smaller basket. Now, translate the words to numbers, variables, and operations: 3 b + 7(10 - b). This is not one of the answer choices, so simplify the expression by distributing the 7 and combining like terms: 3 b + 7(10 - b) = 3 b + 70 - 7 b = 70 - 4 b. This matches (D).