SAT Math Multiple Choice Question 583: Answer and Explanation

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Question: 583

13. 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



Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: The key to answering this question is determining how many beanbags go into each size 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.

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 (10 – b). Now, translate the words to numbers, variables, and operations: 3b + 7(10 – b). This is not one of the answer choices, so simplify the expression by distributing the 7 and then combining like terms: 3b + 7(10 – b) = 3b + 70 – 7b = 70 – 4b.

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