SAT Math Multiple Choice Question 805: Answer and Explanation

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Question: 805

10. The most popular items at a bakery are its raspberry scones and its lemon poppy seedmuffins. The shop sells both items in boxes of 12 at a cost of $15 per box of raspberryscones and $9 per box of lemon poppy seed muffins. On Friday and Saturday, the shopearned $396 by selling a total of 46 boxes of these two items. If r and l represent the number of boxes of raspberry scones and lemon poppy seed muffins soldover the two-day period, respectively, which of the following systems of equationscould be used to find the number of boxes of each type of item sold?

  • A.
  • B.
  • C.
  • D.

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Strategic Advice: In a lengthy word problem that contains lots of numbers, it may help to cross out information that does not impact the answer.

Getting to the Answer: Here, the number of items in each box does not matter because the entire question is about the boxes of items (not the number of items), so cross out the 12. This means you can eliminate B and D right away. The question states that r and l represent the number of boxes of raspberry scones and lemon poppy seed muffins sold and that the shop sold a total of 46 boxes of these items, so the first equation will be r + l = 46. The shop collects $15 for each box of raspberry scones, which translates to 15r, and $9 for each box of lemon poppy seed muffins, which becomes 9l. Put together, the second equation is 15r + 9l = 396, making (A) the correct answer. Note that because the question doesn't ask about the number sold per day, you don't need to incorporate a 2 into either equation.

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