SAT Math Multiple Choice Question 545: Answer and Explanation

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Question: 545

5. Sara is grocery shopping. She needs laundry detergent, which is on sale for 30% off its regular price of $8.00. She also needs dog food, which she can buy at three cans for $4.00. Which of the following represents the total cost, before tax, if Sara buys x bottles of laundry detergent and 12 cans of dog food?

  • A. C = 2.4x + 48
  • B. C = 5.6x + 16
  • C. C = 5.6x + 48
  • D. C = 8.4x + 16

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: Don't peek at the answers. They may confuse you because the numbers look different than the ones given in the question. Instead, write your own equation in words first, and then translate from English into math.

Getting to the Answer: Keep in mind that the laundry detergent is on sale, but the dog food is not. The detergent is 30% off, which means Sara only pays 100 – 30 = 70% of the price, or 0.7($8) = $5.60. The dog food is three cans for $4 and she buys 12 cans, which means she buys 4 sets of 3, so she pays 4 × $4 = $16 for the dog food. The total cost equals the detergent price ($5.60) times how many she buys (x) plus the total dog food price ($16). In math, this translates as C = 5.6x + 16. Note that there are variables in the answer choices, so you could also use the Picking Numbers strategy to answer this question.

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