SAT Math Multiple Choice Practice Question 157: Answer and Explanation

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Question: 157

3. A store sells T-shirts for $15.00 each. If you buy 2, 3, or 4 shirts, every shirt after the first is 20% off. After this, every shirt after the fourth is 50% off the original price. An expression that represents the total cost, C, of buying n shirts, where n > 4, would be

A. C = 15n
B. C = 15 + 12(n - 1) + 7.50(n - 4)
C. C = 15 + 12(n - 4) + 7.5n
D. C = 51 + 7.5(n - 4)
E. C = 51 + 7.5n

Correct Answer: D

Explanation:

D. The question tells you that n > 4, so start by finding the price of the first four shirts. The first shirt costs $15. The next three are 20% off, so they each cost 80% of $15, which is $12. Thus, the total cost of the first four shirts is $15 + 3 × $12 = $51. All subsequent shirts are 50% off $15, or $7.50. But you've already paid for the first four shirts in your formula, so they cost not 7.5n, but 7.5(n - 4). Combining results gives you Choice (D).

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