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2008 AMC 10A Problem 8

Problem 8 of 25EasierAlgebraArithmetic

Heather compares the price of a new computer at two different stores. Store A offers 15%15\% off the sticker price followed by a $90\$90 rebate, and store B offers 25%25\% off the same sticker price with no rebate. Heather saves $15\$15 by buying the computer at store A instead of store B. What is the sticker price of the computer, in dollars?

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Solution

Let xx be the sticker price. Heather pays 0.85x−900.85x - 90 at store A and 0.75x0.75x at store B. Since store A is $15\$15 cheaper, 0.85x−90=0.75x−15, 0.85x - 90 = 0.75x - 15, which gives 0.1x=75,0.1x = 75, so x=750.x = 750. Thus, the correct answer is A.
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