2008 AMC 12A Problem 6

Attempt Problem 6 of the 2008 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 12A solutions, or check the answer key.

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6.

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 rebate, and store B offers 25%25\% off the same sticker price with no rebate. Heather saves $15 by buying the computer at store A instead of store B. What is the sticker price of the computer, in dollars?

750750

900900

10001000

10501050

15001500

Answer: A
Concepts:percentagelinear equation
Difficulty rating: 1270
Solution:

Let xx be the sticker price in dollars. Store A charges 0.85x900.85x - 90 dollars, and store B charges 0.75x0.75x dollars.

Since store A is 1515 dollars cheaper, 0.85x90=0.75x15, 0.85x - 90 = 0.75x - 15, so 0.10x=750.10x = 75 and x=750.x = 750.

Thus, A is the correct answer.

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