2008 AMC 12A Problem 6

Below is the professionally curated solution for Problem 6 of the 2008 AMC 12A, 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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Concepts:percentage linear equation

Difficulty rating: 1270

Heather compares the price of a new computer at two different stores. Store A offers $15\%$ off the sticker price followed by a $90 rebate, and store B offers $25\%$ 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?

$750$

$900$

$1000$

$1050$

$1500$

Solution:

Let $x$ be the sticker price in dollars. Store A charges $0.85x - 90$ dollars, and store B charges $0.75x$ dollars.

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

Thus, A is the correct answer.

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