2008 AMC 12A Problems/Problem 6

Problem

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

$\textbf{(A)}\ 750 \qquad \textbf{(B)}\ 900 \qquad \textbf{(C)}\ 1000 \qquad \textbf{(D)}\ 1050 \qquad \textbf{(E)}\ 1500$

Solution

Let $S$ be the sticker price.

Store A sells the computer for $A=S-0.15S-90=0.85S-90$ dollars. Store B sells the computer for $B=S-0.25S=0.75S$ dollars.

Since she saves <dollar/> $15$ at store A, $15=B-A=0.75S-(0.85S-90)=-0.1S+90$ . Thus, $S=750 \Rightarrow A$ .

2008 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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2008 AMC 12A Problems/Problem 6

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