# 2008 AMC 12A Problems/Problem 6

The following problem is from both the 2008 AMC 12A #6 and 2008 AMC 10A #8, so both problems redirect to this page.

## Problem

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

## Solution

### Solution 1

Let the sticker price be $x$.

The price of the computer is $0.85x-90$ at store $A$, and $0.75x$ at store $B$.

Heather saves $15$ at store $A$, so $0.85x-90+15=0.75x$.

Solving, we find $x=750$, and the thus answer is $\mathrm{(A)}$.

### Solution 2

The $90$ in store $A$ is $15$ better than the additional $10\%$ off at store $B$.

Thus the $10\%$ off is equal to $90$ - $15$ $=$ $75$, and therefore the sticker price is $750$.

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 