# Difference between revisions of "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 thus the answer is $\mathrm{(A)}$.

### Solution 2

The $90$ at store $A$ is $15$ greater than the additional $25\%-15\% = 10\%$ off at store $B$.

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

## See Also

 2008 AMC 12A (Problems • Answer Key • Resources) Preceded byProblem 5 Followed byProblem 7 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 12 Problems and Solutions
 2008 AMC 10A (Problems • Answer Key • Resources) Preceded byProblem 7 Followed byProblem 9 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. Invalid username
Login to AoPS