2008 AMC 10A Problem 8

Question

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

Let

x

be the sticker price and write each store’s final price

Store A costs

0.85x - 90

and store B costs

0.75x,

with A cheaper by

\$15

Let

x

be the sticker price. Heather pays

0.85x - 90

at store A and

0.75x

at store B.

Since store A is

\$15

cheaper,

0.85x - 90 = 0.75x - 15,

which gives

0.1x = 75,

so

x = 750.

Thus, the correct answer is A.

Problem 8 in other years