Difference between revisions of "2008 AMC 12A Problems/Problem 6"
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==Problem == | ==Problem == | ||
− | Heather compares the price of a new computer at two different stores. Store A offers <math>15\%</math> off the sticker price followed by a < | + | Heather compares the price of a new computer at two different stores. Store <math>A</math> offers <math>15\%</math> off the sticker price followed by a <math>\</math><math>90</math> rebate, and store <math>B</math> offers <math>25\%</math> off the same sticker price with no rebate. Heather saves <math>\</math><math>15</math> by buying the computer at store <math>A</math> instead of store <math>B</math>. What is the sticker price of the computer, in dollars? |
− | <math>\ | + | <math>\mathrm{(A)}\ 750\qquad\mathrm{(B)}\ 900\qquad\mathrm{(C)}\ 1000\qquad\mathrm{(D)}\ 1050\qquad\mathrm{(E)}\ 1500</math> |
==Solution== | ==Solution== | ||
− | Let <math> | + | Let the sticker price be <math>x</math>. |
− | + | The price of the computer is <math>0.85x-90</math> at store <math>A</math>, and <math>0.75x</math> at store <math>B</math>. | |
− | |||
− | + | Heather saves <math>\</math><math>15</math> at store <math>A</math>, so <math>0.85x-90+15=0.75x</math>. | |
+ | |||
+ | Solving, we find <math>x=750</math>, and the thus answer is <math>\mathrm{(A)}</math>. | ||
==See Also== | ==See Also== | ||
{{AMC12 box|year=2008|ab=A|num-b=5|num-a=7}} | {{AMC12 box|year=2008|ab=A|num-b=5|num-a=7}} |
Revision as of 23:44, 25 April 2008
Problem
Heather compares the price of a new computer at two different stores. Store offers
off the sticker price followed by a
rebate, and store
offers
off the same sticker price with no rebate. Heather saves
by buying the computer at store
instead of store
. What is the sticker price of the computer, in dollars?
Solution
Let the sticker price be .
The price of the computer is at store
, and
at store
.
Heather saves at store
, so
.
Solving, we find , and the thus answer is
.
See Also
2008 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 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 |