2008 AMC 12A Problems/Problem 6: Difference between revisions

Revision as of 11:13, 17 August 2020

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 $\$ 750$ .

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

2008 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination

@@ Line 11: / Line 11: @@
 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>15<math> at store </math>A<math>, so </math>0.85x-90+15=0.75x<math>.
+Heather saves <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>.
+Solving, we find <math>x=750</math>, and the thus answer is <math>\mathrm{(A)}</math>.
 ===Solution 2===
-The </math>\textdollar 90<math> in store </math>A<math> is </math>\textdollar 15<math> better than the additional </math>10\%<math> off at store </math>B<math>.
+The <math>\$ 90</math> in store <math>A</math> is <math>\$ 15</math> better than the additional <math>10\%</math> off at store <math>B</math>.
-Thus the </math>10\%<math> off is equal to </math>\textdollar 90<math> - </math>\textdollar 15<math> </math>=<math> </math>\textdollar 75<math>, and therefore the sticker price is </math>\textdollar 750$.
+Thus the <math>10\%</math> off is equal to <math>\$ 90</math> - <math>\$ 15</math> <math>=</math> <math>\$ 75</math>, and therefore the sticker price is <math>\$ 750</math>.
 ==See Also==

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