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Difference between revisions of "2008 AMC 12A Problems/Problem 6"

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==Problem ==
 
==Problem ==
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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 <dollar/><math>90</math> rebate, and store B offers <math>25\%</math> off the same sticker price with no rebate. Heather saves <dollar/><math>15</math> by buying the computer at store A instead of store B. What is the sticker price of the computer, in dollars?
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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?
  
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<math>\textbf{(A)}\ 750 \qquad \textbf{(B)}\ 900 \qquad \textbf{(C)}\ 1000 \qquad \textbf{(D)}\ 1050 \qquad \textbf{(E)}\ 1500</math>
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<math>\mathrm{(A)}\ 750\qquad\mathrm{(B)}\ 900\qquad\mathrm{(C)}\ 1000\qquad\mathrm{(D)}\ 1050\qquad\mathrm{(E)}\ 1500</math>
  
 
==Solution==
 
==Solution==
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Let <math>S</math> be the sticker price.  
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Let the sticker price be <math>x</math>.
  
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Store A sells the computer for <math>A=S-0.15S-90=0.85S-90</math> dollars.
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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>.
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Store B sells the computer for <math>B=S-0.25S=0.75S</math> dollars.  
 
  
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Since she saves <dollar/><math>15</math> at store A, <math>15=B-A=0.75S-(0.85S-90)=-0.1S+90</math>. Thus, <math>S=750 \Rightarrow A</math>.  
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Heather saves <math>\</math><math>15</math> at store <math>A</math>, so <math>0.85x-90+15=0.75x</math>.
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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 22:44, 25 April 2008

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

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 $\mathrm{(A)}$.

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
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