Difference between revisions of "1999 AHSME Problems/Problem 5"

(Created page with 'The marked price of a book was 30% less than the suggested retail price. Alice purchased the book for half the marked price at a Fiftieth Anniversary sale. What percent of the …')
 
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The marked price of a book was 30% less than the suggested retail price.  Alice purchased the book for half the marked price at a Fiftieth Anniversary sale.  What percent of the suggested retail price did Alice pay?
 
The marked price of a book was 30% less than the suggested retail price.  Alice purchased the book for half the marked price at a Fiftieth Anniversary sale.  What percent of the suggested retail price did Alice pay?
'''(A) 25%'''
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<math> \mathrm{(A)\ }25\%\qquad\mathrm{(B)\ }30\%\qquad\mathrm{(C)\ }35\%\qquad\mathrm{(D)\ }60\%\qquad\mathrm{(E)\ }65\% </math>
'''(B) 30%'''
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'''(C) 35%'''
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==Solution==
'''(D) 60%'''
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'''(E) 65%'''
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Without loss of generality, let's assume that the retail price was <math>100</math> USD.
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<math>30\%</math> off of <math>100</math> is equal to <math>100-100(0.3)=70</math>
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<math>\frac{70}{2}=35</math>
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<math>100-35=\boxed{65}</math> or <math>\boxed{E}</math>

Revision as of 12:41, 8 June 2011

The marked price of a book was 30% less than the suggested retail price. Alice purchased the book for half the marked price at a Fiftieth Anniversary sale. What percent of the suggested retail price did Alice pay? $\mathrm{(A)\ }25\%\qquad\mathrm{(B)\ }30\%\qquad\mathrm{(C)\ }35\%\qquad\mathrm{(D)\ }60\%\qquad\mathrm{(E)\ }65\%$

Solution

Without loss of generality, let's assume that the retail price was $100$ USD.

$30\%$ off of $100$ is equal to $100-100(0.3)=70$

$\frac{70}{2}=35$

$100-35=\boxed{65}$ or $\boxed{E}$