Difference between revisions of "1999 AHSME Problems/Problem 5"
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| + | ==Problem== | ||
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? | ||
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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> | <math> \mathrm{(A)\ }25\%\qquad\mathrm{(B)\ }30\%\qquad\mathrm{(C)\ }35\%\qquad\mathrm{(D)\ }60\%\qquad\mathrm{(E)\ }65\% </math> | ||
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Without loss of generality, let's assume that the retail price was <math>100</math> USD. | Without loss of generality, let's assume that the retail price was <math>100</math> USD. | ||
| − | <math>30\%</math> off of <math>100</math> is equal to <math>100-100(0.3)=70</math> | + | The marked price of the book is <math>30 \%</math> off of <math>100</math> which is equal to <math>100-100(0.3)=70.</math> |
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| + | Half of that marked price is <math>0.5(70)=35.</math> | ||
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| + | Therefore the percent Alice payed of the suggested retail price is <math>35/100=\boxed{\mathrm{(C) } 35 \%}.</math> | ||
| − | + | ==See Also== | |
| − | + | {{AHSME box|year=1999|num-b=4|num-a=6}} | |
| + | {{MAA Notice}} | ||
Latest revision as of 10:33, 12 July 2014
Problem
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?
Solution
Without loss of generality, let's assume that the retail price was 
USD.
The marked price of the book is 
off of which is equal to 
Half of that marked price is 
Therefore the percent Alice payed of the suggested retail price is 
See Also
| 1999 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
