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?
  

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?

$\mathrm{(A)\ }25\%\qquad\mathrm{(B)\ }30\%\qquad\mathrm{(C)\ }35\%\qquad\mathrm{(D)\ }60\%\qquad\mathrm{(E)\ }65\%$

Solution

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

The marked price of the book is $30 \%$ off of $100$ which is equal to $100-100(0.3)=70.$

Half of that marked price is $0.5(70)=35.$

Therefore the percent Alice payed of the suggested retail price is $35/100=\boxed{\mathrm{(C) } 35 \%}.$

See Also

1999 AHSME (ProblemsAnswer KeyResources)
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

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