1999 AHSME Problems/Problem 5

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 $\boxed{E}$

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1999 AHSME Problems/Problem 5

Solution