1995 AJHSME Problems/Problem 10

Problem

A jacket and a shirt originally sold for $$ (Error compiling LaTeX. Unknown error_msg)80 $and <dollar/>40, respectively. During a sale Chris bought the <dollar/>80 jacket at a$ 40\% $discount and the <dollar/>40 shirt at a$ 55\% $discount. The total amount saved was what percent of the total of the original prices?$ \text{(A)}\ 45\% \qquad \text{(B)}\ 47\dfrac{1}{2}\% \qquad \text{(C)}\ 50\% \qquad \text{(D)}\ 79\dfrac{1}{6}\% \qquad \text{(E)}\ 95\%$.

Solution

Chris would have spent $40 + 80 = 120$ dollars if there were no sale.

The sale means that he saved $80(0.40) + 40(0.55) = 32 + 22 = 54$ dollars.

He saved $\frac{54}{120}\cdot 100\% = 0.45 \cdot 100\% = 45\%$ off the total of the original prices, and the answer is $\boxed{A}$ .

1995 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
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1995 AJHSME Problems/Problem 10

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