# 2013 AMC 8 Problems/Problem 12

## Problem

At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the$150 regular price did he save? $\textbf{(A)}\ 25 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 33 \qquad \textbf{(D)}\ 40 \qquad \textbf{(E)}\ 45$

## Solution

First, find the amount of money one will pay for three sandals without the discount. This would = the regular price, $\textdollar 50$ $\times$ 3 sandals = $\textdollar 150$.

Then, find the amount of money using the discount: 50 + 0.6 $\times$ 50 + $\frac{1}{2}$ $\times$ 50 = $\textdollar 105$.

To find the percentage of the regular, do this: $\frac{105}{150}$ = $70 \%$.

To find the percent saved, do this: $100 \%$ - $70 \%$ = $\boxed{\textbf{(B)}\ 30}$

--Arpanliku 17:29, 27 November 2013 (EST) HIII

## See Also

 2013 AMC 8 (Problems • Answer Key • Resources) Preceded byProblem 11 Followed byProblem 13 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 All AJHSME/AMC 8 Problems and Solutions

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