2012 AMC 8 Problems/Problem 8

Problem

A shop advertises everything is "half price in today's sale." In addition, a coupon gives a 20% discount on sale prices. Using the coupon, the price today represents what percentage off the original price?

$\textbf{(A)}\hspace{.05in}10\qquad\textbf{(B)}\hspace{.05in}33\qquad\textbf{(C)}\hspace{.05in}40\qquad\textbf{(D)}\hspace{.05in}60\qquad\textbf{(E)}\hspace{.05in}70$

Solution

Apply the first discount, so the price is $50$ % of the original. Then apply the next $20$ % discount to find that the price is now $40$ % of the original. However, we need to find the percentage off the original price, not the current percentage of the price. We then subtract $40$ % from $100$ % (the original price of the item), to find the answer, $\boxed{\textbf{(D)}\ 60}$ .

2012 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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2012 AMC 8 Problems/Problem 8

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