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Difference between revisions of "2002 AMC 8 Problems/Problem 14"

Problem

A merchant offers a large group of items at $30\%$ off. Later, the merchant takes $20\%$ off these sale prices and claims that the final price of these items is $50\%$ off the original price. The total discount is $\text{(A)}\ 35\%\qquad\text{(B)}\ 44\%\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\%$

Solution

Solution 1

Let's assume that each item is $100$ dollars. First we take off $30\%$ off of $100$ dollars. $100\cdot0.7=70$

Next, we take off the extra $20\%$ as asked by the problem. $70\cdot0.80=56$

So the final price of an item is $56. We have to do $100-56$ because $56$ was the final price and we wanted the discount. $100-56=44$ so the final discount was $\boxed{\text{(B)}\ 44\%}$. Solution 2 Assume the price was$100. We can just do $100\cdot0.7\cdot0.8=56$ and then do $100-56=\boxed{\text{(B)}\ 44}$. That is the discount percentage wise.

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