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

Problem 14

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 #1

Let's assume that each item is $100. First we take off $30\%$ off of$100. $100\cdot0.70=$&#036;70

Next, we take off the extra$(Error compiling LaTeX. ! Missing$ inserted.)20\%$as asked by the problem. &#036;70\cdot0.80=&#036;56 So the final price of an item is &#036;56. We have to do$ (Error compiling LaTeX. ! Missing $inserted.)100-56 $because$56 $was the final price and we wanted the discount.$100-56=44 $so the final discount was$44\%$$(Error compiling LaTeX. ! Missing$ inserted.) \text{(A)}\ 35\%\qquad\boxed{\text{(B)}\ 44\%}\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\% $Solution #2 Assume the price was$100. We can just do $100\cdot0.7\cdot0.8=56$ and then do $100-56=44$ That is the discount percentage wise. $\text{(A)}\ 35\%\qquad\boxed{\text{(B)}\ 44\%}\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\%$