# 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$ $&#036;100\cdot0.70=&#036;70$ (Error compiling LaTeX. )

Next, we take off the extra $20\%$ as asked by the problem. $&#036;70\cdot0.80=&#036;56$ (Error compiling LaTeX. )

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 $44\%$ $\text{(A)}\ 35\%\qquad\boxed{\text{(B)}\ 44\%}\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\%$ ## 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. $\text{(A)}\ 35\%\qquad\boxed{\text{(B)}\ 44\%}\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\%$