# 2002 AMC 8 Problems/Problem 14

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## 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

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. So the final answer is $44\%$, which is answer choice $B$.

## Video Solution

https://youtu.be/DUqszaQ01lM Soo, DRMS, NM

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