# 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. 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 $100$ 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 $\boxed{(B) 44 \%}$.

## Solution 2

Let $x$ be the price of an item on sale. When the item is $30\%$ off, its new price is $$(1-0.3)x=0.7x.$$ When $20\%$ is taken off of that price, the item's final sales price is $$(1-0.2)\cdot0.7x=0.8\cdot0.7x=0.56x=(1-0.44)x.$$ Therefore, the item was $44\%$ off, so the answer is $\boxed{(B)}$.

## Video Solution

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