# 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 $&#036/100$ (Error compiling LaTeX. ! Misplaced alignment tab character &.). First we take off $30\%$ off of $100. $$100\cdot0.70=$ $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 $44\%$

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

## 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.

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