# 2005 AMC 8 Problems/Problem 11

## Problem

The sales tax rate in Bergville is 6%. During a sale at the Bergville Coat Closet, the price of a coat is discounted 20% from its $90.00 price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up$90.00 and adds 6% sales tax, then subtracts 20% from this total. Jill rings up \$90.00, subtracts 20% of the price, then adds 6% of the discounted price for sales tax. What is Jack's total minus Jill's total? $\textbf{(A)}\ -\textdollar 1.06\qquad\textbf{(B)}\ -\textdollar 0.53 \qquad\textbf{(C)}\ \textdollar 0\qquad\textbf{(D)}\ \textdollar 0.53\qquad\textbf{(E)}\ \textdollar 1.06$

## Solution

The price Jack rings up is $\textdollar{(90.00)(1.06)(0.80)}$. The price Jill rings up is $\textdollar{(90.00)(0.80)(1.06)}$. By the commutative property of multiplication, these quantities are the same, and the difference is $\boxed{\textbf{(C)}\ \textdollar 0}$.

Reminder: Commutative states abc = bac= acb =..... and is the same in any order. This only works for addition and multiplication.

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