¶ 2005 AMC8 Problem 11
Problem:
The sales tax rate in Bergville is . During a sale at the Bergville Coat Closet, the price of a coat is discounted from its price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up and adds sales tax, then subtracts from this total. Jill rings up , subtracts of the price, then adds of the discounted price for sales tax. What is Jack's total minus Jill's total?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
To add sales tax to an item, multiply the price by . To calculate a discount, multiply the price by . Because both actions require only multiplication, and because multiplication is commutative, the order of operations doesn't matter. Jack and Jill will get the same total.
Note: Jack's final computation is and Jill's is . Both yield the same product, .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions