Chapter 10, Problem 69E

You have a coupon worth $x\%$ off any item (including sale items) in a store. The particular item you want is on sale at $y\%$ off the marked price of $P. (Assume that both $x$ and $y$ are positive integers smaller than 100.)

a. Give an expression for the price of the item assuming that you first got the $y\%$ off sale price and then had the additional $x\%$ taken off using your coupon.

b. Give an expression for the price of the item assuming that you first got the $x\%$ off the original price using your coupon and then had the $y\%$ taken off from the sale.

c. Explain why it makes no difference in which order you have the discounts taken.