Problem:
A shopper plans to purchase an item that has a listed price greater than and can use any one of three coupons. Coupon gives off the listed price, Coupon gives off the listed price, and Coupon gives off the amount by which the listed price exceeds .
Let and be the smallest and largest prices, respectively, for which Coupon saves at least as many dollars as Coupon or . What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let dollars be the purchase price of the stem. The savings provided by Coupon , , and respectively are , and . Coupon saves at least as much as Coupon if , so . Coupon saves at least as much as Coupon if , so . Therefore , and .
The problems on this page are the property of the MAA's American Mathematics Competitions