Problem:
A customer who intends to purchase an appliance has three coupons, only one of which may be used:
Coupon : off the listed price if the listed price is at least .
Coupon : off the listed price if the listed price is at least .
Coupon : off the amount by which the listed price exceeds .
For which of the following listed prices will coupon offer a greater price reduction than either coupon or coupon ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the listed price. Then the price reductions in dollars are as follows:
Coupon : .
Coupon :
Coupon : .
Coupon gives a greater price reduction than coupon when , that is, . Coupon gives a greater price reduction than coupon when , that is, . The only choice that satisfies these inequalities is .
The problems on this page are the property of the MAA's American Mathematics Competitions