Problem:
For the consumer, a single discount of is more advantageous than any of the following discounts:
() two successive discounts.
() three successive discounts.
() a discount followed by a discount.
What is the smallest possible positive integer value of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If is the price paid for an item, then the discounted prices with the three given discounts are given by the following calculations:
for a discount of
for a discount of
for a discount of
The smallest integer greater than , and is .
The problems on this page are the property of the MAA's American Mathematics Competitions