Problem:
A store increased the original price of a shirt by a certain percent and then decreased the new price by the same amount. Given that the resulting price was of the original price, by what percent was the price increased and decreased?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Suppose the original price of the shirt was dollars and the price was increased by percent, producing a new price of dollars. Then decreasing the new price by percent is equivalent to multiplying by percent. The resulting price was dollars. Thus
Therefore the perecent of increase and decrease was
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions