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:
Let be the percent converted to a real number. Then the percent increase would multiply the original by . The percent decrease would multiply the new price by . The final price will then be the original price multiplied by:
This tells us that
This tells us that the percent would be . Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions