2019 AMC 8

Complete problem set with solutions and individual problem pages

Problem 22 Hard

A store increased the original price of a shirt by a certain percent and then lowered 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:E

Solution 1

Suppose the fraction of discount is . That means ; so, , and , procuring . Therefore, the price was increased and decreased by %, or .

Solution 2

Let x be the discount. We can also work in reverse such as () = .

Thus, = . Solving for gives us . But has to be positive. Thus, = .