Question

A store increased the original price of a shirt by a certain percent and then decreased the new price by the same percent. Given that the resulting price was $84\%$ of the original price, by what percent was the price increased and decreased?

$16$

$20$

$28$

$36$

$40$

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Written solution:

Let $x$ be the percent converted to a real number. Then the percent increase would multiply the original by $1 + x.$

The percent decrease would multiply the new price by $1 - x.$ The final price will then be the original price multiplied by $(1 + x)(1 - x) = 1 - x^2 = .84.$

This tells us that $x^2 = .16 \Rightarrow x = .4.$

This tells us that the percent would be $40\%.$

Thus, the correct answer is E.

2019 AMC 8 Problem 22

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Problem 22 in Other Years