2019 AMC 8 Problems/Problem 22

Revision as of 20:27, 20 November 2019 by A1337h4x0r (talk | contribs) (Solution 1)

Problem 22

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 84% of the original price, by what percent was the price increased and decreased? $\textbf{(A) }16\qquad\textbf{(B) }20\qquad\textbf{(C) }28\qquad\textbf{(D) }36\qquad\textbf{(E) }40$


Solution 1

Suppose the amount of discount is $x$. That means $(1-x)(1+x)=0.84x$; so $1-x^{2}=0.84$, and $(x^{2})=0.16$, obtaining $x=0.4$. Therefore, the price was increased and decreased by $box{40\%}$, or $\framebox{E}$.

See Also

2019 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 23
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