Difference between revisions of "2019 AMC 8 Problems/Problem 22"

(Solution 1)
(Solution 1)
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==Solution 1==
 
==Solution 1==
Suppose the amount of discount is <math>x</math>. That means <math>(1-x)(1+x)=0.84x</math>; so <math>1-x^{2}=0.84</math>, and <math>(x^{2})=0.16</math>, obtaining <math>x=0.4</math>. Therefore, the price was increased and decreased by <math>\framebox{40\%}</math>, or <math>\framebox{E}</math>.~heeeeeeeeheeeee
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Suppose the amount of discount is <math>x</math>. That means <math>(1-x)(1+x)=0.84x</math>; so <math>1-x^{2}=0.84</math>, and <math>(x^{2})=0.16</math>, obtaining <math>x=0.4</math>. Therefore, the price was increased and decreased by <math>\framebox{40\%}</math>, or <math>\framebox{E}</math>.
  
 
==See Also==
 
==See Also==

Revision as of 22:12, 20 November 2019

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 $\framebox{40\%}$, or $\framebox{E}$.

See Also

2019 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 21
Followed by
Problem 23
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All AJHSME/AMC 8 Problems and Solutions

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