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 +  ==Problem== 
 +  Suppose <math>15\%</math> of <math>x</math> equals <math>20\%</math> of <math>y.</math> What percentage of <math>x</math> is <math>y?</math> 
 +  
 +  <math>\textbf{(A) }5 \qquad \textbf{(B) }35 \qquad \textbf{(C) }75 \qquad \textbf{(D) }133 \frac13 \qquad \textbf{(E) }300</math> 
 +  
 +  ==Solution 1== 
 +  Since <math>20\% = \frac{1}{5}</math>, multiplying the given condition by <math>5</math> shows that <math>y</math> is <math>15 \cdot 5 = \boxed{\textbf{(C) }75}</math> percent of <math>x</math>. 
 +  
 +  ==Solution 2== 
 +  Letting <math>x=100</math> (without loss of generality), the condition becomes <math>0.15\cdot 100 = 0.2\cdot y \Rightarrow 15 = \frac{y}{5} \Rightarrow y=75</math>. Clearly, it follows that <math>y</math> is <math>75\%</math> of <math>x</math>, so the answer is <math>\boxed{\textbf{(C) }75}</math>. 
 +  
 +  ==Solution 3== 
 +  We have <math>15\%=\frac{3}{20}</math> and <math>20\%=\frac{1}{5}</math>, so <math>\frac{3}{20}x=\frac{1}{5}y</math>. Solving for <math>y</math>, we multiply by <math>5</math> to give <math>y = \frac{15}{20}x = \frac{3}{4}x</math>, so the answer is <math>\boxed{\textbf{(C) }75}</math>. 
 +  
 +  ==Solution 4== 
 +  We are given <math>0.15x = 0.20y</math>, so we may assume without loss of generality that <math>x=20</math> and <math>y=15</math>. This means <math>\frac{y}{x}=\frac{15}{20}=\frac{75}{100}</math>, and thus the answer is <math>\boxed{\textbf{(C) }75}</math>. 
 +  
 +  ==Video Solution== 
 +  https://youtu.be/mjSPHTwGE 
 +  
 +  ~savannahsolver 
 +  
 +  ==Video Solution== 
 +  https://youtu.be/xjwDsaRE_Wo 
 +  
 +  ==See also== 
 +  {{AMC8 boxyear=2020numb=14numa=16}} 
 +  {{MAA Notice}} 
Latest revision as of 18:20, 26 February 2021