

(9 intermediate revisions by 5 users not shown) 
Line 1: 
Line 1: 
−  bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot bdot yummy yummy bdot
 +  ==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/xjwDsaRE_Wo 
 +  
 +  ==See also== 
 +  {{AMC8 boxyear=2020numb=14numa=16}} 
 +  {{MAA Notice}} 
Latest revision as of 18:48, 6 January 2021