Difference between revisions of "2020 AMC 8 Problems/Problem 15"

(Created page with "==Problem 15== 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)...")
 
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==Problem 15==
 
 
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>
 
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>
  
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==Solution 1==
 
==Solution 1==
We set up the following equation based on the given information: <cmath>\frac{15x}{100}=\frac{20y}{100}</cmath> Solving for <math>x</math> yields <cmath>\frac{3x}{20}=\frac{y}{5}</cmath> <cmath>20y=15x</cmath> <cmath>x=1.\overline{3}y ==> D</cmath>
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Multiply by <math>5</math> to get <math>75\% x=y</math>. Therefore, <math>\boxed{\textbf{C}}</math> is the answer.

Revision as of 00:20, 18 November 2020

Suppose $15\%$ of $x$ equals $20\%$ of $y.$ What percentage of $x$ is $y?$

$\textbf{(A) }5 \qquad \textbf{(B) }35 \qquad \textbf{(C) }75 \qquad \textbf{(D) }133 \frac13 \qquad \textbf{(E) }300$

Solution 1

Multiply by $5$ to get $75\% x=y$. Therefore, $\boxed{\textbf{C}}$ is the answer.

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