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

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 $0.75x=y$. The $0.75$ here can be converted to $75\%$. Therefore, $\boxed{\textbf{C}}$ is the answer.

## Solution 2

Letting $x=100$, our equation becomes $0.15\cdot 100 = 0.2\cdot y \implies 15 = \frac{y}{5} \implies y=75$. Clearly, $y$ is $75\%$ of $x$ and the answer is $\boxed{\textbf{C}}$.
~ junaidmansuri

## Solution 3

Let us transform the first sentence to an equation. $15\%=\frac3{20}$ and $20\%=\frac15.$ So, $\frac3{20}x=\frac15y.$ Therefore, $\frac1{20}x=\frac1{15}y$ and $x=\frac43y,$ hence $\boxed{\textbf{(C) }75}$.
--Aops-g5-gethsemanea2

## See also

 2020 AMC 8 (Problems • Answer Key • Resources) Preceded byProblem 14 Followed byProblem 16 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AJHSME/AMC 8 Problems and Solutions

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