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 (talk) 07:41, 18 November 2020 (EST)

2020 AMC 8 (Problems • Answer Key • Resources)
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2020 AMC 8 Problems/Problem 15

Contents

Solution 1

Solution 2

Solution 3

See also