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

Solution 4

We are given that $0.15x=0.20y$. Multiplying both sides by $100$ and dividing by $20$ tells us that $y = \frac 34x =0.75x=\textbf{(C) }75$.

-franzliszt

Solution 5

We know that $0.15x=0.20y$. Therefore, we can just assume that $x=20$ and $y=15$, which means that $\frac{y}{x}=\frac{15}{20}=\frac{75}{100}$, so our answer is $\boxed{\textbf{(C) }75}$.

- StarryNight7210