假设$x$的$15\%$等于$y$的$20\%$．那么$x$的百分之几是$y$？

A. 5

B. 35

C. 75

D. $133\frac{1}{3}$

E. 300

1. 2020 AMC 8 官方解析

First note that $15\% = 0.15$, and 20. It is given that $15\%$ of $x$ equals $20\%$ of $y$, so

$0.15x = 0.20y$.

Solving for $y$ yields
$y = \frac{0.15}{0.20}x = \frac{15}{20}x = \frac{75}{100}x$
Therefore $y$ is $75\%$ of $x$.

首先注意到，$15\% = 0.15$，而$20\% = 0.20$．假设$x$的$15\%$等于$y$的$20\%$，则$0.15x = 0.20y$．

求解$y$的值
$y = \frac{0.15}{0.20}x = \frac{15}{20}x = \frac{75}{100}x$
因此，$y$是$x$的$75\%$．

Let $x = 100$. Then $15\%$ of $x$ is 15. This equals $20\%$ of $y$, which is the same as $\frac{1}{5}y$. Solving the equation $15 = \frac{1}{5}y$ yields $y = 5 \cdot 15 = 75$. Therefore $y$ is $75\%$ of $x$.

设$x = 100$．那么$x$的$15\%$是15．又$x$的$15\%$等于$y$的$20\%$，与$\frac{1}{5}y$相同．求解等式$15 = \frac{1}{5}y$，可以得出$y = 5 \cdot 15 = 75$．因此，$y$是$x$的$75\%$．