Question

两个正数的和是它们差的 $5$ 倍。较大数与较小数的比是多少？

The sum of two positive numbers is $5$ times their difference. What is the ratio of the larger number to the smaller number?

$\dfrac{5}{4}$

$\dfrac{3}{2}$

$\dfrac{9}{5}$

$2$

$\dfrac{5}{2}$

设这两个数为 $x$ 和 $y$ ，其中 $x \gt y \gt 0$ ，则 $x+y = 5(x-y)$ 。

展开得 $x+y = 5x-5y$ ，所以 $6y = 4x$ ，于是 $\dfrac{x}{y} = \dfrac{3}{2}.$

因此，正确答案是 B。

Let $x$ and $y$ be the numbers with $x \gt y \gt 0.$ Then $x+y = 5(x-y).$

Expanding gives $x+y = 5x-5y,$ so $6y = 4x$ and $\dfrac{x}{y} = \dfrac{3}{2}.$

Thus, the correct answer is B.