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?

$\dfrac{5}{4}$

$\dfrac{3}{2}$

$\dfrac{9}{5}$

$2$

$\dfrac{5}{2}$

答案：B

知识点：一次方程比与比例

难度评级：900

解答：

设两个数为 $x$ 和 $y$ ，并假设 $x \gt y$ 。则化简得到 $x + y = 5(x - y).$ $x + y = 5x - 5y$ $6y = 4x.$

两边相除，得到 $\dfrac{x}{y} = \dfrac{6}{4} = \dfrac{3}{2}.$

所以正确答案是 B。

Let $x$ and $y$ be the two numbers. Then we have that $x + y = 5(x - y).$ Note that we are assuming $x \gt y.$ This gives us $x + y = 5x - 5y$ $6y = 4x.$

Dividing through yields $\dfrac{x}{y} = \dfrac{6}{4} = \dfrac{3}{2}.$

Thus, B is the correct answer.

2015 AMC 10A 第 6 题

答案：B

难度评级：900

解答：

其他年份的第 6 题