2015 AMC 10A 第 6 题

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}

设较大数为

L

，较小数为

S

。

Let the larger number be

L

and the smaller be

S

化简

L+S=5(L-S)

。

Simplify

L+S=5(L-S)

设两个数为

x

和

y

，并假设

x \gt y

。则

x + y = 5(x - y)\text{。}

化简得到

x + y = 5x - 5y

6y = 4x\text{。}

两边相除，得到

\dfrac{x}{y} = \dfrac{6}{4} = \dfrac{3}{2}\text{。}

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.

其他年份的第 6 题