AMC12 2015 A

AMC12 2015 A · Q4

AMC12 2015 A · Q4. It mainly tests Linear equations, Ratios & proportions.

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

两个正数的和是它们差的 5 倍。较大数与较小数的比值为多少？

(A) \frac{5}{4} \frac{5}{4}

(B) \frac{3}{2} \frac{3}{2}

(D) 2 2

(E) \frac{5}{2} \frac{5}{2}

Answer

Correct choice: (B)

正确答案：（B）

Solution

Let $x$ and $y$ be the two positive numbers, with $x > y$. Then $x + y = 5(x - y)$. Thus $4x = 6y$, so $\frac{x}{y} = \frac{3}{2}$.

设两个正数为 $x$ 和 $y$，且 $x > y$。则 $x + y = 5(x - y)$。由此 $4x = 6y$，所以 $\frac{x}{y} = \frac{3}{2}$。

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