AMC10 2015 A

AMC10 2015 A · Q6

AMC10 2015 A · Q6. 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是多少？

(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

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

答案（B）：设 \(x\) 和 \(y\) 为两个正数，且 \(x>y\)。则 \(x+y=5(x-y)\)。因此 \(4x=6y\)，所以 \(\frac{x}{y}=\frac{3}{2}\)。

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