AMC10 2008 A

AMC10 2008 A · Q4

AMC10 2008 A · Q4. It mainly tests Ratios & proportions.

Suppose that $\frac{2}{3}$ of 10 bananas are worth as much as 8 oranges. How many oranges are worth as much as $\frac{1}{2}$ of 5 bananas?

假设10个香蕉的三分之二的价值等于8个橙子。那么多少个橙子等于5个香蕉的一半的价值？

(A) 2 2

(B) $\frac{5}{2}$ $\frac{5}{2}$

(D) $\frac{7}{2}$ $\frac{7}{2}$

(E) 4 4

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Note that $\frac{2}{3}$ of 10 bananas is $\frac{20}{3}$ bananas, which are worth as much as 8 oranges. So one banana is worth as much as $8\cdot\frac{3}{20}=\frac{6}{5}$ oranges. Therefore $\frac{1}{2}$ of 5 bananas are worth as much as $\frac{5}{2}\cdot\frac{6}{5}=3$ oranges.

答案（C）：注意，10 根香蕉的 $\frac{2}{3}$ 是 $\frac{20}{3}$ 根香蕉，它们的价值等同于 8 个橙子。因此，1 根香蕉的价值等同于 $8\cdot\frac{3}{20}=\frac{6}{5}$ 个橙子。所以，5 根香蕉的 $\frac{1}{2}$ 的价值等同于 $\frac{5}{2}\cdot\frac{6}{5}=3$ 个橙子。

Topics

AR.004 Ratios & proportions