AMC12 2008 A

AMC12 2008 A · Q3

AMC12 2008 A · Q3. It mainly tests Ratios & proportions.

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

假设 $10$ 根香蕉的 $\tfrac{2}{3}$ 的价值与 $8$ 个橙子相同。多少个橙子的价值与 $5$ 根香蕉的 $\tfrac{1}{2}$ 相同？

(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

If $\frac{2}{3}\cdot10\ \text{bananas}=8\ \text{oranges}$, then $\frac{1}{2}\cdot5\ \text{bananas}=\left(\frac{1}{2}\cdot 5\ \text{bananas}\right)\cdot\left(\frac{8\ \text{oranges}}{\frac{2}{3}\cdot10\ \text{bananas}}\right)=3\ \text{oranges}\Longrightarrow\mathrm{(C)}$.

若 $\frac{2}{3}\cdot10\ \text{bananas}=8\ \text{oranges}$，则 $\frac{1}{2}\cdot5\ \text{bananas}=\left(\frac{1}{2}\cdot 5\ \text{bananas}\right)\cdot\left(\frac{8\ \text{oranges}}{\frac{2}{3}\cdot10\ \text{bananas}}\right)=3\ \text{oranges}\Longrightarrow\mathrm{(C)}$。

Topics

AR.004 Ratios & proportions