AMC10 2005 B

AMC10 2005 B · Q3

AMC10 2005 B · Q3. It mainly tests Fractions.

A gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day?

一加仑油漆用于粉刷一个房间。第一天用了三分之一的油漆。第二天，用了剩余油漆的三分之一。第三天可用的油漆占原始油漆的比例是多少？

(A) $\frac{1}{10}$ $\frac{1}{10}$

(B) $\frac{1}{9}$ $\frac{1}{9}$

(D) $\frac{4}{9}$ $\frac{4}{9}$

(E) $\frac{5}{9}$ $\frac{5}{9}$

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) After the first day, $1-\frac{1}{3}=\frac{2}{3}$ of the paint remains. On the second day, $\frac{1}{3}\cdot\frac{2}{3}=\frac{2}{9}$ of the paint is used. So for the third day $1-\frac{1}{3}-\frac{2}{9}=\frac{4}{9}$ of the original gallon of paint is available.

（D）第一天之后，剩余的油漆为 $1-\frac{1}{3}=\frac{2}{3}$。第二天，使用的油漆为 $\frac{1}{3}\cdot\frac{2}{3}=\frac{2}{9}$。因此到第三天，可用的原来一加仑油漆为 $1-\frac{1}{3}-\frac{2}{9}=\frac{4}{9}$。

Topics

AR.001 Fractions