AMC10 2004 B

AMC10 2004 B · Q14

AMC10 2004 B · Q14. It mainly tests Linear equations, Fractions.

A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only $\frac{1}{3}$ of the marbles in the bag are blue. Then yellow marbles are added to the bag until only $\frac{1}{5}$ of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?

一个袋子最初只含有红 marbles 和蓝 marbles，蓝 marbles 多于红 marbles。向袋中添加红 marbles 直到袋中蓝 marbles 只占$\frac{1}{3}$。然后添加黄 marbles 直到袋中蓝 marbles 只占$\frac{1}{5}$。最后，袋中蓝 marbles 的数量加倍。现在袋中蓝 marbles 占的比例是多少？

(A) \frac{1}{5} \frac{1}{5}

(B) \frac{1}{4} \frac{1}{4}

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

(E) \frac{1}{2} \frac{1}{2}

Answer

Correct choice: (C)

正确答案：（C）

Solution

If there are initially $B$ blue marbles in the bag, after red marbles are added, then the total number of marbles in the bag must be $3B$. Then after the yellow marbles are added, the number of marbles in the bag must be $5B$. Finally, adding $B$ blue marbles to the bag gives $2B$ blue marbles out of $6B$ total marbles. Thus $\frac{1}{3}$ of the marbles are blue.

如果最初袋中有$B$个蓝 marbles，添加红 marbles 后，总数必须是$3B$。然后添加黄 marbles 后，总数必须是$5B$。最后添加$B$个蓝 marbles，得到$2B$个蓝 marbles，总数$6B$。因此蓝 marbles 占$\frac{1}{3}$。

Topics