AMC8 2004

AMC8 2004 · Q16

AMC8 2004 · Q16. It mainly tests Fractions, Arithmetic misc.

Two 600 ml pitchers contain orange juice. One pitcher is $\frac{1}{3}$ full and the other pitcher is $\frac{2}{3}$ full. Water is added to fill each pitcher completely, then both pitchers are poured into one large container. What fraction of the mixture in the large container is orange juice?

有两个600毫升的橙汁罐。一个罐子装有\frac{1}{3}的橙汁，另一个装有\frac{2}{3}的橙汁。向每个罐子中加水直到装满，然后将两个罐子倒入一个大容器中。大容器中的混合物中有多少分数是橙汁？

(A) $\frac{1}{8}$ $\frac{1}{8}$

(B) $\frac{3}{16}$ $\frac{3}{16}$

(D) $\frac{11}{19}$ $\frac{11}{19}$

(E) $\frac{11}{15}$ $\frac{11}{15}$

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) Because the first pitcher was $\frac{1}{3}$ full of orange juice, after filling with water it contains 200 ml of juice and 400 ml of water. Because the second pitcher was $\frac{2}{5}$ full of orange juice, after filling it contains 240 ml of orange juice and 360 ml of water. In all, the amount of orange juice is 440 ml out of a total of 1200 ml or $\frac{440}{1200}=\frac{11}{30}$ of the mixture.

（C）因为第一个壶里原本有 $\frac{1}{3}$ 是橙汁，加满水后它包含 200 ml 橙汁和 400 ml 水。因为第二个壶里原本有 $\frac{2}{5}$ 是橙汁，加满后它包含 240 ml 橙汁和 360 ml 水。总共橙汁是 440 ml，总量是 1200 ml，因此所占比例为 $\frac{440}{1200}=\frac{11}{30}$。

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