2015 AMC 10A 第 4 题

Question

Pablo、Sofia 和 Mia 在聚会上得到一些糖果蛋。Pablo 的糖果蛋数量是 Sofia 的三倍，Sofia 的数量是 Mia 的两倍。Pablo 决定把一些糖果蛋给 Sofia 和 Mia，使三人最后数量相同。Pablo 应该把自己糖果蛋的几分之几给 Sofia？

Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as many eggs as Sofia, and Sofia had twice as many eggs as Mia. Pablo decides to give some of his eggs to Sofia and Mia so that all three will have the same number of eggs. What fraction of his eggs should Pablo give to Sofia?

\dfrac{1}{12}

\dfrac{1}{6}

\dfrac{1}{4}

\dfrac{1}{3}

\dfrac{1}{2}

答案：B

知识点：比与比例分数

难度评级：1020

小提示：

把 Mia、Sofia、Pablo 的数量写成

m,2m,6m

。

Write Mia, Sofia, Pablo as

m,2m,6m

大提示：

平均分配意味着每人最后有

3m

个糖果蛋。

Equal sharing means each person ends with

3m

eggs

解答：

设 Mia 有

m

个糖果蛋，则 Sofia 有

2m

个，Pablo 有

6m

个。

糖果蛋总数为

m + 2m + 6m = 9m\text{。}

三人数量相同时，每人应有

9m \div 3 = 3m

个。

Sofia 还需要

3m - 2m = m

个糖果蛋，因此 Pablo 应给她自己原有糖果蛋的

\dfrac{m}{6m} = \dfrac{1}{6}

。

所以正确答案是 B。

Let

m

be the number of candy eggs that Mia had. Then Sofia had

2m

eggs and Pablo had

6m

eggs.

The total number of eggs is then

m + 2m + 6m = 9m.

For all of them to have the same number of eggs, they each must have

9m \div 3 = 3m

eggs.

Sofia needs

3m - 2m = m

more eggs. This means Pablo must give

\dfrac{m}{6m} = \dfrac{1}{6}

of his eggs to Sofia.

Thus, B is the correct answer.

2015 AMC 10A 第 4 题

答案：B

难度评级：1020

小提示：

大提示：

解答：

其他年份的第 4 题