AMC10 2015 A

AMC10 2015 A · Q4

AMC10 2015 A · Q4. It mainly tests Linear equations, Ratios & proportions.

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?

Pablo、Sofia 和 Mia 在派对上得到了一些糖果蛋。Pablo 的蛋是 Sofia 的三倍，Sofia 的蛋是 Mia 的两倍。Pablo 决定把一些蛋分给 Sofia 和 Mia，使得三人蛋数相同。Pablo 应该给 Sofia 他蛋数的几分之几？

(A) \frac{1}{12} \frac{1}{12}

(B) \frac{1}{6} \frac{1}{6}

(D) \frac{1}{3} \frac{1}{3}

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

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Let $m$ be the number of eggs that Mia has. Then Sofia has $2m$ eggs and Pablo has $6m$ eggs. If the total of $9m$ eggs is to be divided equally, each person will have $3m$ eggs. Therefore Pablo should give $2m$ eggs to Mia and $m$ eggs to Sofia. The fraction of his eggs he should give to Sofia is $\frac{m}{6m}=\frac{1}{6}$.

答案（B）：设 $m$ 为米娅拥有的鸡蛋数。那么索菲娅有 $2m$ 个鸡蛋，巴勃罗有 $6m$ 个鸡蛋。若总共 $9m$ 个鸡蛋要平均分配，则每个人将有 $3m$ 个鸡蛋。因此巴勃罗应给米娅 $2m$ 个鸡蛋，给索菲娅 $m$ 个鸡蛋。他应给索菲娅的鸡蛋占他鸡蛋总数的比例为 $\frac{m}{6m}=\frac{1}{6}$。

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