Question

Dunbar 家庭由母亲、父亲和若干孩子组成。全家成员的平均年龄为 $20$ ，父亲 $48$ 岁，母亲和孩子们的平均年龄为 $16$ 。这个家庭有多少个孩子？

The Dunbar family consists of a mother, a father, and some children. The average age of the members of the family is $20,$ the father is $48$ years old, and the average age of the mother and children is $16.$ How many children are in the family?

$2$

$3$

$4$

$5$

$6$

答案：E

知识点：平均数一次方程

难度评级：1240

解答：

设孩子数为 $N$ ，全家总年龄为 $T$ 。

则 $20 = \dfrac{T}{N + 2}$ ，且 $16 = \dfrac{T - 48}{N + 1}$ 。

这给出 $20N + 40 = T$ 和 $16N + 64 = T$ ，所以 $20N + 40 = 16N + 64$ 。

因此 $4N = 24$ ，所以 $N = 6$ 。

所以正确答案是 E。

Let $N$ be the number of children and $T$ the total age of the family.

Then $20 = \dfrac{T}{N + 2}$ and $16 = \dfrac{T - 48}{N + 1}.$

These give $20N + 40 = T$ and $16N + 64 = T,$ so $20N + 40 = 16N + 64.$

Hence $4N = 24$ and $N = 6.$

Thus, the correct answer is E.

2007 AMC 10A 第 10 题

答案：E

难度评级：1240

解答：

其他年份的第 10 题