2007 AMC 10A Problem 10

Problem 10 of 25EasierAlgebra

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?

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Solution

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,

20N + 40 = 16N + 64.

Hence

4N = 24

and

N = 6.

Thus, the correct answer is E.