Problem:
The Dunbar family consists of a mother, a father, and some children. The average age of the members of the family is , the father is years old, and the average age of the mother and children is . How many children are in the family?
Answer Choices:
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E.
Solution:
Let represent the number of children in the family and represent the sum of the ages of all the family members. The average age of the members of the family is , and the average age of the members when the -year-old father is not included is , so
This implies that
so
Hence and .
The problems on this page are the property of the MAA's American Mathematics Competitions