Question
The average age of 4 children is 12 years. The
difference between the ages of the eldest and the youngest child is 10 years. If the second and third children are of the same age and their combined age is 24 years, what is the age of the eldest child?Solution
Let the ages of the second and third children be x years. Their combined age = 2x = 24, so x = 12 years. Let the age of the youngest child be y years, and the eldest be y + 10 years. Average age = (y + (y + 10) + 12 + 12) / 4 = 12 (y + y + 10 + 24) / 4 = 12 (2y + 34) / 4 = 12 2y + 34 = 48 2y = 14 y = 7 years Age of the eldest child = 7 + 10 = 17 years.
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