Family average at birth of youngest: The average age of a family of 6 is 22 years now. The youngest member is 7 years old. What was the family’s average age at the time of the youngest member’s birth?

Introduction / Context:
To find the past average at the birth of the youngest, roll back ages by the youngest’s current age for all older family members and set the infant’s age to 0 at birth. Then compute the average across all six members (including the newborn).

Given Data / Assumptions:

• Family members = 6.
• Present average = 22 years ⇒ present total = 132.
• Youngest's present age = 7 years.

Concept / Approach:
At the birth of the youngest (7 years ago), the five older members were each 7 years younger. Subtract 7*5 from the sum of the older five; the youngest contributes 0. Divide by 6 for the past average.

Step-by-Step Solution:

Verification / Alternative check:
Forward check by adding 7 years to each of the six members’ birth-time ages adds 42 to the total (7*6), raising 90 to 132, which matches the present total.

Why Other Options Are Wrong:

• 17 or 17.5 or 18 years: Overestimate the rolled-back ages for the older five.

Common Pitfalls:
Subtracting 7 years from the group total six times (including the newborn) instead of only for the five older members.

Final Answer: