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?
Correct Answer: 15 years
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:
Present total = 6 * 22 = 132Sum of five elders now = 132 − 7 = 125Sum of five elders 7 years earlier = 125 − 5*7 = 125 − 35 = 90Youngest at birth = 0 ⇒ total at birth = 90Average at birth = 90 / 6 = 15 yearsVerification / 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:
15 years