Backdating family averages: The present average age of a 4-member family is 20 years. The youngest is 4 years old now. What was the average age of the family at the time of the youngest's birth (i.e., 4 years ago, before the baby was counted)?

Introduction / Context:This problem asks for the average at the time of the youngest child’s birth, when only the three older members were counted. We must backdate ages by 4 years for those three and exclude the newborn (age 0 then).

Given Data / Assumptions:

• Current average (4 members) = 20 → current total = 80
• Youngest current age = 4 → youngest was 0 at birth
• At birth time: only 3 members are counted

Concept / Approach:Four years ago, the three older members were each 4 years younger. Subtract 4 for each of those three from the current total, exclude the youngest (who was 0 then), and divide by 3.

Step-by-Step Solution:

Verification / Alternative check:If we included the newborn at age 0 and divided by 4, we would get 16, but the question clarifies “before the baby was counted,” so use 3 members, giving 21 1/3.

Why Other Options Are Wrong:

• 27, 22: do not match the correctly backdated total for three members.
• 23 1/3: overestimates the average.
• 16: corresponds to including the newborn at age 0, which the prompt excludes.

Common Pitfalls:Including the newborn in the average four years ago (age 0) or forgetting to reduce each older member by 4 years when backdating.

Final Answer:21 1/3 yr