The average age of 5 boys is 16 years, while the average age of 4 of those boys is 16 years 3 months. What is the age of the 5th boy?

Introduction: Mixed averages can be separated by converting them into totals. Once you know the total age of all 5 and the total age of 4, the 5th boy’s age is simply the difference of those totals.

Given Data / Assumptions:

• Average (5 boys) = 16 years ⇒ total_5 = 5 * 16 = 80.
• Average (4 boys) = 16 years 3 months = 16.25 years ⇒ total_4 = 4 * 16.25 = 65.

Concept / Approach: Age of 5th = total_5 − total_4. The quarter-year conversion (3 months = 0.25 years) ensures accurate computation without mixing units.

Step-by-Step Solution:

Verification / Alternative check: Recombine: 65 + 15 = 80; 80 / 5 = 16 years, matching the stated average. All units are consistent after converting months to fractional years.

Why Other Options Are Wrong: 15 yr 6 months, 15 yr 4 months, and 15 yr 2 months would change the 5-boy total away from 80. 16 yr contradicts the computed difference of totals.

Common Pitfalls: Forgetting to convert 3 months to 0.25 year, or averaging 16 and 16 years 3 months directly rather than using totals.

Final Answer: 15 yr