Class average with subgroup averages: Average age of 9 students and their teacher (10 persons) is 16 years. The first four students average 19 years; the last five average 10 years. Find the teacher’s present age.

Introduction / Context:
Averages in parts (subgroups) and a grand average allow reconstruction of the missing individual’s value by total-sum arithmetic.

Given Data / Assumptions:

• Total persons = 10 (9 students + 1 teacher); grand average = 16.
• First 4 students average = 19; last 5 students average = 10.

Concept / Approach:
Compute totals for each group, sum them to get students’ total, subtract from the grand total to isolate the teacher’s age.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 36, 30, 28 do not match the computed total balance.

Common Pitfalls:

• Forgetting that 9 students + teacher = 10 persons for the grand average.

Final Answer:
34 yr