The average age of 14 girls plus their teacher is 15 years. Excluding the teacher reduces the average by 1 year. What is the teacher's age?

Introduction / Context:
Removing one person and observing the average drop lets us compute that person’s value by comparing totals with and without that person. This is the inverse of the “added person” scenario.

Given Data / Assumptions:

• With teacher: 15 people; mean = 15 years.
• Without teacher (14 girls): mean = 14 years.
• Find teacher's age.

Concept / Approach:
Teacher age = (15 * 15) − (14 * 14). Derivation: total_with − total_without.

Step-by-Step Solution:

Verification / Alternative check:
Average of girls alone is 14; adding a 29-year-old to 14 girls yields total 225 and average 15, matching the prompt.

Why Other Options Are Wrong:
35 yr, 32 yr, 30 yr: Do not produce the stated averages when recombined with the 14 girls.

Common Pitfalls:
Subtracting the averages directly (15 − 14 = 1) and reporting 1 year (nonsense). The drop of 1 year applies across 14 people, not as the teacher's age.

Final Answer:
29 yr