Coach added raises the average by 20%: The average age of four players is 18.5 years. If the coach is included, the average increases by 20%. What is the coach’s age?

Introduction / Context:
An average increased by a percentage indicates a multiplicative change to the mean. Convert to totals before and after adding the coach to find their age.

Given Data / Assumptions:

• Players: 4 with average 18.5 years ⇒ total 74.
• Including coach: 5 people; new average = 18.5 * 1.20 = 22.2 years.

Concept / Approach:
Coach’s age = (new average * 5) − old total.

Step-by-Step Solution:

Verification / Alternative check:
Average check with ages consistent: (74 + 37) / 5 = 111/5 = 22.2 years, which is 20% higher than 18.5.

Why Other Options Are Wrong:

• 28, 31, 34 years: Too small to raise the average by the stated 20% with count increasing to 5.

Common Pitfalls:
Adding 20% of total instead of 20% of average, or forgetting that headcount increases from 4 to 5.

Final Answer: