The average age of 8 children is 12 years. If the ages of seven children are 12, 8, 14, 11, 9, 13, and 15 years, what is the age of the eighth child?

Introduction / Context:
Average equals total sum divided by count. Multiply average by count to get total; subtract the known seven to find the missing age.

Given Data / Assumptions:

• Average = 12; number = 8 ⇒ total = 96
• Seven ages = 12 + 8 + 14 + 11 + 9 + 13 + 15 = 82

Concept / Approach:
Eighth age = total − sum of known seven.

Step-by-Step Solution:

Verification / Alternative check:
Check: New total 82 + 14 = 96; average 96/8 = 12, correct.

Why Other Options Are Wrong:
12, 13, 15 do not yield the target total of 96 when added to 82.

Common Pitfalls:
Arithmetic errors in adding the seven ages or forgetting to multiply average by total count first.

Final Answer:
14 yr.