Women and children workforce: The combined average age is 15 years. The 16 children average 8 years and the women average 22 years. If 10 of the women are married, how many women workers are unmarried?

Introduction / Context:
Mixture (weighted average) problems with two groups can be solved by equating total ages computed from averages. Once the number of women is known, subtract married to get unmarried.

Given Data / Assumptions:

• Average (all) = 15 years.
• Children: 16 members, average 8 years.
• Women: average 22 years, count unknown.
• Married women = 10; need unmarried women count.

Concept / Approach:
Total age = average * count. If w is women count, set 16*8 + 22*w = 15*(16 + w) and solve for w. Then unmarried = w - married.

Step-by-Step Solution:

Verification / Alternative check:
Totals: 128 + 22*16 = 128 + 352 = 480; group size = 32; 480/32 = 15, consistent.

Why Other Options Are Wrong:

• 16 or 12 or 8: Do not align with the solved women count 16 and 10 married.

Common Pitfalls:
Forgetting to multiply averages by group sizes or mixing up the subtraction of married from total women.

Final Answer: