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: