Family average by subgroup weights: The average age of all members of a family is 25 years. The average of males is 30 years and the average of females is 20 years. If there are 15 females, how many males are there?

Introduction / Context:
Another weighted average problem using two subgroup means to deduce the unknown count.

Given Data / Assumptions:

• Overall average = 25
• Male average = 30; Female average = 20
• Females = 15; let males = m

Concept / Approach:
Use (30m + 20 * 15) / (m + 15) = 25 and solve for m.

Step-by-Step Solution:
(30m + 300) / (m + 15) = 2530m + 300 = 25m + 3755m = 75 → m = 15

Verification / Alternative check:
Totals: males 30 * 15 = 450; females 20 * 15 = 300; combined 750 over 30 persons gives 25 average.

Why Other Options Are Wrong:
Other values do not satisfy the overall average constraint.

Common Pitfalls:
Placing the wrong subgroup count in the numerator or forgetting to add both groups in the denominator.

Final Answer:
15