Population split by gender and children: The male:female ratio is 7:8. Among males, 25% are children; among females, 20% are children. If adult females number 156,800, what is the total population?

Introduction / Context:
This demographic problem uses ratios and within-group percentages. We are given adult females; using the female children percentage, we recover total females, then total males from the ratio, and finally the total population.

Given Data / Assumptions:

• Males : Females = 7 : 8.
• Children among males = 25% ⇒ adults among males = 75%.
• Children among females = 20% ⇒ adults among females = 80%.
• Adult females = 156,800.

Concept / Approach:
Let females = 8k. Adult females = 80% of 8k = 6.4k. Set 6.4k = 156,800 to find k. Then males = 7k. Total population = males + females = 15k.

Step-by-Step Solution:
6.4k = 156,800 ⇒ k = 156,800 / 6.4 = 24,500Females = 8k = 8 * 24,500 = 196,000Males = 7k = 171,500Total population = 196,000 + 171,500 = 367,500

Verification / Alternative check:
Adult females check: 80% of 196,000 = 156,800, matching the given. Ratios align as 171,500 : 196,000 ≈ 7 : 8.

Why Other Options Are Wrong:
245,000 and 312,000 ignore the 20% children among females; 196,000 and 171,500 are subgroup counts, not totals.

Common Pitfalls:
Applying the adult percentage to total population or confusing adult female count with total females.

Final Answer:
367,500