In a television program called Jabardast, 1/8 of the audience were children, 2/5 of the audience were men and the rest were women. If the number of women in the audience was 380, what was the total audience for the program?

Introduction / Context:
This question is a fractions and percentage type word problem about composition of an audience. The audience is divided into three groups: children, men and women. The fractions for children and men are given, and the absolute number of women is given. From this information, we must find the total audience. It is a classic example of using fractional parts of a whole.

Given Data / Assumptions:
- Children constitute 1/8 of the total audience.
- Men constitute 2/5 of the total audience.
- The remaining audience members are women.
- Number of women in the audience = 380.
- We must find the total audience size.

Concept / Approach:
Let the total audience be A. Then children = A / 8, men = (2 / 5) * A, and women = A minus children minus men. Using the given number of women, we can write an equation in A and solve for A. Working with fractions requires careful handling of denominators, but the process is straightforward.

Step-by-Step Solution:
Let total audience be A. Children = 1 / 8 of A = A / 8. Men = 2 / 5 of A = (2A) / 5. Women = A - (A / 8) - (2A / 5). Find a common denominator for 8 and 5, which is 40. Convert fractions: A / 8 = 5A / 40 and 2A / 5 = 16A / 40. So women = A - (5A / 40) - (16A / 40). Rewrite A as 40A / 40. Thus women = (40A / 40) - (5A / 40) - (16A / 40) = (40A - 5A - 16A) / 40. Simplify numerator: 40A - 5A - 16A = 19A. So women = 19A / 40. Given that women = 380, so 19A / 40 = 380. Therefore, A = 380 * 40 / 19. Compute 380 / 19 = 20, so A = 20 * 40 = 800.

Verification / Alternative check:
With A = 800, compute each group: children = 1/8 of 800 = 100, men = 2/5 of 800 = 320. Women = 800 - 100 - 320 = 380, which matches the given number. All fractions and totals are consistent, so 800 is indeed the correct total audience size.

Why Other Options Are Wrong:
600, 500, 400, and 700: None of these values produce 380 women when the given fractional proportions for children and men are applied and subtracted from the total. Checking any of them quickly shows that the resulting number of women is different from 380.

Common Pitfalls:
Students sometimes misinterpret "remaining" and forget that both children and men must be subtracted from the total to find women. Another common error is incorrect fraction arithmetic, such as adding denominators or failing to find a common denominator. Writing all steps clearly, especially when combining fractions, helps avoid mistakes.

Final Answer:
The total audience in the Jabardast program was 800 people.