In a community theater production, for every 4 adults participating, there are 8 children participating. ¼ of the children and ⅕ of the adults are involved in costume design. Which of the following could be the total number of people involved in the production?

Let's break down the problem step by step:

1. **Ratio of adults to children:**  
   According to the problem, for every 4 adults, there are 8 children. This simplifies to a ratio of adults to children of \(1:2\). So for every adult, there are 2 children.

2. **Involvement in costume design:**  
   - ¼ of the children are involved in costume design.
   - ⅕ of the adults are involved in costume design.

3. **Total number of people involved:**  
   Let’s assume the total number of adults is \(a\) and the total number of children is \(2a\) (because the ratio of adults to children is 1:2).

4. **Finding possible total numbers:**  
   The total number of people involved in the production is \(a\) (adults) + \(2a\) (children) = \(3a\) (total people).

   Therefore, the total number of people must be a multiple of 3. This means any possible number that represents the total number of participants in the production must be divisible by 3.

Thus, the total number of people involved in the production must be a multiple of 3, considering the ratio of adults to children is \(1:2\).

Would you like to see specific examples of numbers divisible by 3, or further clarification on any part?

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Here are 5 related questions you can try to explore further:

1. If the total number of adults is 12, how many children are there in the production?
2. If there are 60 people in total, how many of them are children and how many are adults?
3. What fraction of the total people are involved in costume design?
4. If there are 30 people in total, how many children are involved in costume design?
5. How does the number of children change if the ratio of adults to children is \(1:3\)?

**Tip:** Always ensure to simplify ratios to their lowest terms for easier calculations and interpretations.

Learn how to solve a problem involving ratios of adults and children in a community theater production. This problem includes calculating the total number of people involved and determining how many are involved in costume design. Suitable for students in Grades 6-8.

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