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Let's break down the problem step-by-step to set up the equations:

- Let the number of regular tickets be $ r $.
- Let the number of premium tickets be $ p $.
- Let the number of elite tickets be $ e $.

### Key information from the problem:
1. The total number of tickets sold is 440:
   \[
   r + p + e = 440
   \]
   
2. The total revenue from all tickets is $3940. The prices for each type of ticket are:
   - Regular ticket: $5
   - Premium ticket: $15
   - Elite ticket: $25
   
   So, the total revenue equation is:
   \[
   5r + 15p + 25e = 3940
   \]
   
3. The number of regular tickets is three times the number of premium and elite tickets combined:
   \[
   r = 3(p + e)
   \]

### System of equations:
We have three equations:
1. $ r + p + e = 440 $
2. $ 5r + 15p + 25e = 3940 $
3. $ r = 3(p + e) $

I will now solve this system of equations to find the values of $ r $, $ p $, and $ e $.The solution to the system of equations is:

- Number of regular tickets ($r$) = 330
- Number of premium tickets ($p$) = 46
- Number of elite tickets ($e$) = 64

These are the quantities of each type of ticket sold.

Would you like a detailed breakdown of how these values were calculated, or do you have any other questions?

Here are some related questions to extend this topic:
1. How would the solution change if the price of a regular ticket increased to $10?
2. What if the total number of tickets sold was 500 instead of 440?
3. How would the solution change if the number of regular tickets was only twice the number of premium and elite tickets combined?
4. If the total revenue was $4500 instead of $3940, what would the new solution be?
5. What would happen if there were more types of tickets (e.g., VIP) introduced?

**Tip:** When solving systems of equations, always ensure the number of equations matches the number of variables for an exact solution.

A theater group sold a total of 440 tickets for $3940. Each regular price ticket costs $5, each premium ticket costs $15, and each elite ticket costs $25. The number of regular tickets was three times the number of premium and elite tickets combined. How many of each type of ticket were sold?

Solve a real-world system of equations problem where a theater group sells 440 tickets for $3940. Learn how to find the number of regular, premium, and elite tickets sold, using algebra and substitution. Suitable for Grades 9-10.

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