https://file.aiquickdraw.com/mathbot/file/1726967704731thidad6l.jpg

The problem in your image gives the following information:

- **Prices of tickets**:
  - Main floor tickets cost $60.
  - Balcony tickets cost $58.
  - Mezzanine tickets cost $49.
  
- **Conditions**:
  - The total revenue from ticket sales is $70,056.
  - There were 249 more main floor tickets sold than the combined total of balcony and mezzanine tickets.
  - The number of balcony tickets sold was 408 more than four times the number of mezzanine tickets.

### Variables:
Let:
- $ x $ be the number of **main floor** tickets.
- $ y $ be the number of **balcony** tickets.
- $ z $ be the number of **mezzanine** tickets.

### Equations:
From the problem, we can derive the following system of equations:

1. **Total sales revenue**: 
   \[
   60x + 58y + 49z = 70,056
   \]
2. **Main floor ticket relation**: 
   \[
   x = 249 + (y + z)
   \]
3. **Balcony ticket relation**: 
   \[
   y = 408 + 4z
   \]

We will solve this system of equations to find $ x $, $ y $, and $ z $.

Let me calculate it.The solution to the system of equations is:

- **Main floor tickets sold**: 717
- **Balcony tickets sold**: 456
- **Mezzanine tickets sold**: 12

Would you like a detailed explanation of how the solution was derived or any other assistance?

Here are 5 related questions to deepen your understanding:
1. How do you set up systems of equations from word problems?
2. What methods can be used to solve systems of equations?
3. How would the solution change if the ticket prices were different?
4. What is the importance of organizing information in word problems?
5. Can you verify the solution by substituting the values back into the original equations?

**Tip:** When dealing with word problems, clearly define variables and carefully translate each condition into an equation.

The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $60, balcony tickets are $58, and mezzanine tickets are $49. One particular night, sales totaled $70,056. There were 249 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 408 more than 4 times the number of mezzanine tickets. How many of each type of ticket were sold?

Learn how to solve a system of linear equations to determine the number of tickets sold in a Broadway play. The problem involves main floor, balcony, and mezzanine tickets with different prices and constraints. The total revenue from ticket sales is $70,056. Suitable for Grades 10-12 students.

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