5000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sell out performance to generate a total revenue of $148,800?

Let the number of tickets sold at $24 be $ x $ and the number of tickets sold at $40 be $ y $. We are given two key pieces of information:

1. The total number of seats in the theater is 5000, so:
   \[
   x + y = 5000
   \]
   
2. The total revenue is $148,800, so:
   \[
   24x + 40y = 148,800
   \]

### Solving the system of equations:

1. From the first equation, solve for $ y $:
   \[
   y = 5000 - x
   \]

2. Substitute this expression for $ y $ into the second equation:
   \[
   24x + 40(5000 - x) = 148,800
   \]

3. Expand the equation:
   \[
   24x + 200,000 - 40x = 148,800
   \]

4. Simplify:
   \[
   -16x + 200,000 = 148,800
   \]

5. Subtract 200,000 from both sides:
   \[
   -16x = -51,200
   \]

6. Divide by -16:
   \[
   x = 3200
   \]

So, 3200 tickets should be sold at $24.

7. Now, substitute $ x = 3200 $ back into the equation for $ y $:
   \[
   y = 5000 - 3200 = 1800
   \]

Therefore, 1800 tickets should be sold at $40.

### Final answer:
- 3200 tickets should be sold at $24.
- 1800 tickets should be sold at $40.

Would you like more details or have any further questions?

Here are some related questions:
1. What is the total revenue if all tickets are sold at $24?
2. How much additional revenue would result from increasing the $40 ticket price by 10%?
3. If 100 fewer $24 tickets are sold, how many $40 tickets should be sold to maintain the same revenue?
4. What percentage of the total seats are sold at the $40 price?
5. How does the average ticket price change if 100 more $40 tickets are sold?

**Tip**: When solving word problems involving systems of equations, clearly define variables and equations based on the problem's constraints to simplify the process.

Learn how to determine how many tickets should be sold at $24 and $40 to generate a total revenue of $148,800 for a sell-out performance in a 5000-seat theater. This problem explores systems of linear equations and algebraic problem-solving, suitable for students in Grades 9-12.

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