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.