Final answer:
To generate a total revenue of $142,400, 2200 tickets should be sold at $24 and 2800 tickets should be sold at $40.
Step-by-step explanation:
To find out how many tickets should be sold at each price in order to generate a total revenue of $142,400, we can set up a system of equations.
Let's say x represents the number of tickets sold at $24 and y represents the number of tickets sold at $40.
The first equation is: 24x + 40y = 142,400 (since the total revenue is given as $142,400).
The second equation is: x + y = 5000 (since the total number of seats in the theater is 5000).
We can solve these equations simultaneously to find the values of x and y.
Substituting the value of x from the second equation into the first equation:
24(5000 - y) + 40y = 142,400
By simplifying and solving for y, we get y = 2800.
Substituting the value of y into the second equation, we get x = 5000 - 2800 = 2200.
Therefore, 2200 tickets should be sold at $24 and 2800 tickets should be sold at $40 in order to generate a total revenue of $142,400.