Let's assume that x tickets are sold at $26 each, and y tickets are sold at $40 each. We know that the total number of tickets sold is the sum of x and y, which must equal the capacity of the theater, 6000:
x + y = 6000
We also know that the total revenue generated from ticket sales is $195,200. This can be expressed as:
26x + 40y = 195200
We now have two equations with two variables, which we can solve using substitution or elimination. Here, we will use the substitution method:
x + y = 6000 => y = 6000 - x
26x + 40y = 195200 => 26x + 40(6000-x) = 195200
Expanding the second equation, we get:
26x + 240000 - 40x = 195200
Simplifying and solving for x, we get:
-14x = -44800
x = 3200
Therefore, 3200 tickets should be sold at $26 each, and the remaining 2800 tickets should be sold at $40 each, in order to generate a total revenue of $195,200.