Answer: $18,000.
Explanation:
Let X be the number of adult tickets sold and Y be the number of youth tickets sold.
We can set up the following system of equations to represent this situation:
X * 25 + Y * 12.50 = 15000
X + Y <= 1000
The first equation represents the total ticket sales, and the second equation represents the maximum capacity of the theater.
To solve this system of equations, we can use a method such as graphing, substitution, or elimination.
Using the substitution method, we can solve for one variable in terms of the other and substitute it into the other equation. For example, we can solve the first equation for X:
X = (15000 - Y * 12.50) / 25
Then, we can substitute this expression for X into the second equation:
(15000 - Y * 12.50) / 25 + Y <= 1000
Solving this equation for Y gives us the number of youth tickets that can be sold:
Y <= 600
This means that the theater can sell a maximum of 600 youth tickets. We can then use this value to find the maximum number of adult tickets that can be sold by substituting it into the expression for X that we derived earlier:
X = (15000 - 600 * 12.50) / 25
Solving this equation gives us a maximum of 240 adult tickets that can be sold.
Therefore, the theater can sell a maximum of 600 youth tickets and 240 adult tickets for a total of 840 tickets. The total ticket sales for this scenario would be 600 * $12.50 + 240 * $25 = $18,000.