6000 seat theater
tickets for sale $25 and $40 how many tickets should be sold at each price for total revenue of $192,000
assume all seats are sold
number or $25 tickets --- x
number of $40 tickets --- 6000-x
25x + 40(6000-x) = 192000
solve for x , then sub into my definitions
To determine the number of tickets to be sold at each price for a total revenue of $192,000, we can set up a system of equations. Let's assign variables to represent the unknowns:
Let x represent the number of tickets sold at $25 each.
Let y represent the number of tickets sold at $40 each.
We can establish two equations based on the given information:
1. The total number of tickets sold should be equal to the seating capacity of the theater:
x + y = 6000
2. The total revenue is the product of the number of tickets sold and their respective prices:
25x + 40y = 192,000
To solve this system of equations, we can use the substitution method:
From the first equation, we can rewrite it as:
x = 6000 - y
Substitute this expression for x in the second equation:
25(6000 - y) + 40y = 192,000
Simplify and solve for y:
150,000 - 25y + 40y = 192,000
15y = 42,000
y = 2,800
Substitute the value of y back into the first equation to solve for x:
x + 2800 = 6000
x = 3200
Therefore, we should sell 3,200 tickets at $25 each and 2,800 tickets at $40 each to achieve a total revenue of $192,000.