Math Problem Statement
5000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sell out performance to generate a total revenue of $148,800?
Solution
Let the number of tickets sold at $24 be and the number of tickets sold at $40 be . We are given two key pieces of information:
-
The total number of seats in the theater is 5000, so:
-
The total revenue is $148,800, so:
Solving the system of equations:
-
From the first equation, solve for :
-
Substitute this expression for into the second equation:
-
Expand the equation:
-
Simplify:
-
Subtract 200,000 from both sides:
-
Divide by -16:
So, 3200 tickets should be sold at $24.
- Now, substitute back into the equation for :
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:
- What is the total revenue if all tickets are sold at $24?
- How much additional revenue would result from increasing the $40 ticket price by 10%?
- If 100 fewer $24 tickets are sold, how many $40 tickets should be sold to maintain the same revenue?
- What percentage of the total seats are sold at the $40 price?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Formulas
x + y = 5000
24x + 40y = 148,800
Theorems
System of linear equations
Suitable Grade Level
Grades 9-12
Related Recommendation
Solving for Ticket Sales in a 5000-Seat Theater with Revenue Equation
Solving a System of Equations for Theater Ticket Sales and Revenue
Solving Ticket Sales Problem with Systems of Equations: $17 and $27 Tickets for a 13,000 Seat Concert
Solving a System of Equations for Broadway Ticket Sales
Solve for Adult and Child Tickets Sold Using System of Equations