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This problem involves finding how many tickets should be sold at each price to generate a total revenue of $149,300 from a 5000-seat theater. Tickets are priced at $27 and $40.

Let’s set up the problem using variables:
- Let $ x $ represent the number of tickets sold at $27.
- The total number of tickets sold is 5000, so the number of tickets sold at $40 would be $ 5000 - x $.

The total revenue from the tickets sold at $27 and $40 is $149,300. We can form the equation:

\[
27x + 40(5000 - x) = 149,300
\]

Let’s solve for $ x $.

### Step 1: Expand and simplify the equation:
\[
27x + 200,000 - 40x = 149,300
\]
\[
-13x + 200,000 = 149,300
\]

### Step 2: Move the constant to the other side:
\[
-13x = 149,300 - 200,000
\]
\[
-13x = -50,700
\]

### Step 3: Solve for $ x $:
\[
x = \frac{-50,700}{-13} = 3,900
\]

So, **3,900 tickets** should be sold at $27.

Now, the number of tickets sold at $40 is:
\[
5000 - 3900 = 1,100
\]

Therefore, **1,100 tickets** should be sold at $40.

Would you like more details on the process or have any further questions?

Here are 5 related questions:
1. How would the equation change if the prices were different, say $30 and $50?
2. What if the total revenue was different, how would that affect the calculation?
3. Can you solve for the number of tickets if the prices and total revenue were given as variables?
4. How can you check if your answer is correct after solving the equation?
5. What happens if fewer than 5000 tickets are sold—how would that affect the equation?

**Tip**: Always double-check units (like dollars and seats) to make sure they match throughout the problem.

A 5000-seat theater has tickets for sale at $27 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $149,300?

Learn how to calculate the number of tickets sold at $27 and $40 in a 5000-seat theater to generate a total revenue of $149,300. This problem covers key algebraic concepts and linear equations. Suitable for students in Grades 10-12.

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