Producing a musical costs $8,000 plus $300 per performance. One sold-out performance earns $700 income. If every performance sells out, how many performances are needed to break even?
number of performance ----- n
expenses = 8000 + 300n
revenues = 700n
when are they equal?
8000 + 300n = 700n.
To determine the number of performances needed to break even, we need to consider the costs and income associated with each performance.
Let's break down the cost structure:
- The fixed cost (costs that remain the same regardless of the number of performances) is $8,000.
- The variable cost (costs that depend on the number of performances) is $300 per performance.
Next, let's calculate the income per performance:
- A sold-out performance earns $700 income.
To break even, the total cost needs to be equal to the total income. Let's calculate the total cost and total income:
Total Cost = Fixed Cost + (Variable Cost per Performance × Number of Performances)
Total Income = Income per Performance × Number of Performances
Let's substitute the given values into these formulas:
Total Cost = $8,000 + ($300 × Number of Performances)
Total Income = $700 × Number of Performances
To break even, the total cost must equal the total income:
$8,000 + ($300 × Number of Performances) = $700 × Number of Performances
Now, let's solve this equation to find the number of performances needed to break even:
$8,000 + $300 × Number of Performances = $700 × Number of Performances
Transposing the equation:
$300 × Number of Performances - $700 × Number of Performances = -$8,000
Combining like terms:
-$400 × Number of Performances = -$8,000
Divide both sides by -400:
Number of Performances = -$8,000 / -$400
Number of Performances = 20
Therefore, to break even, you would need 20 performances.