Answer:
20 performances.
Step-by-step explanation:
Let x be the number of performances needed to break even.
We have been given that producing a musical costs $8,000 plus $300 per performance. This means that cost of producing x performances will be 300x and total cost of producing x performances will be:
[tex]\text{Total cost of producing x performances}=8,000+300x[/tex].
We are also told that one sold-out performance earns $700 income, so the total income earned from selling x performances will be 700x.
Since we know that break even is the point at which total cost and total income are equal and total profit at the break-even point is zero.
So let us equate total cost of producing x performances with total income earned from selling x performances to get our break even point.
[tex]8,000+300x=700x[/tex]
Upon subtracting 300x from both sides of our equation we will get,
[tex]8,000+300x-300x=700x-300x[/tex]
[tex]8,000=400x[/tex]
Let us divide both sides of our equation by 400.
[tex]\frac{8,000}{400}=\frac{400x}{400}[/tex]
[tex]20=x[/tex]
Therefore, 20 performances are needed to break even.
