Answer: 55 performances are needed to break even.
Step-by-step explanation:
Let x represent the number of musical performances that are made.
Producing a musical costs $88,000 plus $5900 per performance. This means that the total cost of x musical performances would be
88000 + 5900x
One sold-out performance earns $7500 in revenue. If every performance sells out, it means that the total revenue would be
7500 × x = 7500x
In order to break even, total cost would be equal to total revenue. Therefore,
7500x = 88000 + 5900x
7500x - 5900x = 88000
1600x = 88000
x = 88000/1600 = 55
