Producing a musical costs $88,000 plus $5,900 per performance. One sold-out performance earns $7,500 income. If every performance sells out, how many performances are needed to break even?

Answer 1

Let's assume the number of performances needed to break even is x.
The cost of producing x performances is $5,900 * x.
The total cost of producing the musical is $88,000 + $5,900 * x.
The total income from x performances is $7,500 * x.
To break even, the total income from x performances should equal the total cost of producing the musical, so we have the equation:
$7,500 * x = $88,000 + $5,900 * x
$7,500 * x - $5,900 * x = $88,000
$1,600 * x = $88,000
x = $88,000 / $1,600
x = <<55=55>>55
To break even, 55 performances are needed. Answer: \boxed{55}.