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?
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}.