There are 55 performances needed to break even.
Work Step by Step
Let x = the number of performances and let y = the number of dollars of expense or income. Expense: $y = 5900x + 88000 $ Income: $y = 7500x $ Use substitution since both equations have been solved for $y$. $5900x + 88000 =7500x$ $1600x=88000$ $x=55$ There are 55 performances needed to break even.