Chapter 6 - Systems of Equations and Inequalities - 6-4 Applications of Linear Systems - Practice and Problem-Solving Exercises - Page 390: 8

There are 55 performances needed to break even.

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.