Suppose you are starting an office-cleaning service you have spent $315 on equipment to clean each office, you use $4 worth of supplies you charge $25 per office how many offices must you clean to break even

15 offices should be cleaned to break even.

Break even is when your revenue is equal to your expenses resulting to zero profit.

Let x be the number of cleaned offices.

Revenue = 25x

Expenses = Fixed Expense + Variable Expense = 315 + 4x

25x = 315 + 4x

25x - 4x = 315

21x = 315

21x / 21 = 315 / 21

x = 15 offices.

To check:

25 (15) = 315 + 4 (15)

375 = 315 + 60

375 = 375

Profit = Revenue - Expenses

Profit = 12x - (315 + 4x)

Profit = 12 (15) - 315 - 4 (15)

Profit = 375 - 375

Profit = 0