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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

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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

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