How many lawns does he have to landscape to break even?

Jamie wants to start a landscaping business. He buys $750 worth of equipment. Expenses for labor and gas are $12. He charges $50 per lawn. How many lawns does he have to landscape to break even? Write and solve a system of linear equations.

1 Answer
Apr 13, 2017

Answer:

Expenses: #f(n)=750+12n#
Income: #color(white)("xx")g(n)=50n#
#color(white)("XXX")n#: number of lawns cut
#color(white)("XXX")#Both functions in dollar amounts.
Breakeven occurs while cutting the #20^"th"# lawn.

Explanation:

I assumed that the Expenses for labor and gas (#$12#) are per lawn.

The breakeven point occurs when Income #=# Expenses

#50n = 750+12n#

#rarr 38n=750#

#rarr n~~19.73...#

That is the breakeven point does not occur until after the #19^"th"# lawn.

Here are the Income and Expense functions with the intersection point being the breakeven point.
enter image source here