# 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 Expenses: $f \left(n\right) = 750 + 12 n$Income: $\textcolor{w h i t e}{\text{xx}} g \left(n\right) = 50 n$$\textcolor{w h i t e}{\text{XXX}} n$: number of lawns cut $\textcolor{w h i t e}{\text{XXX}}$Both functions in dollar amounts. Breakeven occurs while cutting the ${20}^{\text{th}}$lawn. #### Explanation: I assumed that the Expenses for labor and gas ($12) are per lawn.

The breakeven point occurs when Income $=$ Expenses

$50 n = 750 + 12 n$

$\rightarrow 38 n = 750$

$\rightarrow n \approx 19.73 \ldots$

That is the breakeven point does not occur until after the ${19}^{\text{th}}$ lawn.

Here are the Income and Expense functions with the intersection point being the breakeven point. 