The break-even point occurs when the total cost is equal to the total revenue.
If xx is the number of lawns, then the total cost of Sue is the sum of $665 and the cost in gas per lawn times the number of lawns:
and her revenue is the amount she charges times the number of lawns:
So, we equate and solve for x:
Solve for the cost using either P or R:
The break-even point is (35,700) which means that the cost and revenue are equal for 35 lawns at $700.