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:

\(P(x)=665+1(x)\)

\(P(x)=665+x\)

and her revenue is the amount she charges times the number of lawns:

\(R(x)=20x\)

So, we equate and solve for x:

\(P(x)=R(x)\)

\(665+x=20x\)

\(665=19x\)

\(35=x\)

Solve for the cost using either P or R:

\(R(35)=20(35)=700\)

The break-even point is (35,700) which means that the cost and revenue are equal for 35 lawns at $700.