From the given problem statement alone, we can say that
the equation relating the area of the lawn mowed and the earnings has a linear
relationship. That is because there is a constant increase in the earnings per
area which is $1 per 1000 square feet.
Therefore the equation must be in the form of:
y = m x + b
where,
y = is the total earnings
m = is the fee per area = 1 / 1000
x = is the area of the lawn
b = is the fixed fee = 30
Therefore the equation becomes:
y = 0.001 x + 30
Rewriting this in terms for x since we are to find the
area:
x = (y – 30) 1000
when y = 204
x = (204 – 30) 1000 = 174,000 square feet
when y = 344
x = (344 – 30) 1000 = 314,000 square feet
when y = 450
x = (450 – 30) 1000 = 420,000 square feet
when y = 482
x = (482 – 30) 1000 = 452,000 square feet
when y = 504
x = (504 – 30) 1000 = 474,000 square feet
