Question

Derek owns a landscape business. He charges a fixed fee of $30 plus $1 per 1,000 square feet of lawn mowed. Derek's earnings (in dollars) in the past five weeks are {204, 344, 450, 482, 504}. To find the corresponding square footage of lawn mowed, construct a function that models the total area of lawn that Derek mows based on his earnings.

Answer 1

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