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. Based on Derek's earnings, the corresponding square footage of the lawns he mowed in the past five weeks is

Answer 1

{174,000, 134,000, 420,000, 452,000, 474,000}

Answer 2

Let
x = earnings, dollars
y = area mowed, in 1000's of square feet.

Then the required function is
y = x - 30

Construct a table that shows Derek's weekly earnings versus area mowed.

week x y
------- -------- ----------
1 204 174
2 344 314
3 450 420
4 482 452
5 504 474
----- ------- -----------
Total 1984 1834

A graph of y versus x is shown below.

From the table, obtain the total area mowed in the past five weeks as the sum of the y columns, which is 1,834 thousand square feet.

Answer: 1,834 thousand square feet.