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

Assume Derek mows an area of 1,000x square feet.

then Derek earns 30 $+x $ =30+x ($)

Assume Derek earns y dollars, then 

y= 30+x

to find x, the 1,000 sq feet area Derek mowed, we isolate x, that is we write x in terms of y, his earnings:

y= 30+x

x = y-30

Thus, the function A, which gives the area mowed in terms of the earnings y is :

x= A(y) = y-30

A(204)=204-30=174
A(344)=344-30=314
A(450)=450-30=420
A(482)=482-30=452
A(504)=504-30=474

Thus Derek earned  204, 344, 450, 482, 504 dollars for mowing correspondingly  
174,000;  314,000;  420,000;  452,000 ; 474,000 square feet.


 A(y) = y-30, is the function which gives the 1,000y square feet area mowed when earning y dollars.



Remark:

or A(x)=x-30, since x or y is a 'dummy variable', it doesn't make any difference in describing the function.