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.
Answer: 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.
