A carpenter charges a set fee for each job in addition to his hourly charge.

If a carpenter bills his customer $125 for a job which takes him 3 hours 

and bills a second customer $200 for a 6 hour job, 

:

Let f = fixed fee

Let h = hourly rate

:

Two equations:

3h + f = 125; "$125 for a job which takes him 3 hours" 

6h + f = 200; "$200 for a 6 hr job"

:

Subtract the 1st equation from the 2nd equation 

6h + f = 200 

3h + f = 125

--------------- eliminates f, find h

3h = 75

h = $25 an hr

;

Find f in the 1st equation

3(25) + f = 125

f = 125 - 75

f = $50 set fee

:

:

Check solution in the 2nd equation

6(25) + 50 = 200

150 + 50 = 200 

:

how much would he charge for a job that takes 8 hours?

8(25) + 50 = $250