to find r, the rate the electrician charges per hour, in terms of x and f. If the invoice amount is $450 and the weekend fee is $75, what is the hourly rate?

Question

An electrician sent Bonnie an invoice in the amount of z dollars for the six hours of work done on Saturday.  The electrician charges a weekend fee f in addition to an hourly rate r. Write a formula Bonnie can use to find r, the rate the electrician charges per hour, in terms of z and f. If the invoice amount is $450 and the weekend fee is  $75, what is the hourly rate?

Answer 1

Invoice total as a function of hours worked, hourly rate, weekend fee:

 

I(h,r,f) = hr + f

 

h = # hours worked = 6

r = hourly rate  = tbd

f = weekend fee = 75

 

I(6,r,75) = 450

 

450 = 6r + 75

375 = 6r

375/6 = r

$62.50 = r

 

Check:

450 = 6(62.5) + 75

450 = 375 + 75

450 = 450

 

Note:  If this was normal business hours so there was no "weekend charge"

or "after hours" charge... The invoice total would be:

I(h,r) = hr