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Question

Marty’s plumbing charges a fixed dollar amount per hour plus a fixed a service fee per job. Physicians plumbing charges 10 less per hour than martyrs plumbing, but the fixed service per job charges is 10 more than martyrs plumbing charges. Marty’s plumbing took 5 hours to complete the job. Physicians plumbing would have also taken five hours to complete. Compared to Marty’s plumbing, Physicians plumbing would have charged?

Answer 1

M is the total that Marty's plumbing charges

P is the total that physicians plumbing charges

 

H1 is the hourly rate of Marty's

H2 is the hourly rate of physicians.

 

F1 is the fixed rate that Marty's charges

F2 is the fixed rate that Physician's charges.

 

t is time

 

In general, the amount charged = (hourly rate) x t + fixed rate

 

So: M=H1 x t + F1

      P = H2 x t + F2

 

We are given that physicians charges 10 less per hour than Marty's, so H2 = H1 - 10

physicians fixed service chage is 10 more than marty's: F2 = F1 + 10

 

Then P = (H1 - 10) x t + F1 + 10 = H1 x t - 10 x t + F1 + 10 = H1 x t + F1 + (10 - 10 x t) 

since M = H1 x 10 + F1

P = M + (10 - 10xt)

 

and P - M = 10 - 10 x t

 

For a 5 hour job, the difference is 10 - 10 x 5 = -40

 

That means that Physicians would've charged $40 less

Answer 2

cool so let the fixed dollar amount per hour be x and the service fee per job be y

 

then the total charge for Marty(M) would be :

 

M = 5x + y

 

P =  5 (x - 10) + (y + 10) 

 

=   5x + y - 40 

 

and this is how much Physician would have charged in total .

 

Physician would have charged $40 less than Marty to get the same job done over the same period of time