Thread: Word problem involving billing

I am not sure how to set this problem up. Any help would be appreciated.

Sally received a bill for a total of 8 hours labor on the repair of her bulldozer. She paid $50 to the master mechanic and $90 to his apprentice. If the master mechanic gets $10 more per hour than his apprentice, then how many hours did each work on the bulldozer.

THIS IS WHAT I CAME UP WITH THUS FAR.

We write T for the number of hours the master mechanic
worked, T' for the number of hours the apprentice worked, P for the price
the master charges per hour, and P' for the price the apprentice charges
per hour.

Four variables. We need four equations.

First Equation: Express the fact that the total number of hours worked is
8. (What does this have to do with T, T', P and P'? It involves only two of
these variables.)

Second Equation: Express the fact that the master mechanic earned $50.

Third Equation: Express the fact that the apprentice earned $90.

Fourth Equation: Express the fact that the master's pay rate exceeds the
apprentice's pay rate by $10 per hour.

We'll use what you came up with to illustrate. Okey-doke?.

Let a=hrs apprentice worked

Let m=hrs master worked.

Let x=apprentice's rate

Let y=master's rate.

System of equations:

ax=90....[1]
my=50....[2]
a+m=8....[3]
y-x=10....[4]


90/x=a
50/y=m

Sub into [3]:

90/x+50/y=8

Sub [4] into [3]:

90/(y-10)+50/y=8

Solve for y=25....The masters hourly rate.

That gives $15 for the apprentice's hourly rate.

The apprentice worked 6 hrs and the master worked 2.

15(6)=90, 25(2)=50