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Math Help - Word problem involving billing

  1. #1
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    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.
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  2. #2
    Eater of Worlds
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    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
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