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Math Help - Word Problem

  1. #1
    Junior Member
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    Word Problem

    Tom Smith hires three types of laborers (I, II, III) and pays them $8, $6, and $5 per hour, respectively. If the total amount paid is $2,800 for a total of 500 hours of work, find the possible number of hours put in by the three categories of workers if category III workers must put in the maximum number of hours?
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  2. #2
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    Re: Word Problem

    Let us say we have x, y and z hours put be the three types of laborers, I, II, III respectively
    Thus we get x + y + z = 500 ------ ( 1 )
    where 'z' has to be maximum
    Also we are given the expenditure.
    8x + 6y + 5z = 2800 ----- ( 2 )
    From (1) we get x = 500 - y - z
    Plugging it in equation (2), we get
    8( 500 - y - z ) + 6y + 5z = 2800
    4000 - 8y - 8z + 6y + 5z = 2800
    2y + 3z = 1200
    Since z has to be largest and total number of hours is 500 we try z = 300
    That will give
    y = 150
    Plugging in these values in (1) we get x = 50.
    We can verify that this solution which satisfies the given conditions
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