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How would I represent this problem as three linear equations

  1. Feb 6, 2015 #1
    1. The problem statement, all variables and given/known data

    "A company has a budget of $280,000 for computing equipment. Three
    types of equipment are available: microcomputers at $2000 a piece,
    terminals at $500 a piece, and word processors at $5000 a piece. There
    should be five times as many terminals as microcomputers and two
    times as many microcomputers as word processors. Set this problem up
    as a system of three linear equations. Determine approximately how
    many machines of each type there should be by solving by trial-and-error.

    Note: Check your answer by expressing the numbers of terminals and
    microcomputers in terms of the number of word processors and solving
    the remaining single equation in one unknown . "



    2. Relevant equations

    How would I represent this problem as three linear equations


    3. The attempt at a solution

    I believe that I was able to solve the problem algebraically : number of microcomputers 40, number of word processors is 20, and the number of terminals is 200 but I'm not sure about how to express it as a series of three linear equations.

    So far this is what I have :
    Let x be the number of microcomputers
    Let y be the number of terminals
    Let z be the number of word processors

    2000x+500y+5000z = 280,000
    y = 5x
    x = 2z

    Should the previous three lines suffice?
     
  2. jcsd
  3. Feb 6, 2015 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, that looks perfectly fine. If you are able to solve it algebraically for the correct answer, why would you doubt it?
     
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