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Worded question - matrices

  1. Oct 20, 2009 #1
    Gold courses have 18 holes.
    each hole has a par, with either 3,4,5
    the sum over the holes of one gold course is 78.
    the number of par 5 holes is 6 more than the number of par 3 holes

    if there are x holes with par 3, y holes with par 4 and z holes with par 5
    write down a system of three linear equations linking these quantities

    first two are easy
    ( 1 1 1 18 )
    ( 3 4 5 78 )
    the third one I'm confused how to get to
    ( 1 0 1 7 ) ?
    i solved using row echelon reduction and it dosen't work

    the answers say -1 0 1 6
    how does it get that???
    how am i supposed to know that during a test?
    please help
     
  2. jcsd
  3. Oct 20, 2009 #2
    Your first two equations look fine to me. For the third, the number of par 5 holes is z the number of par 3 holes is x and the number of par 5 holes is 6 more than the number of par 3 holes so

    z = x + 6

    or

    z - x = 6

    Does that help?
     
  4. Oct 20, 2009 #3
    Oh, I was having a hard time trying to figure out why it was -x + z
    cheers
    get it
     
  5. Oct 20, 2009 #4
    Glad to help :smile:
     
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