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Math Help - x1 + x2 + x3 = 100

  1. #1
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    x1 + x2 + x3 = 100

    How many solutions in set N ∪ {0} have equation x1 + x2 + x3 = 100.
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  2. #2
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    lets fix a value of x1, say 5. How many solutions are left?

    The new equation is x2+x3=100-5
    Which has 96 solutions. These correspond to x2 taking every value between 0 and 95, and x3=95-x2.

    Generalising, we could fix x1 at any value between 0 and 100.
    So the number of solutions is:
    \sum_{k=0}^{k=100} 101- k



    Can you finish from there?
    Last edited by SpringFan25; June 25th 2010 at 12:36 PM.
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  3. #3
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    We can put N identical objects into K distinct cells
    in \binom{N+K-1}{N} ways.
    Here we have 100 ones.
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