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Multivariable proofs

  1. Jan 13, 2005 #1
    I'm confronted with the following question that may of may not have a solution:

    You are given eight variables, A, B, C, D, E, F, G, and H.

    These variables are integers.

    You know that:

    A/B > E/F

    and

    C/D > G/H

    Is it possible that (A+C)/(B+D) < (E+G)/(F+H)?

    I've tried everything, such as multiplying, and expanding, but that did not get me anywhere. I also tried trial and error with unsuccessful results.

    Is it even possible?
     
  2. jcsd
  3. Jan 13, 2005 #2
    how about C=D=10000000000, G=1,H=2,A=1000,B=1,E=500,F=1
     
  4. Jan 14, 2005 #3
    That's so astronomically huge!

    I was thinking about it, and found another solution:

    A=1
    B=2
    C=1
    D=2
    E=-200
    F=50
    G=150
    H=-100

    1/2 < -50/-50 = 1

    Now that we found some variables that solved the existence of the question, how can we begin to apporach at deriving the parameters of the variables that will satisfy A+C/B+D < E+G/F+H?
     
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