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Please i need help with Base Mathematics

  1. May 16, 2007 #1
    When fractions F1 and F2 are written as base n decimals, F1=(.7373)base n and F2=(.3737)base n. In base m, F1=(.5252)base m and F2=(.2525) base m. Find (m+n). No trial and error please.
     
  2. jcsd
  3. May 16, 2007 #2

    HallsofIvy

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    Saying "F1= (.7373) base n" means F1= 7/n+ 3/n2+ 7/n3+ 3/n4. Similarly, saying "F1= (.5252) base m" means that F1= 5/m+ 2/m2+ 5/m3+ 2/m4. Putting those together you know that 7/n+ 3/n2+ 7/n3+ 3/n4= 5/m+ 2/m2+ 5/m3+ 2/m4. Likewise, F2= (.3737) base n and F2= (.2525) base m gives 3/n+ 7/n2+ 3/n3+ 7/n4= 2/m+ 5/m2+ 2/m3+ 5/m4. That gives you two equations to solve for the two unknown numbers m and n.

    Edited to replace "y/n3" by "7/n3". My finger slipped!
     
    Last edited: May 18, 2007
  4. May 16, 2007 #3
    where are you getting y/n^3 from
    I tried doing this method without the y variable and was not able to solve for it. I came up with some crazy nubers. Can you please explain further?
     
  5. May 16, 2007 #4
    Im not positive but i think halls of ivy meant 7 and not y, as you can see, they are right nnext to each other on the keyboard
     
  6. May 17, 2007 #5
    dOES ANYONE KNOW HOW TO SOLVE THIS EQUATION SIMULTANEOUSLY?
     
  7. May 18, 2007 #6
    It seems to me that you're supposed to spot the weird symmetry in the numbers here. '7373', '3737', '5252', '2525'. HallsofIvy outlines a general method of solving this problem when the given numbers have no special pattern, but f:grumpy:k only knows how you'd solve those simultaneous equations!

    My thoughts. Try adding F1 and F2 in base m and in base n. Assume, just to make it easier, that n>10 and m>7 (if that's not the case I'm sure it'll turn up in some contradiction or other)


    (eta: well, I'm not making much progress... but I still think that it's important to note the symmetry here. It means something, I'm sure of it.)
     
    Last edited: May 18, 2007
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