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A problem involving bases.

  1. Oct 29, 2009 #1
    How would you solve a problem like this where you have to find what base A is for this equation to be true? So in what base are these numbers.


    24)A + 17)A = 40)A

    Not asking the answer for this particular question but how you'd solve it (other than trial and error obviously)
     
  2. jcsd
  3. Oct 29, 2009 #2
    A two digit number ab)A in base A equals [itex]A\cdot a + b[/itex] so:
    24)A = 2A + 4
    17)A = 1A + 7
    40)A = 4A + 0
    Then substitute in the equation and solve for A.
     
  4. Oct 29, 2009 #3
    Simple:

    [tex]24_A = 2*A^1+4*A^0 = 2A + 4[/tex]

    Similarly, [tex]17_A = 1A + 7[/tex] and [tex]40_A = 4A + 0[/tex]

    Substitute and solve for A
     
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