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Jan 17th 2012 Math Test

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  • Jan 17th 2012 Math Test

    The product N of three positive integers is 6 times their sum , and one of the integers is the sum of the other two.
    Find the sum of all possible values of N .

    product N of 3 positive integers
    A x B x C = N

    is 6 times their sum ,
    = 6 ( A + B + C )

    and one of the integers is the sum of the other two.
    A + B = C

    Find the sum of possible values of N

    A x B x C = N = 6 ( A+ B+ C )
    A + B = C so A+ B = A+ B
    A x B = AB

    AB ( A+ B) = N = 6 ( A + B + A + B ) ...............A+ B is substituted for all C's see A+B = C

    AB ( A + B ) = 6 ( 2A + 2B ) = N
    AB ( A + B ) = 12 ( A + B ) = N

    divide both sides by ( A + B ).
    AB ( A + B ) / ( A + B ) = 12 ( A + B ) / ( A+ B ) =
    AB = 12 = N

    ..........................Product of 3 + integers.........6 ( A+ B + C)
    A + B = C ....................AB(C) = N..................
    1 + 12 = 13 ........ 12 X 13 = 156........... 6 ( 1 +12 +13 ) = 6 x 26 = 156
    2 + 6 = 8 ..........2 x 6 X 8 = 96............6 ( 2 + 6 + 8 ) = 6 x 16 = 96
    3 + 4 = 7 ..........3 x 4 x 7 = 84 ............6 ( 3 + 4 + 7 ) = 6 x 14 = 84


    Find the sum of possible values of N

    156 + 96 + 84 = 336
    Last edited by XXChris123; Wed Jan 18, 2012, 07:22 AM.

  • #2
    Pemdas
    May the tinfoil protect you. MT

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    • #3
      N=6
      A=1
      B=2
      C=3

      Not great at math, but my best guess

      Yawni
      Last edited by Yawni; Tue Jan 17, 2012, 07:43 PM. Reason: Nope I'm wrong
      3 Time Bracelet Winner


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      • #4
        Oh these are great I really liked your birdhouse with the picket fence on it too umbup: (I got 3 sets of possible numbers for A,B,C - is that what you got? )

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        • #5
          very good Sam guess I will repost it

          video of the math problem

          http://www.khanacademy.org/video/200...etition%20Math
          Last edited by XXChris123; Wed Jan 18, 2012, 07:13 AM.

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          • #6
            Maybe people are just shy about like, oh geez, did I do it okay? Is my answer right? Is it part right? Sort of?

            They're getting harder pretty fast! But nice to be able to try and stuff

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            • #7
              I can do a range
              maybe I should back pedal
              If nothing else I want to raise players math skills to the point they can do all the math
              behind poker

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