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math

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ab+cd=34
ac+bd=38
ad+bc=43
what is a+b+c+d=?
multiple choice:
a)15 b)16 c)17 d)18 e)19

First, I tried guessing and testing, but couldn't find the correct answer.
Then I tried isolating a
a=(34-cd)/b

I'm stuck, there are too many variables

  • math -

    In general, you are correct. There are not enough equations to solve for four variable. However they may be looking only for answers a,b,c,d that are integers. That restricts your options. Note that:

    ab + cd + ac + bd = (a+d)(b+c) = 72
    ab + ad + cd + bc = (a+c)(b+d) = 77
    ac + bd + ad + bc = (a+b)(c+d) = 81

    IF the solutions must be single-digit integers, the last equation tells you that
    a + b = 9 and
    c + d = 9

    Therefore
    a + b + c + d = 18

    To solve for all four, you could say that
    a + c = 11
    b + d = 7
    Which is consistent with a+b+c+d = 18

    I can't find a way of satisfying
    (a+d)(b+c) = 72
    such that the sum of the two factors is 18.

    I give up.

  • math -

    Wow, I never thought of combining it, thanks! The problem doesn't ask to solve for a b c & d

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