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Thread: Find b in x/(x+b) = c

  1. #1
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    Find b in x/(x+b) = c

    If x = 5 and c = 0.25, how do I find b in x/(x+b) = c?
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  2. #2
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    Re: Find b in x/(x+b) = c

    Quote Originally Posted by usc00 View Post
    If x = 5 and c = 0.25, how do I find b in x/(x+b) = c?

    Out of different methods, you may want to experiment with this:

    x/(x + b) = c/1

    Invert each side:

    (x + b)/x = 1/c

    x/x + b/x = 1/c

    1 + b/x = 1/c

    b/x = 1/c - 1

    b = x(1/c - 1)

    Substitute the values for x and c and simplify the
    expression to an integer, or fraction, as appropriate.
    Thanks from topsquark
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  3. #3
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    Re: Find b in x/(x+b) = c

    My favorite is criss-cross multiplication;
    example: if a/u = b/v then av = bu

    With yours:
    x/(x+b) = c/1 : x = c(x+b) : x = cx + cb : cb = x - cx : b = x(1-c)/c : same results as greg's
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  4. #4
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    Re: Find b in x/(x+b) = c

    In addition to greg1313 solution, you can also do this way

    x/(x+b) = c

    multiply both sides by (x + b)

    (x + b)x/(x + b) = c(x + b)

    (x + b) on the left side will be cancelled

    x = c(x + b)

    x = cx + cb

    cb = x - cx

    b = (x - cx)/c = (5 - (0.25)(5))/0.25 = 15
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