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Math Help - Please arrange and solve Equation

  1. #1
    Newbie
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    Please arrange and solve Equation

    Please help an old man who has been out of school for many years :-)

    Solve for Tg ...

    R=100-(100/(1+S)

    sub:
    S=G/L

    sub:
    G=(Yg+Tg)/2
    L=(Ys+Ts)/2


    Many Thanks in Advance
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  2. #2
    Super Member Quacky's Avatar
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    Re: Please arrange and solve Equation

    Start by solving for S:

    R=100-\frac{100}{1+S}

    Subtracting 100 from both sides:

    R-100=-\frac{100}{1+S}

    Multiplying through by -1:

    100-R=\frac{100}{1+S}

    Multiplying through by the denominator:

    (100-R)(1+S)=100

    Dividing both sides by (100-R):

    1+S=\frac{100}{100-R}

    Subtracting 1 from both sides:

    S=\frac{100}{100-R}-1

    Writing everything over a common denominator:

    S=\frac{100-(100-R)}{100-R}

    Simplifying:

    S=\frac{R}{100-R}

    S=\frac{G}{L}, so:

    \frac{G}{L}=\frac{R}{100-R}

    Which means that:

    G=\frac{R\cdot{L}}{100-R}

    G=\frac{Yg+Tg}{2}, so:

    \frac{Yg+Tg}{2}=\frac{R\cdot{L}}{100-R}

    See if you can take it from here, using a similar approach. Don't substitute for L until you've solved for Tg
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  3. #3
    MHF Contributor
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    Re: Please arrange and solve Equation

    Quote Originally Posted by goldbh View Post
    Solve for Tg ...
    R=100-(100/(1+S)
    sub:
    S=G/L
    sub:
    G=(Yg+Tg)/2
    L=(Ys+Ts)/2
    Hate your variables!
    a=R, b=S, c=G, d=L, e=Yg, f=Tg, g=Ys, h=Ts ; solve for f

    f = [a(g + h) - e(100 - a)] / (100 - a)
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  4. #4
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    Re: Please arrange and solve Equation

    Thanks to you both for the help
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