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
Start by solving for S:
$\displaystyle R=100-\frac{100}{1+S}$
Subtracting 100 from both sides:
$\displaystyle R-100=-\frac{100}{1+S}$
Multiplying through by $\displaystyle -1$:
$\displaystyle 100-R=\frac{100}{1+S}$
Multiplying through by the denominator:
$\displaystyle (100-R)(1+S)=100$
Dividing both sides by $\displaystyle (100-R)$:
$\displaystyle 1+S=\frac{100}{100-R}$
Subtracting $\displaystyle 1$ from both sides:
$\displaystyle S=\frac{100}{100-R}-1$
Writing everything over a common denominator:
$\displaystyle S=\frac{100-(100-R)}{100-R}$
Simplifying:
$\displaystyle S=\frac{R}{100-R}$
$\displaystyle S=\frac{G}{L}$, so:
$\displaystyle \frac{G}{L}=\frac{R}{100-R}$
Which means that:
$\displaystyle G=\frac{R\cdot{L}}{100-R}$
$\displaystyle G=\frac{Yg+Tg}{2}$, so:
$\displaystyle \frac{Yg+Tg}{2}=\frac{R\cdot{L}}{100-R}$
See if you can take it from here, using a similar approach. Don't substitute for L until you've solved for $\displaystyle Tg$