$\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}=10$
$⇔(\frac{x-85}{15}-1)+(\frac{x-74}{13}-2)+(\frac{x-67}{11}-3)+(\frac{x-64}{9}-4)=0$
$⇔\frac{x-100}{15}+\frac{x-100}{13}+\frac{x-100}{11}+\frac{x-100}{9}=0$
$⇔(x-100)(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9})=0$
$⇔x-100=0$ (Vì $\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\neq0$)
$⇔x=100$
Vậy $S=${$100$}.