Mechanics (Edexcel M2) question

Ok, so I'm looking at question 7 of this paper. (mark scheme.)

I do understand the solution in the mark scheme I'm still missing something. I tried to resolve moments around C, giving:

$\displaystyle w \cos (\alpha )=3 R \cos (\alpha )$

(w = 100N)

This gives R = 1/3 w, which is wrong but I can't see how the original equation is wrong.

Actually, the mark scheme notes that resolving around X gives

$\displaystyle 2 R \cos (\alpha )=S \left(3-2 \cos ^2(\alpha )\right)$

I'm not sure where this comes from either - surely as S is perpendicular to the rod it doesn't need to be multiplied by anything except the distance from X?

Anyway, if anyone could point out the (probably stupid) thing that I'm missing that would be great.

Re: Mechanics (Edexcel M2) question

moments about C ...

$\displaystyle W\cos{\alpha} + 3f\sin{\alpha} = 3R\cos{\alpha}$

Re: Mechanics (Edexcel M2) question

Ah, of course, I'm missing out friction. I knew it would be something like that.

Anyway, that's really helpful, thanks.