A certain tree T of order n has only vertices of degree 1 and 3. Show that T contains (n-2)/2 vertices of degree 3.

Well I know it will have n-1 edges.

I also know by the first theorem of graph theory

that

sum (deg vertices)=2(size)=2(n-1)

I can let x=number of vertices of degree 1 and n-x=number of degree 3.

So

x+(n-x)=2(n-1), but then I get confused because the x's cancel and I have

n=2n-2

Or

n-2=0

n=2...That doesn't make sense though...what is wrong?

Nevermind, I got it...I forgot it was 3x