jmc

Let $t,s,g$ be the weight of one treek, the weight of one squig, and the weight of one goolee, respectively. Then the given information tells us $$\begin{array}{rl}10t& =3s+g\\ 2t+g& =s.\end{array}$$ Since we would like to solve for $s$ in terms of $t$, we want to eliminate $g$. Add the two equations to obtain $$\begin{array}{rl}10t+2t+g& =3s+g+s\\ \Rightarrow 10t+2t& =3s+s\\ \Rightarrow 4s& =12t\\ \Rightarrow s& =3t.\end{array}$$ So one squig weighs $\boxed{3}$ treeks.