jmc

We add up the fractions of non-red bows and get $\frac{1}{5}+\frac{1}{2}+\frac{1}{10}=\frac{2+5+1}{10}=\frac{8}{10}=\frac{4}{5}$. So the 30 bows make up $1-\frac{4}{5}=\frac{1}{5}$ of the total bows, and the total number of bows is $5\times 30=150$. The green bows are $\frac{1}{10}$ of the total, and $\frac{1}{10}\times 150=15$, so there are $\boxed{15}$ green bows.