A transition metal X forms an oxide of formula $$\text{X}_2\text{O}_3$$. It is found that only $$50\%$$ of X atoms in this compound are in the $$+3$$ oxidation state. The only other stable oxidation states of X are $$+2$$ and $$+5$$. What percentage of X atoms are in the $$+2$$ oxidation state in this compound?

Take $$\text{X}_4\text{O}_6$$, where the 4 metal atoms must carry a total charge of $$+12$$. Two atoms are $$+3$$, contributing $$+6$$, so the other two contribute $$+6$$. If $$a$$ of them are $$+2$$ and $$b$$ are $$+5$$, then $$a + b = 2$$ and $$2a + 5b = 6$$, giving $$a = \frac{4}{3}$$. So $$\frac{4/3}{4} = \frac{1}{3}$$, about $$33.33\%$$, of the X atoms are $$+2$$.