# How to determine an unknown metal based on the reaction products with oxygen and fluorine?

The following question is, as it will probably be obvious, a homework question, however I have absolutely no idea how to progress with it beyond what I have already done. This is the question:

$\pu{10 g}$ of an unknown metal reacts with oxygen to produce $\pu{16.58 g}$ of the metal oxide. $\pu{10 g}$ of the same metal reacts with fluorine to produce $\pu{25.63 g}$ of the metal fluoride. The valency of the metal is identical in the metal oxide and fluoride produced. Identify the metal after finding the mass of one mole.

My attempt: \begin{align} m(\ce{O2}) &= \pu{ 6.58 g} & \implies&& n(\ce{O2}) &= \pu{0.206 mol}\\ m(\ce{F2}) &= \pu{15.63 g} & \implies&& n(\ce{F2}) &= \pu{0.411 mol} \end{align}

I also made the equations, where X was the unknown metal: \begin{align} \ce{X + y/2 O2 &-> XO_y}\\ \ce{X + z/2 F2 &-> XF_z}\\ \end{align}

Any help with where to go next would be massively appreciated.