A student analyzes a 10.00 g solid mixture containing only \(\text{FeO(s)}\) and \(\text{Fe}_2\text{O}_3\text{(s)}\). The mixture is heated in a stream of excess \(\text{H}_2\text{(g)}\) until both iron oxides are completely reduced to elemental iron according to the following chemical equations:

\[\text{FeO(s)} + \text{H}_2\text{(g)} \rightarrow \text{Fe(s)} + \text{H}_2\text{O(g)}\]
\[\text{Fe}_2\text{O}_3\text{(s)} + 3\text{ H}_2\text{(g)} \rightarrow 2\text{ Fe(s)} + 3\text{ H}_2\text{O(g)}\]

After the reaction is complete and the tube is cooled, the remaining solid iron has a mass of \(7.35 \text{ g}\).

Substance	Molar Mass (\(\text{g/mol}\))
\(\text{Fe}\)	56.0
\(\text{O}\)	16.0
\(\text{FeO}\)	72.0
\(\text{Fe}_2\text{O}_3\)	160.

Given the information in the table above, what is the mass percent of \(\text{FeO(s)}\) in the original mixture?