A student determines the mass percent of \(\text{CaCO}_3\text{(s)}\) (molar mass \(100.0 \text{ g/mol}\)) in a \(0.500 \text{ g}\) antacid tablet using a back-titration procedure. The tablet is crushed and completely dissolved in \(50.0 \text{ mL}\) of \(0.200 \text{ M } \text{HCl(aq)}\) (an excess). The reaction is represented by the following equation:

\[ \text{CaCO}_3\text{(s)} + 2\,\text{H}^+\text{(aq)} \rightarrow \text{Ca}^{2+}\text{(aq)} + \text{H}_2\text{O(l)} + \text{CO}_2\text{(g)} \]

The resulting solution is then titrated with \(0.100 \text{ M } \text{NaOH(aq)}\) to neutralize the unreacted acid according to the following equation:

\[ \text{H}^+\text{(aq)} + \text{OH}^-\text{(aq)} \rightarrow \text{H}_2\text{O(l)} \]

If \(20.0 \text{ mL}\) of \(0.100 \text{ M } \text{NaOH(aq)}\) is required to reach the equivalence point, what is the mass percent of \(\text{CaCO}_3\) in the tablet?