7 of 100: XX YY ZZ

Algebra Level 2

\[ \begin{array} {ccccc} \huge & & & & \huge \color{purple}{X}& \huge \color{purple}{X}\\ \huge & & & & \huge \color{red}{Y}& \huge \color{red}{Y}\\ \huge + & & & & \huge \color{blue}{Z}& \huge \color{blue}{Z}\\ \hline \huge& & & \huge \color{purple}{X} & \huge \color{red}{Y} & \huge \color{blue}{Z} \end{array} \]

If each letter represents a different nonzero digit, what must \(\large \color{blue}{Z}\) be?