Day 7

# 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?

Solve this your own way and then check out the solutions -- there are at least two very different approaches for solving this one!