Question 30
Joey wrote a system of equations on a blackboard, where each of the equations was of the form $a+b=c$ or $a \cdot b=c$ for some variables or integers $a, b, c$. Then Sean came to the board and erased all of the plus signs and multiplication signs, so that the board reads:
$$
\begin{array}{ll}
x & z=15 \\
x & y=12 \\
x & x=36
\end{array}
$$
If $x, y, z$ are integer solutions to the original system, find the sum of all possible values of $100 x+10 y+z$.
$$
\begin{array}{ll}
x & z=15 \\
x & y=12 \\
x & x=36
\end{array}
$$
If $x, y, z$ are integer solutions to the original system, find the sum of all possible values of $100 x+10 y+z$.