Solution 9e3dc5db-c8fb-4577-9f03-03de3102d91b

Points: 1 pt

Writing both numbers in base ten gives
\[
7a+b=9b+a
\quad\Longrightarrow\quad
6a=8b
\quad\Longrightarrow\quad
3a=4b.
\]
Since $a,b<7$, we see the only solution is $(a,b)=(4,3)$. We then see
\[
a+b=7.
\]

Final answer:
7