Solution 6a70f4c5-ed8d-4ac6-b2eb-57d9745ff515

Points: 1 pt

Taking each shirt's price to be a whole number of cents, the total cost in
cents must be divisible by $36$:
\[
36\mid\overline{ABBBA}.
\]
Since $36=4\cdot 9$, we use the divisibility rules for $4$ and $9$.

\[
\begin{aligned}
3 &\mid 9\mid 2A+3B \\
2 &\mid 4\mid 2B+A
\end{aligned}
\]
We then see
\[
\begin{aligned}
3 &\mid A \\
2 &\mid A
\end{aligned}
\]
Since $A\ne 0$, we have $A=6$.
\[
\begin{aligned}
9 &\mid 3+3B \\
4 &\mid 2B+2
\end{aligned}
\]
Thus $B=5$ is the only possible solution.
\[
A+B=6+5=11
\]

Final answer:
11