Emmy says to Max, "I ordered $36$ math club sweatshirts today." Max asks, "How much did each shirt cost?" Emmy responds, "I'll give you a hint. The total cost was $\$ \underline A~\underline B~\underline B.\underline B~\underline A$ , where $A$ and $B$ are digits and $A \neq 0$ ." After a pause, Max says, "That was a good price." What is $A + B$ ?