AMC 12 2025b Problem 6

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 $A+B$?

$\textbf{(A) } 7 \textbf{(B) } 8 \textbf{(C) } 11 \textbf{(D) } 14 \textbf{(E) } 15$