2025 AMC 10B Problem 8

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 \ne 0.” After a pause, Max says, “That was a good price.” What is A + B?

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.