2014 AMC 12B Problem 10

Danica drove her new car on a trip for a whole number of hours, averaging 55 miles per hour. At the beginning of the trip, abc miles was displayed on the odometer, where abc is a 3-digit number with a \geq{1} and a+b+c \leq{7}. At the end of the trip, the odometer showed cba miles. What is a^2+b^2+c^2?.

\textbf{(A)}\ 26\qquad\textbf{(B)}\ 27\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 37\qquad\textbf{(E)}\ 41

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