Mr. Davis has eight children of different ages. His oldest child, who is 9, spots a 4-digit license plate number in which the first two digits are identical and the last two digits are identical ($AABB$), where $A$ and $B$ are distinct non-zero digits. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Davis, "and the sum of the digits in the license plate number happens to be my age." What is Mr. Davis's age?