A number of 53 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes? Choose the correct choice from the following answers.
A) 10	B) 12	C) 15	D) 16	E) 17

Rationale: "to maximize # of boxes we should minimize marbles per box : 16 * 3 + 1 * 5 = 53 - - > 16 + 1 = 17 . answer : e ."
Answer: E