A number of 47 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:
A) 10  B) 12  C) 15  D) 16  E) 17

Rationale: "to maximize # of boxes we should minimize marbles per box : 14 * 3 + 1 * 5 = 47 - - > 14 + 1 = 15 . answer : c ."
Answer: C