Problem Solving

Can anyone show me how to arrive at the correct answer for this one? thanks!

There is a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?

A)3
B)5
C)8
D)13 (correct answer)
E)15

Thank you.

total books borrowed = 30*2 = 60
Number of students who borrowed books >=3 = 30-2-12-10=6.

Now in case one person has to borrow max books rest (5) have to borrow least = 3.

so 15 books.(3*5)

So total books borrowed = 15 + 12 + 20 = 47. So maximum books borrowed by any student = 60-47 = 13