adam15 wrote:In class of 30 students, 2 did not borrow any books from the liberary, 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 ( arithemtic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?
3
5
8
13
15
, my answer:
28 is the sum of books borrowed by the 6 students, the maximum book that each could have is
5*5+3; thus 5 of 6 will have 5, and one will have 3.
the number of books a single student could borrow will be:
5+3+2+1=11+2=13 (because the 2 students who did not borrow any book.
Assuming your math is correct to this point, here's where you made your mistake.
We want "the maximum number of books that
any single student could have borrowed?"
Whenever you're asked to maximize one thing, you want to minimize everything else.
So, those 6 students must borrow 28 books and each one must borrow at least 3 books. To maximize a single student, we minimize the other 5 at 3 each, giving us:
28 - 5*3 = 28 - 15 = 13 books
