Answer the following 2 questions. The situation is you have 16 new CDs to put on your empty
five-shelf CD rack.
Can you place the CDs so that each shelf contains three or few CDs? Explain how you came to
that conclusion.
Can you arrange them so that each shelf contains exactly three? Explain how you came to that
conclusion.



Answer :

To place the 16 CDs on a five-shelf CD rack, where each shelf contains three or fewer CDs:

1. You cannot place exactly 3 CDs on each shelf because 16 is not evenly divisible by 5 (number of shelves).
2. By distributing the CDs unevenly, you can have shelves with different numbers of CDs: for example, 3, 3, 3, 3, and 4 CDs on each shelf.

To place the 16 CDs on the five-shelf CD rack with each shelf containing exactly three CDs:

1. Since 16 is not divisible by 3 (the number of CDs per shelf), it is not possible to have exactly 3 CDs on each shelf.
2. The closest you can get is by placing 3 CDs on each of the first 4 shelves, totaling 12 CDs. Then, you can place the remaining 4 CDs on the fifth shelf.

In summary, for the first part, where each shelf can have three or fewer CDs, you can distribute them unevenly across the five shelves. For the second part, where each shelf must have exactly three CDs, you can place 3 CDs on the first 4 shelves and 4 CDs on the last shelf since 16 is not evenly divisible by 3.