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 fewer CDs? Can you arrange them so that each shelf contains exactly three?
Can you place the CDs so that each shelf contains three or fewer CDs? - Yes
Can you arrange them so that each shelf contains exactly three? - No
To determine if it is possible to place the 16 new CDs on the five-shelf CD rack in a way that each shelf contains three or fewer CDs, we can use division. If we divide 16 by 5, we get an uneven result of 3.2 CDs per shelf.
Since each shelf can only contain whole numbers of CDs, it is not possible to arrange the CDs so that each shelf contains exactly three CDs. However, it is possible to arrange them so that each shelf contains three or fewer CDs.
One possible arrangement is as follows:
- Shelves 1 to 4: Each contains 3 CDs.
- Shelf 5: Contains 4 CDs.
This way, each shelf contains three or fewer CDs, but none of them contains exactly three CDs.
To find this arrangement, we can follow this process:
1. Start by placing three CDs on each of the first four shelves, totaling 12 CDs.
2. We are left with four CDs to distribute. Place these four CDs on the fifth shelf, which can hold a maximum of 5 CDs.
That's how we can place 16 new CDs on the empty five-shelf CD rack so that each shelf contains three or fewer CDs, but not exactly three CDs.