Roger has a collection of 10 total items. He can have baseball cards, records, or a combination of baseball cards and records. What combinations of items could be in the collection?

Question

Fill in some combinations of items in the collection to have a total of 10 items.
Number of baseball cards Number of records
9
6
4
0

Answer 1

To determine the combinations of baseball cards and records that sum up to a total of 10 items, we can fill in the table based on the constraint that the total should always equal 10.

Here's how the combinations work out for different values of baseball cards:

1. Number of baseball cards: 9

   • Number of records: 10 - 9 = 1
   • Combination: 9 baseball cards, 1 record

2. Number of baseball cards: 6

   • Number of records: 10 - 6 = 4
   • Combination: 6 baseball cards, 4 records

3. Number of baseball cards: 4

   • Number of records: 10 - 4 = 6
   • Combination: 4 baseball cards, 6 records

4. Number of baseball cards: 0

   • Number of records: 10 - 0 = 10
   • Combination: 0 baseball cards, 10 records

Thus, the combinations can be filled in as follows:

| Number of baseball cards | Number of records | |-------------------------|------------------| | 9 | 1 | | 6 | 4 | | 4 | 6 | | 0 | 10 |

These combinations represent all the possible distributions of 10 total items between baseball cards and records.