stamps are sold in booklets of 100, 50, 10 find as many different ways to buy 200 stamps as you can record your work I the chart
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Modelling 3- digit numbers
To find different ways to buy 200 stamps using booklets of 100, 50, and 10, we can use a systematic approach. Let's create a chart to keep track of the different combinations:
| Booklet of 100 | Booklet of 50 | Booklet of 10 |
|--------------|-------------|--------------|
| | | |
We'll start by considering the booklet of 100. Since we need to buy 200 stamps, the maximum number of booklets of 100 we can get is 2.
1. Option 1: 2 booklets of 100 stamps
| Booklet of 100 | Booklet of 50 | Booklet of 10 |
|--------------|-------------|--------------|
| 2 | 0 | 0 |
Next, let's explore the possibilities using the booklet of 50 stamps.
2. Option 2: 1 booklet of 50 stamps
To make up for the remaining 150 stamps, we need to consider combinations using the booklet of 10 stamps. Since we can have a maximum of 1 booklet of 50, the maximum number of booklets of 10 we can have is 15.
For each possibility, let's record the number of booklets of 10 in the chart:
| Booklet of 100 | Booklet of 50 | Booklet of 10 |
|--------------|-------------|--------------|
| 2 | 1 | Variable |
We'll fill the chart table by trying different values for the variable:
2.1 Option 2.1: 1 booklet of 50 stamps, 0 booklets of 10
| Booklet of 100 | Booklet of 50 | Booklet of 10 |
|--------------|-------------|--------------|
| 2 | 1 | 0 |
2.2 Option 2.2: 1 booklet of 50 stamps, 1 booklet of 10
| Booklet of 100 | Booklet of 50 | Booklet of 10 |
|--------------|-------------|--------------|
| 2 | 1 | 1 |
2.3 Option 2.3: 1 booklet of 50 stamps, 2 booklets of 10
| Booklet of 100 | Booklet of 50 | Booklet of 10 |
|--------------|-------------|--------------|
| 2 | 1 | 2 |
Continue this process until you have considered all possibilities for the booklet of 50 stamps.
Now, let's explore the possibilities using the booklet of 10 stamps.
3. Option 3: Only booklets of 10 stamps
To buy 200 stamps using only the booklet of 10, we can have a maximum of 20 booklets:
| Booklet of 100 | Booklet of 50 | Booklet of 10 |
|--------------|-------------|--------------|
| 2 | 0 | Variable |
We'll fill the chart table by trying different values for the variable:
3.1 Option 3.1: 20 booklets of 10 stamps
| Booklet of 100 | Booklet of 50 | Booklet of 10 |
|--------------|-------------|--------------|
| 2 | 0 | 20 |
Now, let's summarize the different ways to buy 200 stamps:
1. 2 booklets of 100 stamps
2. 1 booklet of 50 stamps
- 0 booklets of 10 stamps
- 1 booklet of 10 stamps
- 2 booklets of 10 stamps
3. Only booklets of 10 stamps
- 20 booklets of 10 stamps
Throughout this process, we filled out the chart, considering different combinations using each booklet size.