Brynn owns a printing company that makes customized stickers. The cost to print a batch of customized stickers increases at a constant rate with respect to the number of stickers ordered. Use the information in the table to complete the table for this constant relationship.
Explain your reasoning.
To complete the table for the constant relationship, we need to find the difference between the costs for each consecutive pair of sticker quantities.
Let's look at the table:
| Quantity of Stickers | Cost |
|---------------------|------|
| 100 | $50 |
| 200 | ? |
| 300 | ? |
| 400 | ? |
Let's find the difference between the cost for 200 stickers and 100 stickers.
Cost difference = Cost for 200 stickers - Cost for 100 stickers
We don't have the cost for 200 stickers in the table, so let's assume it is $x.
Cost difference = $x - $50
Similarly, we can find the difference for the remaining pairs:
Cost difference for 300 stickers = $y - $x
Cost difference for 400 stickers = $z - $y
Since the question states that the cost increases at a constant rate, the cost difference for every pair of consecutive sticker quantities should be the same.
Therefore, the differences between the costs for the pairs 100-200, 200-300, and 300-400 should all be the same.
By finding the common difference, we can complete the table.