To find the cost of buying 10 trees based on the given data, we can determine the average cost per tree and use it to estimate the cost for 10 trees. Here's a detailed, step-by-step explanation:
1. Number of Trees and Their Costs:
- For 6 trees, the cost is [tex]$210.
- For 13 trees, the cost is $[/tex]455.
- For 18 trees, the cost is [tex]$630.
2. Calculate the Cost per Tree:
We have the costs for different numbers of trees, so we can calculate the cost per tree between pairs of points to check for consistency:
- Cost per tree between 6 and 13 trees:
\[
\text{Cost per tree} = \frac{\text{Cost for 13 trees} - \text{Cost for 6 trees}}{\text{Number of trees (13 - 6)}} = \frac{455 - 210}{13 - 6} = \frac{245}{7} = 35
\]
- Cost per tree between 13 and 18 trees:
\[
\text{Cost per tree} = \frac{\text{Cost for 18 trees} - \text{Cost for 13 trees}}{\text{Number of trees (18 - 13)}} = \frac{630 - 455}{18 - 13} = \frac{175}{5} = 35
\]
Both calculations give us a consistent result of $[/tex]35 per tree.
3. Average Cost per Tree:
Since both calculations give us the same cost per tree, the average cost per tree is:
[tex]\[
\text{Average Cost per Tree} = 35
\][/tex]
4. Calculate the Cost for 10 Trees:
Now that we know the cost per tree is [tex]$35, we can estimate the cost for 10 trees. We need to find the increment in cost from 6 trees to 10 trees:
- Difference in the number of trees from 6 to 10:
\[
\text{Difference} = 10 - 6 = 4 \text{ trees}
\]
- Additional cost for 4 more trees:
\[
\text{Additional cost} = 4 \text{ trees} \times 35 \text{ dollars/tree} = 140 \text{ dollars}
\]
- Total cost for 10 trees:
\[
\text{Total cost} = \text{Cost for 6 trees} + \text{Additional cost} = 210 \text{ dollars} + 140 \text{ dollars} = 350 \text{ dollars}
\]
Based on this pattern, the cost to buy 10 trees would be $[/tex]350.
