To find the number of notebooks James bought, we need to determine the total amount of money he spent and the cost of each notebook. The expression for the total money spent is given by [tex]\(2y^2 + 6\)[/tex], and the cost of each notebook is [tex]\(y^2 - 1\)[/tex].
First, we need to express the number of notebooks James bought in terms of total money spent divided by the cost per notebook. The expression to find the number of notebooks James bought is:
[tex]\[
\frac{2y^2 + 6}{y^2 - 1}
\][/tex]
Next, let’s substitute [tex]\(y = 3\)[/tex] into the expressions to calculate the actual values.
1. Calculate the total money spent:
[tex]\[
2(3)^2 + 6 = 2 \cdot 9 + 6 = 18 + 6 = 24
\][/tex]
So, James spent [tex]$24.
2. Calculate the cost of each notebook:
\[
(3)^2 - 1 = 9 - 1 = 8
\]
So, each notebook costs $[/tex]8.
3. Determine the number of notebooks bought:
[tex]\[
\text{Number of notebooks} = \frac{\text{Total money spent}}{\text{Cost per notebook}} = \frac{24}{8} = 3
\][/tex]
Therefore, if [tex]\(y = 3\)[/tex], James bought 3 notebooks.
