To find the maximum number of shirts the store owner can purchase, we can divide the total amount of money available by the cost of each shirt.
The total amount of money the store owner has is $2,578, and each shirt costs $17.
We can perform the calculation as follows:
\[ \text{Number of shirts} = \frac{\text{Total Money}}{\text{Cost per shirt}} = \frac{2578}{17} \]
Now, let's calculate:
\[ \frac{2578}{17} = 151.05882352941177 \]
Since the store owner cannot purchase a fraction of a shirt, we take the whole number part of the division. Therefore, the maximum number of shirts the store owner can purchase is:
\[ \text{Maximum number of shirts} = 151 \]
To verify, we can calculate the total cost of 151 shirts:
\[ 151 \times 17 = 2567 \]
Since this is less than $2,578, the store owner can indeed afford 151 shirts. If we check one more shirt:
\[ 152 \times 17 = 2584 \]
This exceeds $2,578, confirming that buying 152 shirts is not possible.
Thus, the maximum number of shirts the store owner can purchase is:
\[ \boxed{151} \]
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