To determine the maximum number of shirts the store owner can purchase, we divide the total amount of money available by the cost of each shirt.
Total money available: $2,578 Cost per shirt: $17
Now, perform the division:
\[ \text{Maximum number of shirts} = \frac{2578}{17} \]
Calculating the division:
\[ 2578 \div 17 = 151.05882352941 \]
Since the store owner cannot purchase a fraction of a shirt, we take the whole number part, which is 151.
To verify, we can multiply the number of shirts by the cost per shirt:
\[ 151 \times 17 = 2567 \]
Calculating the remaining money:
\[ 2578 - 2567 = 11 \]
Since the store owner cannot afford another shirt (as $17 > 11), we confirm that the maximum number of shirts the store owner can purchase is:
\[ \boxed{151} \]
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