To determine how many tickets Joseph can buy, we first need to calculate how much money he has left after buying the hat.
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Cost of the hat: $12.50
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Total money Joseph has: $34.25
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Money left after buying the hat:
\[ 34.25 - 12.50 = 21.75 \]
Next, we find out how many tickets he can buy with the remaining money:
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Cost of each ticket: $7.25
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Number of tickets he can buy:
\[ \frac{21.75}{7.25} \approx 3 \]
Now, let's check if he can buy 3 tickets, and the total cost for 3 tickets:
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Cost of 3 tickets:
\[ 3 \times 7.25 = 21.75 \]
Adding the cost of the hat:
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Total spent:
\[ 12.50 + 21.75 = 34.25 \]
Joseph can buy 3 tickets and still have enough money.
So the answer is:
3 tickets