To determine how many tickets Joseph can buy, we first need to find out how much money he has left after buying the hat.
- Cost of the hat: $12.50
- Total amount Joseph has: $34.25
Now, we calculate how much money he has left after buying the hat:
\[ \text{Money left} = \text{Total amount} - \text{Cost of the hat} = 34.25 - 12.50 = 21.75 \]
Next, we need to determine how many tickets he can buy with the remaining money. The cost of each ticket is $7.25.
Now we divide the money left by the cost of each ticket:
\[ \text{Number of tickets} = \frac{\text{Money left}}{\text{Cost of each ticket}} = \frac{21.75}{7.25} \]
Calculating that gives:
\[ \frac{21.75}{7.25} = 3 \]
Therefore, Joseph can buy 3 tickets.
The correct response is: 3 tickets.