To determine how many tickets Joseph can buy, we first need to subtract the cost of the hat from his total amount of money.
- Calculate the remaining amount after buying the hat:
\[ \text{Remaining amount} = \text{Total amount} - \text{Cost of the hat} = 34.25 - 12.50 = 21.75 \]
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Next, we need to find out how many tickets he can buy with the remaining amount. The cost of each ticket is $7.25.
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We can find the number of tickets by dividing the remaining amount by the cost of one ticket:
\[ \text{Number of tickets} = \frac{\text{Remaining amount}}{\text{Cost of one ticket}} = \frac{21.75}{7.25} \]
- Performing the division:
\[ \frac{21.75}{7.25} \approx 3 \]
Thus, Joseph can buy 3 tickets.