Budget et calcul de coûts : Thanksgiving et Noël

You are organizing a school trip to celebrate Thanksgiving and Christmas. You have a total budget of $500$ pounds ($£$).

1. The Thanksgiving dinner costs $25$ $£$ per student.
2. The Christmas gift exchange costs $12$ $£$ per student.
3. There are $12$ students in your group.

Calculate the total cost for the activities using the formula $C_{total} = (25 + 12) \times 12$. Determine if your budget of $500$ $£$ covers the costs and calculate how much money remains from the initial budget.