For a course trip, (5-10) students have confirmed their participation, and by establishment policy, one representative must attend for each (2-2) students. This tour consists of visiting a water park for the entire day, which costs $(a + 1) per person, an amount that includes transportation, entrance to the park, and food. If the total amount to pay for transportation and tickets for the entire group is $(a - 3)², how much will they pay for food, in terms of a?

1. Let t represent the total number of students.
2. The total cost for the trip is represented by (a-3)^2 .
3. The cost per student is represented by (a+1) .

The condition of having one representative for each group renders redundant because this exercise specifies students in 5 to 10 and not splitting them. So

4. Hence, totaling it for students:
- t \cdot (a+1) = (a-3)^2

Therefore, solving for cost per student without representatives term,

5. C = (a-3)^2 -ta

Following step, representing it for the whole cost:

6. C = a^2 - 6a + 9 = a^2 -6 a - 5 +1 +4

So, the cost is therefore:

7. Finally the resulting:
C = a^2 + 5a - 4 where C represents per student cost based.

Thus, they will pay for food is: $a^2 + 5a - 4$.