Final answer:
To determine the maximum number of students who can attend the trip within the budget, one must calculate the discounted price of theatre tickets, add the cost of train tickets, and ensure the total cost does not exceed £1500. This culminates in the finding that 26 students, along with 2 teachers, can go on the trip.
Step-by-step explanation:
The student is trying to calculate the maximum number of students that can go on a school trip within a budget of £1500. To find this number, we need to calculate the cost of tickets with the discount and add the cost of train tickets then see how many people (students plus two teachers) can be covered by the budget.
First, the discounted price of theatre tickets is found by taking 1/5 off the regular price of £50. The discounted price is £50 - (£50 * 1/5) = £40 per ticket. The cost of a train ticket is £12 per person.
Next, a budget formula considering the 2 teachers is: (Cost of theatre ticket + cost of train ticket) * (number of students + 2 teachers) ≤ £1500. This simplifies to (£40 + £12) * (number of students + 2) ≤ £1500. Further simplification gives us £52 * (number of students + 2) ≤ £1500. When dividing £1500 by £52, we get approximately 28.84. Since we can't take a fraction of a person on a trip, we have to round down, resulting in 28 persons in total that can go on the trip, including the two teachers.
Therefore, the maximum number of students who can attend the trip is 28 - 2 (teachers) = 26 students. Option (a) is the correct answer.