Final answer:
To find the maximum total cost for tickets, consider the maximum number of chaperones which maximizes the number of adult tickets sold. With 10 chaperones, you can have 110 students, totaling 120 people. The maximum cost is 110 students x $6/student + 10 chaperones x $10/chaperone, amounting to $760.
Step-by-step explanation:
The question asks for the maximum total cost for tickets for a field trip with certain constraints on the number of students and adult chaperones. Tickets cost $6 for students and $10 for adult chaperones.
Let's start with the requirement that there must be no more than one adult chaperone for every three students. To maximize the total cost, we should have as many adult chaperones as possible since their tickets cost more. This means we want one chaperone per three students. If we designate 'S' as the number of students and 'C' as the number of chaperones, the ratio would therefore be 3S = C. Given that there can be a maximum of 120 people on the trip, the maximum group is reached when 3S + C = 120.
Substituting the first ratio into the second, we get 3S + S = 120 or 4S = 120. Solving for S, we get S = 30. If there are 30 students, then there must be 10 chaperones because 3S = C, and 3(30) = 90/3 = 30, thus C = 10.
The total cost would be (30 students x $6 per student) + (10 chaperones x $10 per chaperone), which equates to $180 + $100 = $280. However, this doesn't maximize the cost with the given ratios. To get the maximum cost, we also need to consider the ratio regarding the minimum requirement of adult chaperones, which is at least one adult chaperone for every 11 students.
If we set up a ratio of S/11 = C, with the maximum number of chaperones being C, we can then calculate the maximum cost by finding the largest value of S where 11S + S is less than or equal to 120, which allows for the maximum number of students while still adhering to the rule of at least one chaperone per 11 students.
If we have 10 chaperones (maximum based on the 3:1 ratio), then we would have 110 students (11 students per chaperone). This gives us 120 people exactly.
Thus, the total cost would be (110 students x $6 per student) + (10 chaperones x $10 per chaperone), which equates to $660 + $100 = $760.