Problem:
Your school is planning a trip for Year 9 students and has come up with three options: a visit to a local amusement park, a trip to a science museum, or a tour of a historical site. The cost for each option is as follows:
- Amusement park: $30 per student plus $500 for transportation.
- Science museum: $20 per student plus $400 for transportation.
- Historical site: $25 per student plus $450 for transportation.
The school has a budget of $3000 for the trip, and there are 100 students in Year 9. The school wants to choose the option that maximizes the number of students who can go on the trip while staying within the budget.
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Write a linear equation to represent the total cost (C) of each option in terms of the number of students (x) going on the trip.
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Solve the linear equation to find the maximum number of students that can go on each trip option while staying within the budget.
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Determine which trip option allows the maximum number of students to go on the trip while staying within the budget.
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Explain your reasoning and justify why the chosen option is the best choice for the school trip.
Note: You may assume that the number of students going on the trip can only be a whole number.