A school is planning a field trip and needs to rent buses an...

Question

A school is planning a field trip and needs to rent buses and vans. Each bus can carry 40 students, and each van can carry 12 students. The school has 400 students and a budget of $2500. Renting a bus costs $150, and renting a van costs $80. Let b be the number of buses and v be the number of vans. Write the system of inequalities that represents this situation. __________.

Question Analysis
This question tests the student's ability to convert a real-world scenario into a system of inequalities.

Key Concept Explanation
The key concept here is understanding how to translate verbal descriptions into mathematical inequalities. The student must identify the variables, constraints, and then express these as inequalities.

Step-by-step Solution
1. Define the variables: = number of buses, = number of vans.
2. Write the system of inequalities based on the given constraints:
Total students:
Budget:
Non-negativity: ,

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Algebra-1

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