Let x be the<u> number of buses</u> and y be the <u>number of vans</u> needed to transport 107 people.
1. If each bus can seat 31 people and 3 of them should be teachers, then x buses can seat (31-3)x=28x students. If each van can seat 9 people and 1 of them should be teacher, then y vans can seat (9-1)y=8y students.
2. Grant Valley School has hired a fleet of buses and vans to transport 96 students to a picnic.Thus,
28x+8y=96.
3. It will take to accommodate 107 people, including the 96 students and teachers, then the number of teachers is 107-96=11.
x buses will take 3x teachers and y vans will take y teachers,
Therefore, 3x+y=11.
4. Solve the system of equations:
Solve the first equation:
Then
Answer: 2 buses and 5 vans