Question

Grant Valley School has hired a fleet of buses and vans to transport 96 students to a picnic. Each bus can seat 31 people, and each van can seat 9 people. The school authorities want to have three teachers traveling in each bus and one teacher in each van.
It will take to accommodate 107 people, including the students and teachers, with no seats left vacant.
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Answer 1

Let x be the number of buses and y be the number of vans 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:

$\left\{\begin{array}{l}28x+8y=96\\3x+y=11\end{array}\right.\Rightarrow \left\{\begin{array}{l}28x+8(11-3x)=96\\y=11-3x\end{array}\right..$

Solve the first equation:

$28x+88-24x=96,\\ \\4x=8,\\ \\x=2.$

Then $y=11-3x=11-6=5.$

Answer: 2 buses and 5 vans

Answer 2

2 buses and 5 vans............