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

Answer 1

Answer:

Number of buses = 2

Number of vans = 5

Step-by-step explanation:

Solution:

Number of buses = a

Number of vans = b

Number of people= 107

Now according to given statement each bus can seat 31 people and there are three teachers travelling in each bus.

Then the number of students in 'a' buses = (31-3)a = 28a students

Each van can seat 9 people and each van has one teacher. Then the number of students in 'b' vans= (9-1)b = 8b students.

The Grant Valley school has hired a fleet of buses and vans to transport 96 students to a picnic

Then the equation we get is:

28a+ 8b= 96

The buses and vans will take to accommodate 107 people including the teachers and 96 students.

Then the number of teachers will be:

Subtract the number of students from the number of people.

107-96 = 11

'a' number of buses will take 3a teachers and  'b' number of vans will take b teachers

So we got another equation:

3a+b=11

Now we have 2 equations:

28a+8b=96 ------- equation1

3a+b=11   -----------equation2

Solve the system of equation:

We will apply elimination method.

Multiply equation 2 by 4 and then subtract equation 2 from equation 1:

28a+8b=96

24a+8b=88            ------- (equation 2 after multiplication)

__________

4a        =8

Divide both the sides by 4

4a/4 = 8/4

a= 2

Now put the value of a in any of the above equation. We will put the value of a in equation 1.

28(2)+8b=96

56+8b=96

8b = 96-56

8b = 40

Divide both the sides by 8:

8b/8 = 40/8

b= 5

Number of buses = 2

Number of vans = 5....