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....
