College A and College B made it to the state championship

which was held at a large sporting arena far away from both

institutions.

To travel to the arena, College A rented and filled 8 vans and 8

buses with 240 students. College B rented and filled 4 vans

and 1 bus with 54 students. Every van and bus had the same

number of students in.

Let x be the number of students in each van and y be the

number of students in each bus. Find the number of students in

each van and each bus. Write your answer as an ordered pair

(x, y).

The number of students in vans and bus are (8,22)

Step-by-step explanation:

Let the number of students in the van be "x"

Let the number of students in the bus be "y"

It is given that each bus and van have same number of students.

For college A-

8 vans and 8 bus were rented to ferry 240 students

No of students in 8 bus = 8y (since y students were in each bus)

No of students in 8 van = 8x (since x students were in each van)

Hence 8x+8y=240 cancelling the equation with common factor 8, the equation becomes ⇒ x + y=30

For College B

4 vans and 1 bus were rented to ferry 54 students

No of students in 1 bus = 1y (since y students were in each bus)

No of students in 4 van = 4x (since x students were in each van)

4x+y=54

Comparing the both equation we get and subtracting equation 2 from 1

x+y-30-4x-y-54=0 ∵ Cancelling y

-3x=-24

∴ x=8 putting the value of x in equation 1 we get y as 22

Thus the answer is (8,22)