Question

the state fair is a popular field trip destination. This year the señior class at High school A and the señior class at High school B both planned trips there the señior class A rented and filled 8 vans and 8 buses with 240 students. High school B rented and filled 4 vans and 1 bus with 54 students. every van had the same number of students in it as did the buses. find the number of students in each van and each bus

Answer 1

The number of student in each van is 8. The number of student in each bus is 22.

Explanation:

Consider the provided information.

Let the number of student in each van is x.

The number of student in each bus is y.

School A rented and filled 8 vans and 8 buses with 240 students.

This can be written as:

`8x+8y=240`......(1)

School B rented and filled 4 vans and 1 bus with 54 students.

`4x+y=54`

`y=54-4x`......(2)

Substitute the value of y in equation (1).

`8x+8(54-4x)=240`

`8x+432-32x=240`

`8x-32x=240-432`

`24x=192`

`x=8`

Thus, the number of student in each van is 8.

Substitute the value of x in equation (2).

`y=54-4(8)`

`y=54-32`

`y=22`

Thus, the number of student in each bus is 22.

Answer 2

8v + 8b = 240
4v + b = 54....multiply by -2
-------------------
8v + 8b = 240
-8v - 2b = - 108 (result of multiplying by -2)
------------------add
6b = 132
b = 132/6
b = 22 <== buses hold 22 students

4v + b = 54
4v + 22 = 54
4v = 54 - 22
4v = 32
v = 32/4
v = 8 <== vans hold 8 students