Question

The senior classes at High School A and High School B planned separate trips to the indoor

climbing gym. The senior class at High School A rented and filled 9 vans and 3 buses with 132
students. High School B rented and filled 3 vans and 8 buses with 205 students. Every van had
the same number of students in it as did the buses. Find the number of students in each van and
in each bus.

Answer 1

The number of students in each van are 7 and number of students in each bus are 23.

Explanation:

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

Given:

High School A:

Number of students = 132

Number of buses = 3

Number of vans = 9

As per question,

`9x+3y=132`-------1

High School B:

Number of students = 205

Number of buses = 8

Number of vans = 3

As per question,

`3x+8y=205`-------2

Multiplying equation (2) by -3 and adding the result to equation (1), we get:

`-3(3x+8y)=-3(205)\\-9x-24y=-615`

`-9x-24y=-615\\9x+3y=132\\---------\\-21y=-483\\y=(-483)/(-21)=23`

Now, plug in 23 for 'y' in equation (1) and solve for 'x'. This gives,

`9x+3(23)=132\\9x+69=132\\9x=132-69\\9x=63\\x=(63)/(9)=7`

Therefore, the number of students in each van are 7 and number of students in each bus are 23