Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

$-9x-24y=-615\\9x+3y=132\\---------\\-21y=-483\\y=\frac{-483}{-21}=23$

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

$9x+3(23)=132\\9x+69=132\\9x=132-69\\9x=63\\x=\frac{63}{9}=7$

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