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,
[tex]9x+3y=132[/tex]-------1
High School B:
Number of students = 205
Number of buses = 8
Number of vans = 3
As per question,
[tex]3x+8y=205[/tex]-------2
Multiplying equation (2) by -3 and adding the result to equation (1), we get:
[tex]-3(3x+8y)=-3(205)\\-9x-24y=-615[/tex]
[tex]-9x-24y=-615\\9x+3y=132\\---------\\-21y=-483\\y=\frac{-483}{-21}=23[/tex]
Now, plug in 23 for 'y' in equation (1) and solve for 'x'. This gives,
[tex]9x+3(23)=132\\9x+69=132\\9x=132-69\\9x=63\\x=\frac{63}{9}=7[/tex]
Therefore, the number of students in each van are 7 and number of students in each bus are 23
