Answer: Each van had 8 students and each bus had 22 students
Step-by-step explanation: We shall start by assigning a letter to represent the unknown variables in this question. Each bus shall be represented by by B while each van shall be represented by V. So if in high school A, 8 vans and 8 buses were filled with 240 students in total, we can derive the expression
8V + 8B = 240. Also if in high school B, 4 vans and 1 bus were filled with 54 students in total, we can as well derive the following expression,
4V + B = 54
What we have at this point is a pair of simultaneous equations with unknown variables V and B
8V + 8B = 240 —————(1)
4V + B = 54 ——————-(2)
From equation (2), we shall make B the subject of the equation. Hence
B = 54 - 4V
We can now substitute for the value of B into equation (1) and equation (1) can now be written as
8V + 8(54 - 4V) = 240
8V + 432 - 32V = 240
By collecting like terms we now have
8V - 32V = 240 - 432
(Note that when a positive value crosses to the other side of an equation it becomes negative and vice versa)
-24V = -192
Divide both sides of the equation by -24
V = 8
That means there 8 students in each van. Now we substitute for the value of V into equation (2)
4V + B = 54
4(8) + B = 54
32 + B = 54
Subtract 32 from both sides of the equation
32 - 32 + B = 54 - 32
B = 22
That means there were 22 students in each bus.
Therefore each van had 8 students and each bus had 22 students
