Each van can carry 12 students while each bus can carry 20 students each.
Step-by-step explanation:
Step 1; Assume x is the number of students in a van and y is the number of students in a bus. It is given that 8 vans and 5 buses are filled with 196 students in one high school. So
8x + 5y = 196, take this as equation 1.
In another high school, 216 students are fitted into 3 vans and 9 buses. So,
3x + 9y = 216, take this as equation 2.
Step 2; We multiply equation 1 with 3 and equation 2 with 8 so we can cancel out the variable x in both equations. By doing this we get
24x + 15y = 588, take this as equation 3
,
24x + 72y = 1,728, take this is equation 4,
If we subtract equation 4 from equation `3, we cancel out the x variable and can calculate the value of y.
-57y = -1,140,
Since both sides are negative they cancel out
y = -1,140/-57 = 20.
Step 3; Substituting this value of y in any of the previous equations we will get x's value. Here this value of y is substituted in equation 1.
8x +5(20) = 196, 8x + 100 = 196 , 8x = 96, x= 12.
So we have x = 12 and y = 20.
So 12 students can fit in a van and each bus can carry 20 students.
