For a trip, one high school rented and filled 8 vans and 5 buses with 196 students.
another high school instead fit its 216 students into 3 vans and 9 buses. with each bus and van seating the same number of students, how many students can a bus carry? how many students can a van carry?

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.

the answer is b.)

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