For a trip, one high school rented and filled 2 vans and 8 buses with 176 students. another high school instead fit its 164 students into 3 vans and 7 buses. with eachbus and van seating the same number of students, how many students can a bus carry. how many students can a van carry?

A bus can carry 20 students

A van can carry 8 students

Step-by-step explanation:

Let x represent the number of students a van can carry

Let y represent the number of students a bus can carry.

In the first high school, 2 vans and 8 buses was occupied by 176 students i.e.

2x + 8y = 176 (eqn 1)

In the second high school, 3 vans and 7 buses occupied 164 students i.e.

3x + 7y = 164 (eqn 2)

We have two equations which we will solve simultaneously using the elimination method

2x + 8y = 176

3x + 7y = 164

To eliminate the x variable, we multiply eqn 1 by 3 and eqn 2 by 2 i.e.

3 × 2x + 8y = 176

2 × 3x + 7y = 164

We have;

6x + 24y = 528 (eqn 3)

6x + 14y = 328 (eqn 4)

We subtract eqn 4 from eqn 3

10y = 200

Divide both sides by 10

y = 20

Since y=20, we substitute the value of y into eqn 1

2x + 8y = 176

2x + 8(20) = 176

2x + 160 = 176

2x = 176 - 160

2x = 16

x = 8

Hence, the number of students that a van can carry denoted by x is 8 while the number of students a bus can carry denoted by y is 20.