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.

what the question so we can you out

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right