Question

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?

Answer 1

A bus can carry 20 students

A van can carry 8 students

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.

Answer 2

A bus carries 20 students while the van carries 8 students

Explanation:

Let's assume that the number of students that the bus can carry is X And

The number of students that the van can very be y

From first statement,

8x + 2y = 176______ first equation

From Second statement,

7x + 3y = 164______ second equation

The above is a simultaneous equation and we will use the elimination method to solve for both x and y

But if we take a look at both equations,we will find out that we can't make use of the elimination method since the coefficients of both x and y aren't same in both equations.

What we have to do now is to multiply equation 1 by 3 and multiply equation 2 by 2 so as to get the coefficients of y in both equation to be the same.

Initially, both equation are

8x + 2y = 176____ first equation

7x + 3y = 164____ second equation

They will now be :

24x + 6y = 528(was multiplied by 3)

14x + 6y = 328(was multiplied by 2)

Now subtract equation 2 from 1 and we have

10x = 200

X = 20

Now substitute x = 20 in equation 1 above

8x + 2y = 176

(8 × 20) + 2y = 176

2y = 176 - 160

Y = 8

Remember that we assumed that the number of students that each bus carried was x and van was y,now we know the values of c and y to be 20 and 8 respectively.

Therefore, each bus carried 20 students and each van had 8 students on it