Answer:
A bus carries 20 students while the van carries 8 students
Step-by-step 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
Answer:
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.
