a bus company requires 4 busses and 8 vans to take 240 school children to the library. It requires 2 busses and 9 vans to take 170 children to the museum. Calculate the number of children a bus can carry and the number of children a van can carry.
Let's assume a bus can carry x number of children, and a van can carry y number of children.
According to the first scenario:
4x + 8y = 240 ---(Equation 1)
And based on the second scenario:
2x + 9y = 170 ---(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From Equation 1, we can solve for x:
4x = 240 - 8y
x = (240 - 8y) / 4
x = 60 - 2y ---(Equation 3)
Substituting Equation 3 into Equation 2:
2(60 - 2y) + 9y = 170
120 - 4y + 9y = 170
5y = 50
y = 10
Substituting the value of y into Equation 3:
x = 60 - 2(10)
x = 60 - 20
x = 40
Therefore, a bus can carry 40 children, and a van can carry 10 children.