Answer:
A bus can carry 40 children and a van can carry 10 children.
Step-by-step explanation:
Let the number of children in a bus be 'x' and number of children in a can be 'y'.
Given:
4 buses and 8 vans are required to take 240 school children to the library.
2 buses and 9 vans are required to take 170 children to the museum.
So, 1 bus = 'x' children
4 buses = [tex]4x[/tex] children (Unitary method)
Similarly, 8 vans = [tex]8y[/tex] children.
The sum of number of children going to library is 240. So,
[tex]4x+8y=240----1[/tex]
Similarly, framing an equation for the total number going to museum, we get:
[tex]2x+9y=170----2[/tex]
Multiplying equation (2) by -2 and then adding the result to equation (1), we get:
[tex](2x+9y=170)\times -2\\\\-4x-18y=-340\\4x+8y=240\\---------(Adding\ both\ equations)\\-10y=-100\\\\y=\frac{-100}{-10}=10[/tex]
Now, plug in the value of 'y' in equation (1) and solve for 'x'. This gives,
[tex]4x+8(10)=240\\\\4x+80=240\\\\4x=240-80\\\\4x=160\\\\x=\frac{160}{4}=40[/tex]
Therefore, there are 40 children in a bus and 10 children in a van.
