Question

A bus company requires 4 buses and 8 vans to take 240 school children to the library. It requires 2 buses 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. Use X as buses and Y as vans.

Answer 1

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 = $4x$ children (Unitary method)

Similarly, 8 vans = $8y$ children.

The sum of number of children going to library is 240. So,

$4x+8y=240----1$

Similarly, framing an equation for the total number going to museum, we get:

$2x+9y=170----2$

Multiplying equation (2) by -2 and then adding the result to equation (1), we get:

$(2x+9y=170)\times -2\\\\-4x-18y=-340\\4x+8y=240\\---------(Adding\ both\ equations)\\-10y=-100\\\\y=\frac{-100}{-10}=10$

Now, plug in the value of 'y' in equation (1) and solve for 'x'. This gives,

$4x+8(10)=240\\\\4x+80=240\\\\4x=240-80\\\\4x=160\\\\x=\frac{160}{4}=40$

Therefore, there are 40 children in a bus and 10 children in a van.