Question

A trip for 681 person group required 12 vans and 9 buses. The next year, 882 people go on the trip and it requires 6 vans and 14 buses. Find the number of people that can fit on a van and on a bus

Answer 1

14 people can fit on a van and 57 on a bus.

Explanation:

Given:

A trip for 681 person group required 12 vans and 9 buses. The next year, 882 people go on the trip and it requires 6 vans and 14 buses.

Now, to get the number of people that can fit on a van and on a bus.

Let the number of people fit on a van be
`x.`

And let the number of people fit on a bus be
`y.`

So, the total number of people on 12 vans and 9 buses are:

`12x+9y=681\ \ \ \ ...(1)`

And, the total number of people on 6 vans and 14 buses are:

`6x+14y=882\ \ \`

Now, multiplying the above equation by 2 we get:

`12x+28y=1764` ....(2)

Then, solving the system of equations by subtracting the equation (1) from equation (2):

`(12x+28y)-(12x+9y)=1764-681\\\\12x-12x+28y-9y=1764-681\\\\19y=1083`

Dividing both sides by 19 we get:

`y=57.`

The number of people fit on a bus = 57.

Now, to get the number of people fit on a van b y substituting the value of
`x` in equation (1):

`12x+9y=681\\\\12x+9(57)=681\\\\12x+513=681`

Subtracting both sides by 513 we get:

`12x=168`

Dividing both sides by 12 we get:

`x=14.`

The number of people fit on a van = 14.

Therefore, 14 people can fit on a van and 57 on a bus.