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

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

Step-by-step 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

And let the number of people fit on a bus be

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

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

Now, multiplying the above equation by 2 we get:

  ....(2)

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

Dividing both sides by 19 we get:

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 in equation (1):

Subtracting both sides by 513 we get:

Dividing both sides by 12 we get:

The number of people fit on a van = 14.

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