Respuesta :
Answer:
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 [tex]x.[/tex]
And let the number of people fit on a bus be [tex]y.[/tex]
So, the total number of people on 12 vans and 9 buses are:
[tex]12x+9y=681\ \ \ \ ...(1)[/tex]
And, the total number of people on 6 vans and 14 buses are:
[tex]6x+14y=882\ \ \[/tex]
Now, multiplying the above equation by 2 we get:
[tex]12x+28y=1764[/tex] ....(2)
Then, solving the system of equations by subtracting the equation (1) from equation (2):
[tex](12x+28y)-(12x+9y)=1764-681\\\\12x-12x+28y-9y=1764-681\\\\19y=1083[/tex]
Dividing both sides by 19 we get:
[tex]y=57.[/tex]
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 [tex]x[/tex] in equation (1):
[tex]12x+9y=681\\\\12x+9(57)=681\\\\12x+513=681[/tex]
Subtracting both sides by 513 we get:
[tex]12x=168[/tex]
Dividing both sides by 12 we get:
[tex]x=14.[/tex]
The number of people fit on a van = 14.
Therefore, 14 people can fit on a van and 57 on a bus.
