A group of students are going on a field trip. If the group takes 3 vans and 1 car, 22 students can be transported. If the group takes 2 vans and 4 cars, 28 students can be transported. How many students can fit in each van?

Can someone show me how to solve this please?

Question

A group of students are going on a field trip. If the group takes 3 vans and 1 car, 22 students can be transported. If the group takes 2 vans and 4 cars, 28 students can be transported. How many students can fit in each van? 

Can someone show me how to solve this please?

phi · Answer

let x be the number of people that fit in a van
and y be the number that fit in a car

then
3 vans and 1 car, 22 students
means
3x + y =22

 2 vans and 4 cars, 28 students
means
2x +4y=28

you have two equations and two unknowns
do you know how to solve this ?

tatumlee · Answer

Do I have to add the equations together some how?

tatumlee · Answer

@phi

phi · Answer

there are two ways to solve these. Substitution or elimination I usually use elimination (as that is how you solve 3 equations and 3 unknowns) 
3x + y =22 
2x +4y=28 
the first thing to notice is that we can divide the 2nd equation by 2 (that means both sides and all terms) to get 
x + 2y = 14
 that makes it a little simpler

phi · Answer

3x+ y= 22
x + 2y = 14 

Next, I would multiply the first equation by -2 (that means both sides and all terms are multiplied by -2)

tatumlee · Answer

I am confused on where the -2 came from, and is there some sort of steps to follow in equations like these? Like first divide, then multiply then... I feel like I'm missing something

tatumlee · Answer

@phi

phi · Answer

when you have two equations like
3x+ y= 22 
x + 2y = 14 

and want to (for example) "get rid of the y",  I notice that if the top equation had a -2y
then when we add the two equations (term by term)
the -2y+2y would add up to 0 (cancel out)

so let's multiply the top equation by -2
(that means multiply both sides and all terms by -2)
can you do that ?

phi · Answer

you should get
-6x+ -2y = -44  for the 1st equation
   x  +  2y  = 14
now add term by term
-5x  + 0     = -30
or
5x=30
x=6

tatumlee · Answer

thank you for your help, I really don't understand but I will keep looking over what you've said and try to understand how you got where you did

phi · Answer

If you have time, see https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-systems-of-equations-by-multiplication

tatumlee · Answer

this video is making a lot of sense to me thank you! The other videos answer some of my other questions as well.