Question

A class of 118 students went on a field trip. They took 10 vehicles, some vans (x) and some buses (y). Find the number of vans and the number of buses they took if each van holds 6 students and each bus hold 35 students. Express your answer as a solution set {x, y} or (x, y).

Answer 1

{ 8, 2}

Explanation:

Basic algebra, the object which is not in a set quantity, which we have to find, is the "some vans" and the "some buses"

So let the number of van be x

Let the number of buses be y

So, since there are 10 vehicles,

x+y=10

Makes sense right

Now, it says that every car can carry 6 students, and every van can carry 35 students, so in another way, we could represent this by saying

6 x Number of van + 35 x Number of buses

thus,

6x + 35y

And since 118 students went on the field trip, this means that

6x +35y = 118

So now we have two equations,

x + y = 10

6x + 35y = 118

We can solve this with substitution

x + y = 10

x = 10 - y

Thus, x = 10-y

Put this in this

6(10-y)+ 35y= 118

60-6y+35y=118

60+29y=118

29y=118-60

29y= 58

y = 58/29

y = 2

Thus, the number of buses, y, is 2

Now since there are 10 vehicles, and 2 are buses, then the other are 8 van

Answer 2

Solve for x+y=10

6x+35y=118

Explanation:

I would solve it for you but my calculator isn't working rn. You could also use a picture calculator and it will give you a more in depth explanation. Hope this helps!