Question

In 2014 a class went to the holocaust museum. They traveled in vans and busses. Each van held 10 students and each bus held 15 students. 14 vehicles total wwent on the trip. If 180 students went on the trip, how many of each type of vehicle did we use.

Answer 1

So first off... you gave to divide what?

Answer 2

wwhat

Answer 3

What do we divide here?

Answer 4

idk

Answer 5

Okay... we divide 180 and 14.

That gives your average in each vehicle. What do you get when you divide 180 and 14?
180/14

Answer 6

first how many buses went on the trip

Answer 7

then find out how many student swent total

Answer 8

okay since no one here knows how to really solve the question lol, I'll take over


The real way to solve this question is by coming up with two equations

Answer 9

what letters or variables do you want to use? @zunairah

x and y

or V for vans and B for bus

Answer 10

We make the two equations from the information they gave us

Each van held 10 students and each bus held 15 students.
14 vehicles total went on the trip.
180 students went on the trip

The first equation is based on 14 vehicles total went on trips

that means
number of vans + number of buses = 14

so depending on what variables/letters you want to use, you can replace it accordingly

Answer 11

The silence is deafening but I will presume you are afk and continue

The second equation would be using

Each van held 10 students and each bus held 15 students.
180 students went on the trip

How many students can a van hold?
And a bus?

15 in a bus and 10 in a van
and a total of 180 students went

so 15*bus + 10*van = 180

Does that make sense?

Answer 12

basically the variable is going to tell us how many of the buses we took or how many vans we took

so when we multiply 15*bus

it will tell us how many people took the bus in all

and similarly for the vans

Answer 13

and since you haven't chosen any variables,

I'll just stick with

V = # of vans
B = # of buses

so we have two equations

V + B = 14
10V + 15B = 180

Do you know how to solve a system of equations? @zunairah

Answer 14

what

Answer 15

oh

Answer 16

yes i do

Answer 17

did all of that make sense? how I came up with the equations?

can you solve for V and B now?

Answer 18

ummm

Answer 19

we can use x and y instead

x = # of vans
y = # of buses

so we have two equations

x + y = 14
10x + 15y = 180

Answer 20

yeah i did that and after that i got 11x+16y =194

Answer 21

you can't just add the equations like that

if you're doing substitution, you need to do something so that way one of the letters gets ELIMINATED

Answer 22

so that way you can solve for just one variable at a time

Answer 23

so i multiply the top equation by something and the bottom equation by something

Answer 24

yes, but in this case, you only have to multiply the first equation by something to get it to have the same number as the second one so you can cancel out one of the letters

so do you want to get rid of x or y first?

Answer 25

x

Answer 26

okay, so what would you need to multiply the first equation with?

we have 10x in the second one

we want the first one to start with -10x then

so what do you multiply to get -10x from x

Answer 27

-10

Answer 28

Good, so multiply the entire equation on both sides by -10

x + y = 14
-10 *(x+y) = -10 * 14

what do you get

Answer 29

-10x-10y=-140

Answer 30

good now let's add the two equations

-10x-10y=-140
10x + 15y = 180

Answer 31

i got 8 for y

Answer 32

correct!

and so if y is 8, then what is x?

remember x + y = 14

Answer 33

6 for x

Answer 34

and you got it!!

and remember we said:

x = # of vans
y = # of buses

so that means 6 vans and 8 buses

Answer 35

you remind me of my math teacher 😡 and thx bye

Answer 36

LOL yw bye