Question

The Cyclone Coaster has 16 cars. Some of them hold 2 passengers and some hold 3 passengers. If there is room for 36 people altogether, how many cars hold 3 passengers?

Answer 1

we can fit 36 people in 12 cars that fit 2 people and 4 cars that fit 3 people.

Explanation:

so in this problem we have a total of 16 cars where some proportion can hold 2 versus 3. We are also given that there are 36 people in these cars. I can write this mathematically as

`16=x+y`
`36=2x +3y`

we can now solve the system of equations thus I will subtract one from the other and solve
`20=x+2y`
so `x=20-2y`

lets plug that back in and solve for y
`16=20-2y+y`
so `y=4`

now i plug this back in to get
`36=2x+12`
so `x=12`

In summary we can fit 36 people in 12 cars that fit 2 people and 4 cars that fit 3 people.