# 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?

Sep 22, 2016

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

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

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

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

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

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