Modeling with multiple variables: Roller coaster | Modeling | Algebra II | Khan Academy

We're told a roller coaster has c cars, each containing 20 seats, and it completes r rides a day. Assuming that no one can ride it more than once a day, the maximum number of people that can ride the roller coaster in a single day is p. Write an equation that relates p, c, and r. Pause this video and see if you can do that.

All right, before I even look at the variables, I'm just going to try to think it out in plain language. So what we want to think about is what is the max number of people per day? People per day, and so that's going to be equal to the number of cars in our roller coaster, so number of cars times the maximum number of people per car. Times the max number per car, so this would just tell you the maximum number of people per ride.

So then we have to multiply it times the number of rides per day. So times, we do this in a new color, times number of rides per day. Now what are each of these things? They would have either given us numbers or variables for each of them. The max number of people per day, that's what we're trying to set on one side of the equation. That is this variable p right over here.

So we'll say capital P is equal to what's the number of cars per coaster? I guess you could say, let me write it this way, per coaster, per roller coaster. So they give us that right over here. A roller coaster has c cars, so that's going to be this variable here in orange, or this part of it, that's c.

Now, what's the maximum number of people per car? Well, they say each containing 20 seats, so I'd multiply that times 20 for this part. And then I want to multiply that times the number of rides per day for the entire roller coaster, so that's going to be times r. And we're done.

We could rearrange this a little bit; we could write this as p is equal to 20 times c times r, and we're done.