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# Modeling with multiple variables: Roller coaster

Modeling the relationship between three quantities (or more) isn't that different from modeling the relationship between two quantities. Here is an example of a model that relates different quantities in the context of roller coaster rides. Created by Sal Khan.

## Want to join the conversation?

• because of the "the maximum number of people that can ride the roller coaster in a single day is P"
I'd assume it's not
P = 20cr
but
P => 20cr
wouldn't that be more accurate?
• It would be if you just wanted the number of people. But P is specifically the maximum number of people. So the specific one number that is the maximum.
• Ei Sal, what roller coaster ride are you referencing?
• I was assume that the question need equation for `p` and `c` and `r`
not just `p`?
how you figure out that the question need just `p`?
(1 vote)
• The equation P = 20cr does use all three variables.

I assume you're asking how to know which variable to solve for.

Keep in mind that he first wrote out the equation "in plain language", which helped to see what variables go where. Based on the problem, he figured out which variables he could combine as an expression. In this case, it's 20cr. He knew that gave him the maximum amount of people each day, which is the variable P.
(1 vote)

## Video transcript

- [Narrator] We're told a rollercoaster 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 rollercoaster 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 gonna 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 rollercoaster, 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, 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 take 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 rollercoaster. So they give us that right over here, rollercoaster 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 rollercoaster. So that's going to be times r, and we're done. We can rearrange this a little bit, We can write this as P is equal to 20 times cr, and we're done.