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Modeling with multiple variables: Pancakes

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 making pancakes. Created by Sal Khan.

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Video transcript

- [Instructor] We are told that Jade is making pancakes using flour, eggs and milk. This table gives the cost per kilogram of each ingredient and the amount in kilograms that Jade uses. All right, the total amount Jade spends on ingredients is $6. Write an equation that relates a, b, c, and d. Pause this video and see if you can have a go at this. All right, now let's go through this together. So I like to do these in real time so that you can see my thought process. So I'm here with you right now. So let's see, the total Jade spends, and this is going to be on flour, eggs and milk, is going to be $6. So one way to think about it is, and I'll do this in different colors, the flour dollars plus the eggs. Eggs dollars, or the amount that Jade's gonna spend on eggs, plus the amount that Jade spends on milk, I'll call that the milk dollars, is going to be equal to the total amount, is going to be equal to $6. And so what's the total amount that Jade is going to spend on flour? Well, we can just look right over here. 0.9 dollars per kilogram times a kilograms. So Jade's going to spend 0.9a dollars. I'm just going to multiply these two things to figure out how much Jade spends on flour. And so this is going to be equal to, and I'll lose the dollar symbol just so that we can focus on the numbers and the variables, 0.9a, 0.9a, and this is, of course, is going to be in dollars, which is important. I'm going to add dollars plus dollars plus dollars to get dollars. Now what about eggs? Well, the same notion. 0.2 kilograms times b dollars per kilogram. If I take the product of these two, I'm gonna get 0.2b dollars. Or I could just think of it as 0.2b if I don't write the dollar symbol. And then last but not least, on milk. Let me look at the product of these two things, of this and of this. So d kilograms at c dollars per kilogram, that's just going to be cd dollars, so plus cd, and all of that is going to be equal to $6, and we're done. We wrote an equation that relates a, b, c, and d.