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### Course: Integrated math 3 > Unit 9

Lesson 5: Modeling with multiple variables- Modeling with multiple variables: Pancakes
- Modeling with multiple variables: Roller coaster
- Modeling with multiple variables
- Interpreting expressions with multiple variables: Resistors
- Interpreting expressions with multiple variables: Cylinder
- Interpreting expressions with multiple variables

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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.

## Want to join the conversation?

- Why can't you write b * 0.2?(3 votes)
- You definitely can. It's just a convention that when you have a number multiplied by a variable, you put them together like "0.2b". It just makes the equation more clear.(3 votes)

- How can you sell milk in a kilogram you should use liters.(2 votes)
- There's no rule like that. If you know the density of something, you can sell in volume units or in mass units.(1 vote)

## 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.