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### Course: 7th grade (Illustrative Mathematics)>Unit 2

Lesson 10: Lesson 12: Using graphs to compare relationships

# Comparing constants of proportionality

Working example comparing constants of proportionality.

## Video transcript

- [Instructor] Betty's Bakery calculates the total price D in dollars for C cupcakes using the equation D is equal to two times C. What does two mean in this situation? So pause this video and see if you can answer that. Alright, before I even look at the choices, let me just interpret this. This says D equals 2C tells us that however many cupcakes someone buys, we multiply that times two to get the amount of dollars, the price that they need to pay. So this must mean that each cupcake is two dollars. Or that it's two dollars per cupcake. Because however many cupcakes we get, we multiply that by two dollars per cupcake to get the actual price. So let's see, choice A says the bakery charges two dollars for each cupcake. Yeah, that's pretty close to what I just said. So I'll go with that one. The bakery sells two cupcakes for a dollar. No, that would not be the case. And you could even try it out. If we had one cupcake. So if C is one, what is D going to be? And actually, let me just do that for you 'cause it's interesting. C and D. So if you get one cupcake, you're gonna multiply it by two. It's going to be two dollars. Two cupcakes, we're gonna multiply it by two and be four dollars. It's consistent with this first choice, but to sell two cupcakes, it's not gonna be four dollars, it's gonna be for four dollars. The bakery sells two types of cupcakes. Well, they don't say anything about that, so I'll rule that out, as well. Let's do another one. Here, we are told, select the store with the least expensive ice cream per scoop. There's definitely a dessert theme going on over here. Alright, so pause this video and see if you can work it out. Is it choice A, choice B or choice C. Alright, now let's go through these together. Choice A calculates the total price D in dollars of ice cream with S scoops using the equation D is equal to 0.75S. So whatever the number of scoops are, we're gonna multiply that times 75 cents or 75 hundredth of a dollar to get the price. And so based on the logic we just used in that last example, in store A, it is 75 cents, 75 cents per, per scoop. So we know the price there. And anything like this, when you're comparing, you wanna put it all in the same terms. Okay, here it's 75 cents per scoop. Let's think about how many, how much per scoop it is at B. And how many, how much per scoop it is for C. Alright, now store B. So, when I get three scoops, I multiply that times one to get three dollars. When I get eight scoops, I multiply it times one to get eight dollars. When I have 12 scoops, I multiply it by one to get 12 dollars. So the equation that store B must use is that the dollar is D. That's going to be equal to one times the number of scoops. Or you could view this as, hey, it's a dollar per scoop at store B. So one dollar, one dollar per scoop. So we already know that store A is cheaper than store B. 'Cause 75 cents per scoop is cheaper than one dollar per scoop. Store C, alright, so here this, this relationship is described with a graph but we can put it in the same forms that we saw before. So for store C. Make a little table here. And so if I have the scoops and I have the dollars. So let's see. When I get two scoops, it looks like, and I'm just picking values where it looks like I can read the graph easily. Two scoops looks like three dollars. Two scoops, three dollars. Four scoops, it is six dollars. Four scoops, it's six dollars. So it looks like I'm multiplying times one point half, one and a half, I was gonna say one point half. 1.5 or one and a half to go from scoops to dollars. Or another way you can think about it is the dollars is equal to 1.5 times the scoops. Or another way to think about it, at store C, they're charging a 1.50, 1.50 per, per scoop. So store C is the most expensive followed by B and then store A is the cheapest and that's what they're asking us. The least expensive ice cream per scoop is store A.