Comparing constants of proportionality | 7th grade | Khan Academy

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.

All right, before I even look at the choices, let me just interpret this. They say 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 is 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 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 because 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 are gonna multiply it by two and be four dollars. It's consistent with this first choice, but to sell two cupcakes it's not going to be for a dollar; 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 to select the store with the least expensive ice cream per scoop. There's definitely a dessert theme going on over here. All right, so pause this video and see if you can work it out—is it choice A, choice B, or choice C?

All right, 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 0.75 s. So whatever the number of scoops are, we're going to multiply that times 75 cents or 75 hundredths 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 scoop. So we know the price there.

And anything like this, when you're comparing, you want to put it all in the same terms. Okay, here at 75 cents per scoop. Let's think about how much per scoop it is for B and how much it is per scoop for C.

All right, 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 twelve scoops, I multiply it by one to get twelve dollars. So the equation that store B must use is that the dollars 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 because 75 cents per scoop is cheaper than one dollar per scoop. Store C, all right, so here this relationship is described with a graph, but we can put it in the same forms that we saw before.

So for store C, let me 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 five—one and a half, I was going to say one point five.

To go from scoops to dollars, or another way you could 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 dollar fifty—a dollar fifty 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.