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# Comparing constants of proportionality

## Video transcript

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 to C tells us that however many cupcakes someone buys we multiply that times 2 to get the amount of dollars the price that they need to pay so this must mean that each cupcake is \$2 or that is \$2 per cupcake because however many cupcakes we get we multiply that by \$2 per cupcake to get the actual price so let's see choice a says the bakery charges \$2 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 \$1 no that would not be the case and you could even try it out if we had one cupcake so if C is 1 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 going to multiply it by 2 it's going to be \$2 two cupcakes are gonna multiply it by two and be \$4 it's consistent with this first choice but to sell two cupcakes it's not going to be for \$1 it's gonna be for \$4 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 desert 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 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 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 term so okay here at 75 cents per scoop let's think about how many how much per scoop it is it be and how many how much it per scoop it is for C all right now store our 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 this relationship is described with the graph but we can put it in the same forms that we saw before so for store C we 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 hat one and a half I'm gonna say one point half 11.5 for one and a half to go from scoops to dollars or another way you could think about it is the dollars is equal to one point five times the scoops or another way to think about it at stores see they're charging a dollar fifty a dollar fifty 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 hystory