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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.

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- Hi! Here is some practice to help you succeed.

Which table has a proportionality of 3?

A

x y

1 2

2 3

3 4

4 5

B

x y

5 15

6 18

7 21

C

x y

1 5

3 15

5 25

If there are any problems, please notify me; I a just a learner like you.

Edit- Please do not read the comments until you answer the question. Have a good day!(98 votes) - why is it 1 cupcake for $2? if d=2c. wouldn't it be 2 cupcakes for $1? we could assume the is a 1 before the d, so 1d=2c.(10 votes)
- The coefficient of "d" is 1. But that doesn't tell you that there is d=$1 when c=2 cupcakes. use the equation. If c=2 cupcakes, then: d = 2(2) = 4

So 2 cupcakes costs $4. The ratio of 1 cupcake to $2 if you reduce the ratio.

Hope this helps.(16 votes)

- Wouldn't D=0.75S mean that it's one dollar for .75 o a scoop? Or 1.25 for one scoop? Help!(7 votes)
- I think you might be confusing a variable with a unit. For example, when we use m to represent meters, you would write 10 m if something was 10 meters long. D does not represent the unit, or word, dollars. It represents a quantity in number of dollars. S doesn't represent the unit, or word, scoop. It represents a quantity in number of scoops. When you read D = 0.75 S, you should say something like, the cost in dollars is equal to 0.75 times the number of scoops. I think you might be reading it as one dollar (1D, or just D) is equal to 0.75 scoops. I'm not sure where you got $1.25 for one scoop from. Perhaps you just added $0.25 to each side. However, if the ice cream was $1 for 0.75 scoops, you could multiply each amount by 4/3 to calculate the unit rate per scoop. I hope this helps.(15 votes)

- This was on a quiz of mine...

A dog has 34 bones but his owner takes away 4. How many bones does the cat have.

I NEED HELP(9 votes) - Store A is the correct answer, right?(8 votes)
- By the way, there is a very easy way to know your nine multiplication problems. All you have to do is put down the finger on your hand that your multiplying by Here is an example 9 times 6 I'm going to hold up all ten fingers and then put down my sixth finger on the right of the finger you have 5 on the other side you have 4 put 5 and 4 together you have 54 which is your answer or you can just memorize you multiplication problems but I'm not very good at that.(8 votes)
- imagen an imagen could imagen an imagen(8 votes)
- hey everyone im new to khan academy its a great wedsite!(5 votes)
- this is the wedsite of all time(1 vote)

- Sal: "one point half"

Me: "I love these videos."

Oh Sal, you slay me. I shall remember the one point half. :))))))))*_)*)_)_(4 votes) - man this is so hard whats 5 x 9(5 votes)

## 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.