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I'm in the mood to improve my flexibility

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a little bit so I decide to take some Yoga classes

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so I show up at the local yoga place called Super Yoga

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and ask them, "how much does it cost?"

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And they say, "we've got a basic plan"

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"and we've got a trial plan."

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The trial plan, if you just want to try things out,

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you can come to any of the sessions

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and it's going to cost you $12 per 1hr session.

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but if you like what you're doing here

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you might want to get a monthly membership

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That'll be $20/month,

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that you can view that as the basic plan

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It's $20/month and then you get a discount per session

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It'll only be $8 per session

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So this seems interesting, but I'm a little bit confused.

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Which plan should I take?

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So the first place, I might start is to think about

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how much I would pay

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depending on how many sessions I actually take

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And to do a little short hand here

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let's just define some variables

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Let's say that S = "Number of Sessions" I attend per month

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Number of sessions per month that I attend

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I decided to attend at Super Yoga

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And let's say that C = "Total Monthly Cost"

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My Total Monthly Cost

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So with these variables defined this way,

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let's think about how much I would pay

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under each of these plans

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depending on how many sessions I would attend

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So first, let's think about the, we'll start with the Trial Plan

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cause that seems a little simplier

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and I'll draw a little column here

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I have a cost, actually, let me see, I'll draw my number of sessions

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Number of sessions and then I have my cost

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and then I'm going to draw a little table here

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A little table, that'll be for my trial plan

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and then let's also do the same thing,

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since we're doing it for the trial plan

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let's do it for the basic plan so that we can compare

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Let's do it for the basic plan

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so I have the Number of sessions I attend

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and my Total Cost

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So let's first think about, if I decide to attend no sessions

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So if I decided to attend no sessions

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under my trial plan, what will be my cost?

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Well, $12 per session, 12 x no sessions

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Well, I'm not going to have to pay anything

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My cost is going to be zero

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Now what about that same question

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under the basic plan

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If I have the basic plan, but in a given month

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I attend no sessions,

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I don't go to the gym, I don't go to this yoga gym at all

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How much am I going to have to pay?

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Well, it's $8 per sessions

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I didn't have to go to any sessions

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So I'm not going to have to pay anything

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on a per session basis

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but I will have to pay that $20/month

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So I will have to pay $20

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even though I didn't even attend

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That doesn't seem so good in that scenario

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But let's keep working through other scenarios

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Let's think about the scenario where I attend 1 session

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Where I attend 1 session

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Under the trial plan, how much will I have to pay?

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Well, it's $12/session x 1 session

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I'm going to pay $12

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Let's think about that same scenario under the basic plan

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Under the basic plan, if I attend 1 session

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Well, it's $8/session x 1 session

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$8 for that

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Plus just the basic monthly

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So I'm just going to have to pay $20 + ($8 x 1)

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So $28.

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I'm going to have to pay $28

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So still that trial plan still looks pretty good

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even if I attend 1 session

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Let me make it clear

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That's in dollars

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and that over here is $28

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and I could keep going

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and I encourage you to keep going

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but let's try 1 more

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just to see how, just to get a feel for the numbers here

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If I attend 2 sessions under the trial plan

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How much am I going to pay?

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Well, it's $12/session x 2 sessions

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i'm going to pay $24

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Let's think about the basic plan

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if I attend 2 sessions

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-- let me do that in a yellow colour --

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if I attend 2 sessions

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2 x $8/session, that's going to $16

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plus the $20 I'm going to have to spend every month

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So it's going to 2 x $8

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+ $20

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= $16 + $20

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= $36

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So at least for the scenarios that we set up here

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if I attend 0 or 1 or 2 sessions

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the trial plan seems to be winning out

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but I want to explore at what point

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does the trial plan actually become a little bit worse

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But before we do that

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let's think about if we can represent this

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this a little algebraically

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because it's going to allow us to be a little bit more precise

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with coming up with our answers

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So if we say that, S is the "Number of Sessions per Month"

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and C is the "Monthly Cost"

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How can we express the trial plan as an equation?

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Well, we could say our Total Cost

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our Total Monthly Cost

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so this is for our trial plan right over here

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let me draw a dotted line over here to show

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well, the dotted line goes around there

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so under the trial plan our total cost is going to be equal to

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well, it's $12/session x # of sessions

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times S

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So under the trial plan I could say my total cost is equal to

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$12 x # of Sessions

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$12/session x the Number of Sessions

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Let's so the same thing with the basic plan

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How can we express that as an equation?

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Well, we have our total cost

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our total cost is going to be equal to

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well, regardless of what we do

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any given month, we're going to have to pay

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the $20/month

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we're going to have to pay that 20

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So no matter what we do,

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we're going to have to pay that 20

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just from the get-go

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and then we're going to pay $8/session

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so it's going to be $20 + ($8 x # of Sessions)

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so that's interesting and you can see

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if you put S is 0 here,

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if you make S = 0

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you get 20 + (8 x 0) which is 20

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if you say S is 1, you get 20 + (8 x 1)

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which is 28

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so you see that each of these S's and C's

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they satisfy this equation

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Same thing over here

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and we can keep trying more and more

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What's neat about these equations is

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just this equation encapsulates

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all of the possible combinations here

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and just this equation encapsulates

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all the possible combinations there

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and so for the next few videos,

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what I want to do is explore

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How can we use these equations

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to come up with more insights as to

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which plan is better for me