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### Course: Operations and Algebraic Thinking 222-226 > Unit 2

Lesson 6: Two-step equation word problems- Equation word problem: super yoga (1 of 2)
- Equation word problem: super yoga (2 of 2)
- Two-step equation word problem: computers
- Two-step equation word problem: garden
- Two-step equation word problem: oranges
- Interpret two-step equation word problems
- Two-step equations word problems

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# Equation word problem: super yoga (1 of 2)

Using information from the Super Yoga word problem, explore all the possible combinations and create equations which express the possibilities. Let's figure out which plan is best! Created by Sal Khan.

## Want to join the conversation?

- How would you account for when you hit the second month and an additional $20 is spent?(154 votes)
- I guess you could modify your equation to include a second variable (let's make it 'M') that represents the number of months, thus:

C = 20*M + 8*S

This means that you also have to include another column to the table, 'M', which tells you in which month you currently are.(172 votes)

- Bruh I would just take the trial plan. You only pay 12 bucks. Why even get a membership it's not even anything extra.(11 votes)
- I did the math (I like to do try to do it before they explain it), and it seems that if you have a budget above $60 or are going for more than 5 sessions a month, then the basic plan is more worth it (68 for 6 sessions for example). Anything less than $60 OR less than 5 sessions, then the trial is worth it.

In this video, they solve for C (the total monthly cost). Using a formula of subject C can give you the total price given the amount of sessions you require. For example, the basic membership for 6 sessions would be:

C = 20 + 8s

C = 20 + 8(6)

C = $68 per month for 6 sessions

And for the trial it would be:

C = 12s

C = 12(6)

C = $72 for 6 sessions

However, if you care more about which one is cheaper for a certain budget limit (you don't care about number of sessions, you just want to know how much 's' sessions would cost), then you can switch the subject of the formula to 's'. In such case, the formula for basic membership would be:

s = (C-20)/8

and for trial, it would be:

s = C/12

For example, let's say you have a budget of $45 (to spend on one month) but you don't know which one will give you more sessions, you just plug that $50 where 'C' is and you get the total session count. In this case, it would be:

Basic membership:

s = (45-20)/8

s = 3.125 sessions

Trial:

s = 45/12

s = 3.75 sessions

Therefore, for the budget of $45, trial wins out in terms of sessions you get.

Using either one of the 2 formulas, you can confirm my original statement. You will also note that 5 sessions is equal price between trial and membership, so in that case it wouldn't matter which one you choose.(3 votes)

- How many Sessions are per month though? If there is 1 each week he would only have to pay $20 plus the $8 for the sessions.(7 votes)
- I guess you just have to assume that a session is there whenever you want it.(6 votes)

- on every math test, I always be like aww man I wish I was Khan who else?(6 votes)
- Just like me, he has years of experience on you, so if you enjoy math and look back 10 years from now, you will say how easy this was looking back, but new things always take time to learn. I am proof that you can still teach old dogs new tricks.(3 votes)

- Wait, how come you pay 20$ even if you don't attend? That makes no sense whatsoever. So basically if you get the Basic Plan your literately negative 20$😕🤯😔🤷?(4 votes)
- Assuming that you are thinking about attending, you are correct, if you never go, there is no use buying the basic plan. If you attend less than 5 times, then you are best off with the trial plan. At 5 times, each plan costs the same, and if you attend more than 5 times, you are better off with the basic plan. This happens all the time in real life, people make a new years resolution to get fit and join a club, but within a few months, they are paying and not always going.(4 votes)

- Why would you have to pay an addition of $8 if you already have the monthly plan of $20(5 votes)
- The monthly plan simply gives you a $4 discount per session(when compared to the trial plan).(1 vote)

- This is how I do this in my head: I need to make up the $20 extra for the monthly plan in savings to make it worth it. The savings is made through the difference in per-sessions cost, which is $4 ($12 - $8). So how many sessions does it take until I've absorbed the $20 fee (how many times does 4 go into 20)? 5. So I know that the cost equals out at 5 sessions, and beyond that, monthly plan is better. Thoughts? Maybe I'm missing the point?(6 votes)
- That's right, actually. At 5 sessions in a month, both the Trial Plan and the Basic Plan cost $60. However, if you attend 6 sessions in a month, the Trial Plan will cost $72 and the Basic Plan will cost only $68.(1 vote)

- i did not understand at all(4 votes)
- if he drew that himself, tops to him(4 votes)
- You can find when using the basic plan becomes cheaper than the trail plan by solving this equation:

20+8s=12s

Which comes out to 5 sessions, so the cost of 5 sessions of the basic plan would cost $60, and with the trial plan it will also cost you $60 for 5 sessions.

So the amount of sessions you would need to do with the basic plan to make it worth it would be 6 sessions.(2 votes)

## Video transcript

I'm in the mood to improve my flexibility a little bit so I decide to take some Yoga classes so I show up at the local yoga place called Super Yoga and ask them, "how much does it cost?" And they say, "we've got a basic plan" "and we've got a trial plan." The trial plan, if you just want to try things out, you can come to any of the sessions and it's going to cost you $12 per 1hr session. but if you like what you're doing here you might want to get a monthly membership That'll be $20/month, that you can view that as the basic plan It's $20/month and then you get a discount per session It'll only be $8 per session So this seems interesting, but I'm a little bit confused. Which plan should I take? So the first place, I might start is to think about how much I would pay depending on how many sessions I actually take And to do a little short hand here let's just define some variables Let's say that S = "Number of Sessions" I attend per month Number of sessions per month that I attend I decided to attend at Super Yoga And let's say that C = "Total Monthly Cost" My Total Monthly Cost So with these variables defined this way, let's think about how much I would pay under each of these plans depending on how many sessions I would attend So first, let's think about the, we'll start with the Trial Plan cause that seems a little simplier and I'll draw a little column here I have a cost, actually, let me see, I'll draw my number of sessions Number of sessions and then I have my cost and then I'm going to draw a little table here A little table, that'll be for my trial plan and then let's also do the same thing, since we're doing it for the trial plan let's do it for the basic plan so that we can compare Let's do it for the basic plan so I have the Number of sessions I attend and my Total Cost So let's first think about, if I decide to attend no sessions So if I decided to attend no sessions under my trial plan, what will be my cost? Well, $12 per session, 12 x no sessions Well, I'm not going to have to pay anything My cost is going to be zero Now what about that same question under the basic plan If I have the basic plan, but in a given month I attend no sessions, I don't go to the gym, I don't go to this yoga gym at all How much am I going to have to pay? Well, it's $8 per sessions I didn't have to go to any sessions So I'm not going to have to pay anything on a per session basis but I will have to pay that $20/month So I will have to pay $20 even though I didn't even attend That doesn't seem so good in that scenario But let's keep working through other scenarios Let's think about the scenario where I attend 1 session Where I attend 1 session Under the trial plan, how much will I have to pay? Well, it's $12/session x 1 session I'm going to pay $12 Let's think about that same scenario under the basic plan Under the basic plan, if I attend 1 session Well, it's $8/session x 1 session $8 for that Plus just the basic monthly So I'm just going to have to pay $20 + ($8 x 1) So $28. I'm going to have to pay $28 So still that trial plan still looks pretty good even if I attend 1 session Let me make it clear That's in dollars and that over here is $28 and I could keep going and I encourage you to keep going but let's try 1 more just to see how, just to get a feel for the numbers here If I attend 2 sessions under the trial plan How much am I going to pay? Well, it's $12/session x 2 sessions i'm going to pay $24 Let's think about the basic plan if I attend 2 sessions -- let me do that in a yellow colour -- if I attend 2 sessions 2 x $8/session, that's going to $16 plus the $20 I'm going to have to spend every month So it's going to 2 x $8 + $20 = $16 + $20 = $36 So at least for the scenarios that we set up here if I attend 0 or 1 or 2 sessions the trial plan seems to be winning out but I want to explore at what point does the trial plan actually become a little bit worse But before we do that let's think about if we can represent this this a little algebraically because it's going to allow us to be a little bit more precise with coming up with our answers So if we say that, S is the "Number of Sessions per Month" and C is the "Monthly Cost" How can we express the trial plan as an equation? Well, we could say our Total Cost our Total Monthly Cost so this is for our trial plan right over here let me draw a dotted line over here to show well, the dotted line goes around there so under the trial plan our total cost is going to be equal to well, it's $12/session x # of sessions times S So under the trial plan I could say my total cost is equal to $12 x # of Sessions $12/session x the Number of Sessions Let's so the same thing with the basic plan How can we express that as an equation? Well, we have our total cost our total cost is going to be equal to well, regardless of what we do any given month, we're going to have to pay the $20/month we're going to have to pay that 20 So no matter what we do, we're going to have to pay that 20 just from the get-go and then we're going to pay $8/session so it's going to be $20 + ($8 x # of Sessions) so that's interesting and you can see if you put S is 0 here, if you make S = 0 you get 20 + (8 x 0) which is 20 if you say S is 1, you get 20 + (8 x 1) which is 28 so you see that each of these S's and C's they satisfy this equation Same thing over here and we can keep trying more and more What's neat about these equations is just this equation encapsulates all of the possible combinations here and just this equation encapsulates all the possible combinations there and so for the next few videos, what I want to do is explore How can we use these equations to come up with more insights as to which plan is better for me