Super Yoga Plans- Solving One-Step Equations Solving one-step equations to see how many sessions can be attended
Super Yoga Plans- Solving One-Step Equations
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- Now that we set up our equation. Let's see if we can answer some more interesting questions.
- This is a warm-up. We are gonna do a little bit of what we did in the last video.
- But I will do it with the equations now.
- The equations are really just a mathematically representation of the same information that we have up here.
- As a starting point, let's think about how much, under this basic plan, it will cost for us to attend 3 sessions in a given month.
- We have our equation right over here. Our total cost in that month is going to be equal to 20 plus 8 times the number of session.
- The number of sessions is "s". "s" is 3 in this circumstance. So we replace "s" with the 3.
- So we get that our cost is 20 + 8 times 3. Or 20 + 24. Or $44. So it's gonna cost us $44.
- Now lets do the same under the trial plan
- How much is it gonna cost up to attend 3 sessions?
- Well, this is more straight forward, our total cost is gonna be equal to 12 times the number of sessions.
- The number of sessions is 3.
- so it is 12 times 3, so our total cost is going to be $36.
- But we could also answer more interesting questions with these equations.
- For example, how many sessions can I attend in a month for $54.
- When I look at my salary and my budget for health and fitness, this is what I can afford. And based on that I wanna ask.
- How many session can I attend with each of these situations?
- First let's think about it for the trail plan. How many session can I attend for $54.
- Now let's just assume that this is some kind of special yoga studio, where
- you can even attend a half session and they will just charge you half the cost, 6 dollars. If you attend a 1/4 of a session they charge you 3 dollars.
- so they keep track of exactly what fraction of a session that you attend.
- You don't have to attend a whole number of sessions.
- You could attend 2 1/2 and they will bill you accordingly.
- So with that said, how many session under the trial plan can I attend for $54?
- Well, lets think about it this a little bit.
- So my cost now is 54. 54 is "c". It's my monthly cost. 54 is equal to 12 times the number of session.
- So now I have set this equation. In order to answer this question. I just need to figure the number of session that satisfy it.
- Now this is "s" is an unknown variable.
- What number of sessions times 12 is equal to 54.
- Well you might say, if I could just get "s", just the "s" on the right side here, then I have the answer.
- "s" will be equal to some value.
- And if I want just an "s" on the right hand side, I divide this by 12.
- 12s divided by 12 is s. The number of sessions.
- But if I have an equal sign, I can't just willy-nilly divide one side by 12 without doing the exact same thing to the other side.
- If that is equal to that, in order for them still be equal we have to do the same thing to both sides.
- So on the right hand side, I'm left with just an s, and on the left hand side, I have 54 divided by 12.
- Let me think about that. 12 goes into 54.
- 4 times. 4 times 12 is 48.
- You are left with a remainder of 6.
- So you could say 12 goes into 54. Or you could say 54/12 is equal to 4 and 6/12.
- or 4 and a 1/2.
- So the number of session that I can attend are 4 1/2.
- If I 54 to spend, I can attend 4 1/2 sessions under the trial plan.
- If this was yoga studio that said, you can't attend half sessions, then
- it would only be 4 sessions, because 5 sessions would get me above my budget.
- But I said you can attend fractional sessions, so it is 4 1/2.
- Now lets answer the same question for the basic plan.
- Under the basic plan how many sessions can I attend for 54 dollars?
- Once again this will be our total cost for that months, so we say,
- 54 is equal to 20 + 8 times the number os sessions.
- And once again, I'd like to have just session on the right hand side of this equation.
- So I can say session are going to be equal to something.
- This is the number of session I can attend.
- But I have this 20 here and this 8 here, so i have to think about how I can get rid them.
- So the first thing to think about is how can I get rid of this 20 on the right hand side of this equation?
- what am I gonna do to the entire equation?
- well the simplest thing, I could subtract 20 from the right hand side, but if subtract 20 from the right hand side,
- iI also have to subtract from the left hand side to maintain the equality.
- And so I'm left with.
- on the left hand side: 54 minus 20 gets me 34,
- and thats equal to 8s,
- so 8s has to equal 34
- in order for 8 times the number of session plus 20 to be equal to 54
- and you can add 20 both sides to get the original.
- So we're almost done, we just need to isolate the s right here and you can imagine that the easiest way
- would be to divide the right hand side by 8 but if divide the right hand side by 8,
- we have to do the same to the left.
- and so what do we for the number of session that we would have to attend?
- well, these cancel out, and so you get the number of session is equal to 34/8
- 34/8 is equal to, lets see.
- 8 goes into 34 four times with the remainder 2.
- so 4 and 2/8.
- or it's 4 1/4.
- So I can attend 4 1/4 session under the basic plan.
- So assuming I can do fractional session, for which one can attend more sessions in?
- The basic or the trial plan?
- Well for 54 I can attend a slight longer amount of session under the trial plan.
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