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Now that we set up our equation. Let's see if we can answer some more interesting questions.

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This is a warm-up. We are gonna do a little bit of what we did in the last video.

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But I will do it with the equations now.

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The equations are really just a mathematically representation of the same information that we have up here.

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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.

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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.

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The number of sessions is "s". "s" is 3 in this circumstance. So we replace "s" with the 3.

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So we get that our cost is 20 + 8 times 3. Or 20 + 24. Or $44. So it's gonna cost us $44.

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Now lets do the same under the trial plan

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How much is it gonna cost up to attend 3 sessions?

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Well, this is more straight forward, our total cost is gonna be equal to 12 times the number of sessions.

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The number of sessions is 3.

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so it is 12 times 3, so our total cost is going to be $36.

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But we could also answer more interesting questions with these equations.

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For example, how many sessions can I attend in a month for $54.

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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.

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How many session can I attend with each of these situations?

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First let's think about it for the trail plan. How many session can I attend for $54.

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Now let's just assume that this is some kind of special yoga studio, where

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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.

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so they keep track of exactly what fraction of a session that you attend.

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You don't have to attend a whole number of sessions.

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You could attend 2 1/2 and they will bill you accordingly.

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So with that said, how many session under the trial plan can I attend for $54?

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Well, lets think about it this a little bit.

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So my cost now is 54. 54 is "c". It's my monthly cost. 54 is equal to 12 times the number of session.

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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.

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Now this is "s" is an unknown variable.

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What number of sessions times 12 is equal to 54.

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Well you might say, if I could just get "s", just the "s" on the right side here, then I have the answer.

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"s" will be equal to some value.

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And if I want just an "s" on the right hand side, I divide this by 12.

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12s divided by 12 is s. The number of sessions.

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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.

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If that is equal to that, in order for them still be equal we have to do the same thing to both sides.

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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.

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Let me think about that. 12 goes into 54.

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4 times. 4 times 12 is 48.

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You are left with a remainder of 6.

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So you could say 12 goes into 54. Or you could say 54/12 is equal to 4 and 6/12.

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or 4 and a 1/2.

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So the number of session that I can attend are 4 1/2.

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If I 54 to spend, I can attend 4 1/2 sessions under the trial plan.

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If this was yoga studio that said, you can't attend half sessions, then

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it would only be 4 sessions, because 5 sessions would get me above my budget.

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But I said you can attend fractional sessions, so it is 4 1/2.

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Now lets answer the same question for the basic plan.

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Under the basic plan how many sessions can I attend for 54 dollars?

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Once again this will be our total cost for that months, so we say,

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54 is equal to 20 + 8 times the number os sessions.

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And once again, I'd like to have just session on the right hand side of this equation.

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So I can say session are going to be equal to something.

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This is the number of session I can attend.

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But I have this 20 here and this 8 here, so i have to think about how I can get rid them.

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So the first thing to think about is how can I get rid of this 20 on the right hand side of this equation?

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what am I gonna do to the entire equation?

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well the simplest thing, I could subtract 20 from the right hand side, but if subtract 20 from the right hand side,

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iI also have to subtract from the left hand side to maintain the equality.

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And so I'm left with.

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on the left hand side: 54 minus 20 gets me 34,

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and thats equal to 8s,

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so 8s has to equal 34

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in order for 8 times the number of session plus 20 to be equal to 54

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and you can add 20 both sides to get the original.

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So we're almost done, we just need to isolate the s right here and you can imagine that the easiest way

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would be to divide the right hand side by 8 but if divide the right hand side by 8,

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we have to do the same to the left.

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and so what do we for the number of session that we would have to attend?

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well, these cancel out, and so you get the number of session is equal to 34/8

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34/8 is equal to, lets see.

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8 goes into 34 four times with the remainder 2.

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so 4 and 2/8.

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or it's 4 1/4.

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So I can attend 4 1/4 session under the basic plan.

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So assuming I can do fractional session, for which one can attend more sessions in?

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The basic or the trial plan?

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Well for 54 I can attend a slight longer amount of session under the trial plan.