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Current time:0:00Total duration:7:40
CCSS.Math:

Video transcript

now that we've set up our quote our equations let's see if we can answer some more interesting questions and this is a warm-up we're going to do a little bit of what we did in the last video but I'll do it with the equations now the equations really are just a mathematical representation of the same information that we had up here so as a starting point let's think about how much under the basic plan let's think about how much it'll cost for us to attend three sessions in a given month well we've got our equation right over here our total cost in that month is going to be equal to 20 20 plus 8 plus 8 plus 8 times the number of sessions the number of sessions is SS is 3 in this circumstance so we'll replace the s with the 3 and so you get our cost in this circumstance is going to be 20 plus 8 times 3 or 20 plus 24 or $44 so let me erase this right over here so this is going to cost us 44 $44 now let's do the same thing under the trial plan how much is it going to cost us to attend three sessions well this is more straightforward or slightly more straightforward our total cost is going to be equal to 12 12 times the number of sessions the number of sessions in this circumstance are three sessions so it's going to be 12 times 3 so our total cost is going to be equal to $36 so let me write that down so it's going to be equal to $36 but we could also answer more interesting questions with these equations for example how many sessions how many sessions sessions can I attend can I attend in a month attend four oh I don't know let's throw out something for $54 for $54 let's say that's just my budget when I look at my salary and how much money I have budgeted to health and fitness this is what I can afford and so based on that I want to ask how many sessions can I attend in each of these situations so first let's think about it for the trial plan how many sessions can I attend for $54 and let's just assume let's just assume that this is some type of a special special yoga studio where you can even attend half a session so if you tend half a session they'll charge you six dollars if you attend a fourth of a session they'll charge you three dollars so they'll actually keep track of exactly what fraction of a session you're attending so you can you don't have to just attend whole number of fret sessions you could attend two and a half and they'll bill you accordingly so with that said with that said how many sessions under the trial plan can I attend for $54 well let's think about this a little bit so my cost now is going to be $54 $54 is C it's my monthly cost so 54 is going to be equal to 12 $12 per session times the number of sessions times the number of sessions so now I set up this equation in order to answer this question I just need to figure out what's the number of sessions that satisfy it now the this s is an unknown variable what number of sessions times 12 is equal to 54 well you might say well if I could just get an S just an S on the right hand side here then I'll have an answer s will be equal to some value and if I want just an S on the right hand side I'd ideally just like to divide this by 12 12s divided by 12 is just going to give me an S it's just going to give me the number of sessions but if I have an equal sign I can't just really nearly 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 to both still be equal have to do the same thing to both sides so on the right hand side I am 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 I'll just work it out 12 goes into 54 goes into 54 4 times 4 times 12 is 48 you're left with a remainder of 6 so you could say 12 goes into 12 goes into 54 or could say 54 over 12 is equal to four and six twelve or four and a half so the number of sessions that I could attend are four and a half under if I have fifty-four dollars to spend I can attend four and a half sessions under the trial plan if this was a yoga studio that said oh you can't attend half sessions then it would then you could say well at most I could attend four sessions because five sessions would get me above my budget but I said that you can attend fractional sessions so we're going to say four and a half now let's do the same let's answer the same question let's answer the same question for the basic plan under the basic plan how many sessions can I attend for $54 well once again this is going to be our cost our total cost for that month so we say $54 $54 is equal to 20 plus 8 times the number of sessions plus 8 times times the number of sessions and once again I'd like to just have sessions maybe on the right-hand side of this equation so I could say all sessions are going to be equal to something this is the number of sessions that I can attend but I have this 20 year and this 8 here and so I have to think about how I can get rid of them so the first thing I to think about is how can I get rid of this 20 from the right-hand side of this equation what am I going to have to do to the entire equation well the simplest thing is I could subtract 20 from the right-hand side but if I subtract 20 from the right-hand side I also have to subtract 20 from the left-hand side in order to maintain the equality and so I'm left with on the left-hand side 54 minus 20 gets me 34 and that's going to be equal to well the whole point of subtracting 20 is so that these negate each other and then I have just an 8's it's just 8's so 8 times the number of sessions has to be equal to 34 in order for eight times the number of sessions plus 20 to be equal to 54 and you could add 20 to both sides of this equation to get our original so we're almost done we just want to isolate the s right here and could imagine the easiest way would do be to divide the right-hand side by eight but if we're dividing the right-hand side by eight we have to do the same to the left and so what do we get for the number of sessions that we would have to attend well these cancel out and so you get the number of sessions number of sessions is equal to 34 divided by eight 34 divided by eight is equal to let's see 8 goes into 34 4 times with remainder 2 so 4 + 2 8 or it's 4 and 1/4 so I could attend 4 and 1/4 sessions under under the basic plan so under assuming I can do fractional sessions for $54 which one can I attend more sessions in the basic plan or the trial plan well for $54 I could attend a slightly longer amount of sessions under the trial plan