This video shows how variables and equations can be used to find values within ratio tables.

okay so in today's math lesson westarted talking about equations and variables and all kinds of fun stuff like that and it was interesting a little bit challenging but basically what we spoke about with regard to variables is the fact that that can be a symbol that represents some some value so we have a chart here and we have malaya and she's on a road trip and during the first five minutes of her trip she sees eighteen cars and six trucks assuming the ratio of cars to trucks remains a constant or the same complete the ratio table and we're going to let T represent there's our very variable right we want to let T represent the number of trucks and C which is another variable represent the number of cars that she sees so that eighteen and six is real is a very important deal over here so we have eighteen cars and six trucks watch the order though because the cars are over here and we have the eighteen cars so we have six trucks so we need to fill in this this chart a little bit here so we're gonna look for a pattern what I notice is I have a times three right over here so essentially she sees three times as many cars as she sees trucks so

we're gonna hold that pattern and continue it going up and we're going to continue it going down okay so if I see one truck I see three cars okay if I see three trucks I'm gonna multiply that by three and I see nine cars twelve times three if I need to do any work on the side that's fine I'm not embarrassed it's okay I get thirty six cars and here we have to work backwards a little bit okay I'm gonna run the inverse operation we're going to divide instead of multiply so if I needed three groups or take sixteen split into three groups I would therefore have 20 in each so there's my twenty okay so there's my chart and I'm noticing I had this x three deal going all the way down now that's going to help me a bit in about a second it's so let's go to the questions what is the value of the ratio of the number of cars to the number of trucks number of cars to the number of trucks watch that because they want the car is first so cars to trucks or c-to-t if I want to use the variable or the letter or the symbol and the cars is three so I have a three to one ratio okay or you can use : three to one ratio and it says now all

right so the next question what equation would model the relationship between the cars and the trucks okay this is interesting what equation would model the relationship between the cars and the trucks well I do notice that the cars are always the number of cars is always three times the amount of trucks so if I want the value of the car or see in this case what I really am doing here is taking the number of trucks I have I'm going to multiply it by three now as an equation using that or writing that as an equation I don't want to write the words I want to use the symbols or the variables so I'm going to use T to represent trucks and I'm going to use C to represent cars okay so I'm going to take the number of trucks I have multiplied by three and I should get the number of cars okay in other words I'm going to take once again I'm going to take T I'm going to multiply it by 3 and I get the number of cars now there are a lot of ways you can write this that's one of them they put a little squiggly there I can also write okay house take the number of cars and I can take the 3 and put it in front of the T just like that because if I take a

number and I put it right smack next to a variable it's an automatic multiply and that's what it means okay now there other variables and other things we can find excuse me other equations we can find what if I just want to find C let me change colors for a second what if I want to find T the number of trucks is what I'm looking for well in that case I'm going to make that my beginning there so trucks equals some number of cars but um but I do notice that it's one third the number of trucks two cars it's actually one third so I can actually write that I can say that well the number of trucks is actually one third the number of cars so I'll write it just like that or I can say wait a minute the number of trucks is the number of cars divided by three I could do that too because that's true if I take a look and we did it over here I took 16 I divided it by three and that gave me the 20 okay so I'm using variables that I'm using operations that I'm tossing in a constant here in there and that's basically what we were working on today the kids some of the guys got a little uh even more advanced

they started talking about the totals so if we had some totals which was kind of fun so if I have one truck let me change the colors again if I had one truck and I had three cars that would give me a total of four and if I had three trucks and nine cars that would give me twelve and then they were coming up with some fun things about you know variables or excuse me equations using T as a variable let's do you want to do t we have trucks already so let's do vehicles vehicles let's just V okay so V or the total number of vehicles is T or the number of trucks plus to see the number of cars okay so they're having some fun with that okay lastly it says at the end of the trip malaya had counted 1250 for trucks and that number let me erase some things over here that number would go on the bottom somewhere down here way down low would be a 1250 for some number of trucks here I need to find a number of cars or C and that's what they want here how many cars did she see well if I use my formula I use my equation here if I'm looking for the number of cars I'm going to use this guy right over here so that'll be the first thing I write C

equals three times the amount of trucks which C equals three times T and now I'm going to plug and play a little bit here I'm going to say all right so C equals three times and the number of trucks I have here is one thousand two hundred fifty four and all I really have to do here is evaluate so take my 1254 i'll multiply it by three and i should arrive at my answer so three times four gives me 12 three times five gives me 15 plus 1 is 16 three times two gives me 6 plus 1 7 and 3 times one gives me three for a grand total three thousand seven hundred sixty two cars alright so I don't know why I would ever want to count that many cars and trucks but hey that's the alright folks well that's it that's all good luck take care bye-bye