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Video transcript

let's say that I'm working in a restaurant and I'm making $10 per hour but on top of my hourly wage I also get tips each hour so this entire expression you can view this is how much I might make in a given hour now you might also realize that the number of tips or the amount of tips I might make in an hour can change dramatically from hour to hour it can vary one hour it might be lunchtime get a lot of tips people might get some big-ticket items the next hour um I don't have any customers and then my tips might be really low so the tips part right over here we consider that the entire word we consider that to be a variable from scenario to scenario it can change so for example in one scenario maybe it's lunch time I'm getting really big tips so tips is equal to let's say it's equal to 30 dollars and so the total amount I might make in that hour is going to we can go back to this expression right over here it's going to be 10 plus instead of writing tips here I'll write 30 because that's what my tips are in that hour and so that is going to be equal to it's going to be equal to 40 who didn't let me do that in yellow color it's going to be equal to 40 dollars but let's say right after that the restaurant slows down we're out of the lunch hour for whatever reason maybe the restaurant next door has a big sale or something and so the next hour my tips go down dramatically my tips go down to $5 for that hour now I go back to this expression the total I make is my hourly wage plus the five dollars and tips plus the five dollars in dips which is equal to fifteen dollars as you see this entire expression the ten plus tips it changed depending on what the value of the variable tips is now you won't see whole words typically used in algebra as variables we get lazy and so instead we tend to use just easier to write symbols and so in this context we instead of writing tips maybe we could have just written 10 plus T where T where T represents the tips that we get in an hour and so then we would say okay what happens when T is equal to 30 well if T is equal to 30 then we'd have let me write so what happens when T is equal to 30 well then we have a situation T is equal to 30 this evaluates to 10 plus 30 which would be 40 what would happen if T is equal to 5 well then this would evaluate to 10 plus 5 which is equal to 15 now I want to be clear we didn't even have to use T we didn't even really have to use a letter although in traditional algebra you almost do use a letter we could have written that as we could have written it as 10 plus X where X is your tips per hour X might not be as natural it's not the first letter in the word tips or you could have even written 10 plus you could have even written 10 plus star where you could say star represents the number of tips in an hour but it just might have not made as much intuitive sense but hopefully this gives you a general idea of just what a variable is all it is is a symbol all it is is a symbol that represents different that a symbol that represents varying values and that's why we call it a variable