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Studying for a test? Prepare with these 10 lessons on Algebra foundations.
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Let's say that I'm working at a restaurant and I'm making 10 dollars per hour. But on top of my hourly wage I also get tips each hour. So this entire expression you can do this as how much i might make in a given hour. Now you might also realized that the number of tips or the amount of tips I may make in an hour can change dramatically from hour to hour. It can vary. One hour it might be lunch time, get a lot of tips. People might get some big ticket item. And the next hour, there might not have any customers, the tips might be really low. So the tip's 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. So the total amount I might make in that hour is going, we can go back to this expression right over here, it's going to be 10 plus, instead of going to write tips over here, I'll write 30, because that's what my tips are in that hour. So that is going to be equal to, it's going to be equal to 40. ... I'm gonna do that, do that yellow color. It's going to be equal to 40 dollars. But let's say right after that, the restaurant slows down, 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 dollars for that hour. Now I go back to this expression, the total I make is my hourly wage plus the 5 dollars in tips, plus the 5 dollars in tips, which is equal to 15 dollars. As you see, this entire expression, the 10 plus tips, it changed depending on the value of the variable tips is. Now you won't see a whole word typically use in Algebra as variables. We get lazy, so instead, we tend to use this, easier to write symbols. So in this contexts, we instead of writing tips, maybe we could have just written, 10 + t, where t, where t represents the tip that we earned in a hour. So then we will say, okay, what happen when t is equal to 30. Well 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 the 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. I wanna 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 that as 10 + x, where x is your tips for a hour, x might not be as natural, it's not the first letter in the word tips. Or you could've even written 10 plus, you could've even written 10 plus star, where you can say star represents the number of tips in a hour. But it just might have not made as much intuitive sense. But hopefully it gives you a general idea, just what a variable is. All it is a symbol, all it is a symbol that represents different varying values, that's why we called it a variable.