 Okay, this is a Solving Percent Problems video. This is my first attempt at a video with a lot of writing in it, so we'll see how well this goes. Okay, so this is a percent type of problem. We're gonna use proportions to solve this. But before that, I'm gonna read through this to see what we have going on. Okay, so a poll taken the day before an election showed that 22.5% of voters planned to vote for a certain candidate. If 1800, 1800 voters participated, how many voted for that candidate? Okay, now when you have these type of percent problems, one thing that we need to do is we need to look through the problem and try to identify certain pieces of it, mainly just the numbers. Whenever you read a word problem, we wanna try to identify in the numbers. So the first two that jump out at me is 22.5% and 1800 voters. Okay, those two numbers I'm gonna use somehow some way to try to figure out this percent problem. Okay, now whenever you encounter a percent problem, there is one kind of formula, I can kinda call it a formula, that is really very useful for these type of problems. And that formula is the percent over 100 is equal to the part over the whole. Now, notice earlier I said that we talked about solving this using proportions. Remember that a proportion is just a fraction equal to a fraction. And so that's kinda what we have here. This formula, if you wanna call it that, is just a proportion, I guess, just something we commonly use for percent problems to make it a little bit simpler. Okay, so now the thing is, is we got three pieces of this formula. We got a percent that we gotta plug in, we got a part that we gotta plug in, and we have a whole that we gotta plug in. So there's only three things that we really need to figure out. One of those things, actually, we will not be able to figure out, that's kinda gonna be our variable when we get there in a minute. So as I read through this again, we're gonna try to figure out which numbers are the percent, which ones the parts, and which ones are the whole. Okay, a poll taken the day before an election showed that 22.5% of voters plan to vote for a certain candidate. If 1,800 voters participated, how many voted for that candidate? Okay, now, as I read through it again and again, whenever you work out these word problems, you might have to read through them again and again and again to figure out everything you need to know about them. The first number that comes out is 22.5%. Okay, that right there, that's kinda easy to figure out where that's gonna go here in our little formula. That's gonna go in the percent spot. So over here, I'm gonna do a little bit of work. 22.5 over 100 is equal to the part over the whole. Okay, now I gotta figure out out of this problem what the part is and what the whole is. Okay, if 1,800 voters participated, how many voted for that candidate? Okay, now as I read that, I gotta think, okay, that 1,800, is that gonna be part or is that gonna be the whole? Okay, now this is where the understanding of the problem comes in handy. I know that 1,800 is gonna be my largest number. That's the total number of voters that came in and filled out ballots on that certain day or maybe the certain couple of days. Okay, so that's gonna be, that's the large number. That's the big number. So that right there, this 1,800 is gonna be the whole. Okay, the part right here is gonna be how many voted for that candidate? So this empty spot right here, we'll call it the variable. So, well, we're talking about a candidate, so I'm gonna use C for a variable. That's the part. That C stands for how many people voted for that candidate. That's the empty spot. That's the part that I don't know. Okay, so out of 1,800 voters, how many of them voted for that certain candidate? Okay, so now I have a nice little equation to solve. This is just like the proportions video that we did just a couple of videos ago. Anyway, to solve this, we have to use a cross product, cross product, so I have to take 22.5 times 1,800, using parentheses to denote multiplication. Okay, equals C times 100. Well, I was gonna put 100 C, and there we are. Okay, now one thing I'm actually gonna show here, I'm not actually gonna multiply those numbers quite yet. What I'm gonna do is I look at the right side, I wanna get C by itself, and I wanna know how many votes that candidate got. So what I'm gonna do first is actually I'm gonna divide by 100. This is one technique to use when solving equations. You don't have to do all the mathematics all at once. Sometimes you can wait a little bit. So what I'm gonna do is I'm actually gonna take this 100 and divide it over to the other side. So I'm going to divide by 100, divide by 100. I'm losing some space right here, so I'm gonna go that way. So what this ends up being is C is equal to 22.5 times 1,800, all of that divided by 100. And notice I kind of switched things around just a little bit. This C on this side is last, and I kind of flipped it so it's first, then this over here was first. I switched that so it's last. You can flip those around a little bit, just as long as everything stays equivalent. That's kind of a technique that I like to use. I like my variables to come first, so that's why I use that. But anyway, so what I have now is I have 22.5 times 1,800 and then divide by 100. If you're pretty good with the math, you realize that I can actually divide this first. So this is actually 22.5 times 18. These zeros are gonna cancel out. The 1,800 divided by 100 is just gonna leave me 18. You don't need to know that, but this right here, you can plug into your calculator. It's one nice easy step divided by 100. And so in this case, C is equal to 405. C is equal to 405, that's a little bit lower than I want to in my paper. But anyway, so what I'm gonna do is I'm gonna erase this just a little bit so I can actually write my answer. This right down here, C is equal to 405. C is equal to 405, that is not my answer. Okay, a lot of students will make this mistake once they get down to this point, they think, oh, okay, C is equal to 405, my teacher's gonna know what that is, boom, that's my answer. Well, in the real world, the thing is, when somebody tries to read this problem or tries to figure out what you did or you're trying to explain this to somebody, 405, C equals 405 means absolutely nothing to them. If you look back up into our problem up here, there's no C's, there's no variables, there's nothing to that effect. So C makes no sense whatsoever. So make sure when you have a problem like this, make sure you actually write what the answer is. C equals 405, I have no idea what that means. But this tells me, because I use C for a variable, C stands for the number of people who voted for that candidate. Now the only label I have for that candidate is just that, it's that candidate. I really actually, honestly, the problem doesn't really tell me much more than that. Anyway, this tells me, since C is equal to 405, that tells me that 405 people voted for that candidate. That right there is your answer, okay? You'll save a lot of people, a lot of heartache, you'll save your former, or excuse me, your future employers, a lot of heartache, and you'll save your teachers a lot of heartache if you actually write your answer. Just don't assume that everybody knows what this bottom part means. Not everybody's gonna know that. So you have to use plain English right at your answer. 405 people voted for that candidate. Okay, that is just one example of a percent problem. I will do more examples in later videos, but that just gives you a basic idea. Real quick, I want to rewrite this. Okay, so that was the answer to the problem. 405 people actually voted for that candidate, but we used this little formula. Percent over 100 is equal to part over whole. This is a very useful formula to memorize. It's not, I hate calling it a formula because it's not technically a formula, but it's a nice little tool for us to use to solve these type of percent problems. So that right there is probably the most important part of this problem.