Проценттой өгүүлбэртэй бодлого
Percent word problem: magic club
- [Instructor] In a video game, Val scored 30% fewer points than Peeta. Peeta scored 1,060 points. How many points did Val score? Pause this video and see if you can figure out how many points Val scored. Alright, now let's do this together. And there's a couple of ways that you could think about it. One way to think about is Peeta scored 1,060 points, and Val scored 30% fewer. When we're saying 30% fewer, we're saying essentially take 30% of 1060 and subtract that from 1060. So 30%, so we could write that as a decimal as 0.30. 30/100 is the same thing as 30%, or we could even write this as .3. And then we would want 30% of 1060. So if you take Peeta's score and then subtract 30% of Peeta's score, then this would give you Val's score. So that's one way to calculate it. Another way to think about is whatever you're starting with, let's call that 100%, and if you were to take out 30% of it, if you were to have 30% less, then you're going to have 70% of what you started with. So another way to think about it is we could take Peeta's score of 1060 and multiply it by 70%. And multiplying it by 70% is the same thing as multiplying it by 0.70, which is the same thing as multiplying it by 70/100, is the same thing as 7/10. So let's just do this. So if I have 1060, and I multiply by 0.7, what do I get? Seven times zero is zero. Seven times six is 42. Seven times zero is zero, plus four is four. Seven times one is seven. And I have one digit to the right of the decimal. So there you have it, it is 742. 742. That is how many points Val scored. Let's do another example. So we're told there are 20% more goblins than wizards in a magic club. There are 220 goblins and wizards altogether in magic club. How many goblins are in the magic club? So pause the video and see if you can work through this on your own. So this one is an interesting one. It's gonna involve a little bit of algebra here. So what we wanna do is let's set a variable. Let's say w is the number of wizards. So that's the number of wizards. And then if we said g for goblins, let's say g for goblins. So w plus g is equal to 220, is equal to 220. And you're like, well, how does that help me? How does that help me actually figure out how many goblins are in the magic club? I have two variables here with one equation. Well, one way to think about it is, remember, they give us some more information. They tell us there are 20%, let me box that, there are 20% more goblins than wizards. So we also know one other thing. We know that the goblins, we know that the goblins are equal to the number of wizards plus 20%. So you could view this as wizards plus 20% of wizards. And I'm writing that as 20/100, or you could even write that as 2/10, plus 2/10 times the number of wizards. Or another way of thinking about it, goblins are equal to, if I have one of something and then I have another 2/10 of that something, then I'm gonna have 1.2 of that something. So goblins is equal to 1.2 times the wizards. And so we could use that to substitute back in here, and then we could say the number of wizards plus the number of goblins, which happens to be 20% more than the number of wizards, is going to be equal to 220. Let me do that in that same color. Is equal to 220. Now this is pretty straightforward to solve. What is w plus 1.2w? Well, that is going to be 2.2w, 2.2w. You could view this as one w plus 1.2w is 2.2w is equal to 220. And so just divide both sides. Let me scroll down a little bit. Divide both sides by 2.2, 2.2, and what do you get? You get w, the number of wizards is equal to, let's see, this is going to be equal to 100. The number of wizards is equal to 100. Now is that our answer? No, they're asking how many goblins are in the magic club? Well, we know that goblins are 1.2 times the wizards. So the number of goblins is going to be 1.2 times 100, which is equal to 120. So there's 120 goblins, does that make sense? 120 is 20% more than 100. And if you add the 100 wizards to the 120 goblins, you get 220 goblins and wizards altogether. Let's do another example. Here we're told Cody was 165 centimeters tall on the first day of school this year, which was 10% taller than he was on the first day of school last year. How tall was Cody on the first day of school last year? Pause this video, see if you can figure that out. So let's just define a variable here. Let's just say that his height on the first day of school last year, let's say that that is x. So his height on the first day of school last year is x. This year he is 10% taller, so we would add 10%, which we could say is 10/100, or we could even say that as 1/10. He's 1/10 taller. So whatever his height was last year, we're going to add 1/10 of that same height again to get to his height this year, which they tell us is 165 centimeters. And so here we could say well, one x plus 1/10 of an x is going to be one and 1/10x is equal to 165. And now to solve for x, which remember, was his height on the first day of school last year, we divide both sides by 1.1. And so x is equal to, well, let's see what this is going to be. If I were to take 165 divided by 1.1, the first thing I would wanna do is multiply them both by 10. So that has the effect of moving this decimal place one to the right. So really, I am now trying to figure out what 11 goes into 1,650 is. And so let's see, let me just do that step by step. 11 goes into 16 one time. One times 11 is 11. Subtract, we get a five, and we bring down a five. 11 goes into 55 exactly five times. Five times 11 is 55. Subtract. We have no remainder, but then we bring down this zero and we do it one more time. 11 goes into zero zero times. Remember, the decimal place is right over here. Zero times 11 is zero, and then we have no remainder. So last year he was 150 centimeters. And it's always good to do a reality check. Make sure, if for example, if I divided wrong and I somehow got 15, or I got 1500, just to make sure that that wouldn't make any sense. 150 centimeters, you add 10% of that. 10% of 150 is 15 centimeters. So you add 10% of that, you indeed do get to 165 centimeters for the first day of school this year.