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CCSS.Math:

in a video game Val scored 30% fewer points than Peeta Peeta scored 1060 points how many points did Val score pause this video and see if you can figure out how many points Val scored alright well now let's do this together and there's a couple of ways that you could think about it one way to think about it is Peeta scored 1060 points and Val scored thirty percent fewer when we're saying 30% fewer we we're saying essentially take 30% of 1060 and subtract that from 1060 so 30% so that we could write that as a decimal is zero point three zero 30 hundredths is the same thing as thirty percent or we could even write this as 0.3 and then we would want 30% of 1060 so if you take pita score and then subtract 30% of pita score then this would give you val score so that's one way to calculate it another way to think about it is whatever you're starting with let's call that a hundred percent and if you were to take out 30 percent of it if you were to have thirty percent less then you're going to have 70 percent of what you started with so another way to think about it is we could take pita score of 1060 and multiply it by 70 percent and multiplying it by 70 percent is the same thing as multiplying it by zero point seven zero which is the same thing as multiplying it by 70 hundredths is the same thing as seven tenths so let's just do this so if I have ten sixty and I multiply by zero point seven what do I get seven times zero is zero 7 times 6 is 42 seven times 0 0 plus 4 is 4 seven times one is seven and I have one digit to the right of the decimal so there you have it it is 740 to 742 that is how many points Val scored let's do a another example so we're told there are 20% more goblins than wizards in a magic club there are 220 goblins and wizards all together 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 want to 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 GE 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 hundredths or you could even write that as 2 tenths plus 2 tenths times the number of wizards or another way of thinking about it goblins are equal to if I have 1 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 200 220 that in that same color is equal to 220 now this is pretty straightforward to solve what is W plus 1.2 W well that is going to be 2 point 2 w 2 point 2w cabooses 1 W plus 2 plus 1 point 2w is to point to W is equal to 220 and so just divide both sides let me scroll down a little bit divide both sides by two point two two point two and what 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 a hundred and 20 goblins and that makes sense 120 is 20% more than 100 and if you add the hundred wizards to the 120 goblins you get 220 goblins and wizards all together let's do another example here we're told Kody 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 Kody 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 the 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 hundredths 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 a tenth 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 1 X plus 1/10 of an X is going to be 1 and 1/10 X 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 want to do is move this 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 1 times 11 is 11 subtract we get a 5 and we bring down a 5 11 goes into 55 exactly 5 times 5 times 11 is 55 subtract we have no remainder but then we bring down this 0 and we do it one more time 11 goes into 0 zero times remember the decimal place is right over here 0 times 11 is 0 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 for example if I divide it 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 percent of that 10 percent of 150 is 15 centimeters so you add 10 percent of that you indeed do get to 165 centimeters for the first day of school this year