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Percent word problem: 78 is 15% of what number?

CCSS.Math:

Video transcript

seventy-eight is 15% of what number so there's some unknown number out there and if we take 15% of that number we will get 78 so let's just call that unknown number X and we know that if we take 15% of X so if we take 15% of X so multiply X by 15% we will get we will get 78 and now we just literally have to solve for x now 15% mathematically you can deal directly with percentages but it's much easier if it's written as a decimal and we know that 15% is the same thing as 15 per 100 that's literally percent cent means 100 which is the same thing as 0.15 this is literally 1500s 15 hundredths so we could rewrite this as 0.15 times some unknown number times X times X is equal to is equal to 78 and now we can divide both sides of this equation by 0.15 to solve for X so you divide the left side by 0.15 and I'm literally picking 0.15 to divide both sides because that's what I have out here in front of the X so if I'm multiplying something by 0.15 and then I divide it by 0.15 I'll just be left with an X here that's the whole motivation if I do it to the left-hand side I have to do it to the right-hand side 0.15 these cancel out and I get X X is equal to 78 divided by 0.15 now we have to figure that out what that is if we had a calculator pretty straightforward but let's actually work it out so we have 78 divided by and we're going to going to be at some decimal number so it's going to be some decimal number it's going to be larger than 78 but let's figure out what it ends up being so let's store some zeros out there it's not going to be a whole number and we're dividing it by 0.15 0.15 now so to simplify things let's multiply both this numerator and this denominator by 100 and that's so that 0.15 becomes 15 so 0.15 times 100 is 15 we're just moving the decimal two to the right let me put that in a new color right there that's where our decimal goes and let me erase the other one so we don't get confused and if we did that for the 15 we also have to do that for the 78 so if we move the decimal two to the right one two it becomes seventy eight hundred seventy eight hundred or seven thousand eight hundred so one way to think about it 78 divided by 0.15 is the same thing as seven thousand eight hundred divided by 15 multiplying the numerator and the denominator by 100 so let's figure out what this is 15 does not go into seven fifteen so you could go zero times and you could do all of that or you could just say okay that's not going to give us anything so then how many times does 15 go into 78 so let's think about it 15 goes into 60 four times it'll go it's 15 times 5 is 75 that looks about right so we say 5 times 5 times 15 5 times 5 is 25 put the 2 up there 5 times 1 is 5 plus 2 is 7 75 you subtract 78-75 is 3 bring down a 0 bring down a 0 15 goes into 30 exactly 2 times 2 times 15 is 30 subtract no remainder bring down the next zero we're still to the left of the decimal point the decimal point is right over here if we write it up here which we should it's right over there so we have one more place to go so we bring down this next zero 15 goes into 0 zero times zero times 15 is zero subtract no remainder so 78 divided by 0.15 is exactly 520 so X is equal to 520 so 78 is 15 percent of 520 and if we want to use some of the terminology that you might see in a math class the 15% is obviously the percent this is the percent that is the percent 520 or the what number before we figured out it was 520 that's what we're taking the percentage of this is sometimes referred to as the base that is the base and then when you take fit some percentage of the base you get what sometimes refer to as the amount so in this circumstance 78 would be the amount you could view it as the amount is the percentage of the base but we were able to figure that out it's nice to know those if that's used that's the terminology used in your class but the important thing is to be able to just answer this question and it makes sense because 15% is a very small fraction so 78 is a is or it's a small percentage if 78 is a small percentage of some number that means that number has to be pretty big has to be pretty big and our answer it gels with that this looks about right 78 is about 15% of or it is exactly 15% of 520