Percent word problem: 78 is 15% of what number? (video) | Khan Academy

Video transcript

78 is 15 % of what number ? So there ‘s some obscure number out there, and if we take 15 % of that number, we will get 78. So let ‘s good call that unknown number x. And we know that if we take 15 % of x, so multiply adam by 15 %, 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 lapp thing as 15 per 100. That ‘s literally per cent. penny means 100, which is the lapp thing as 0.15. This is literally 15 hundredths. So we could rewrite this as 0.15 times some stranger number, times x, is equal to 78. And immediately we can divide both sides of this equality by 0.15 to solve for ten. So you divide the left field 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 divided by 0.15, I ‘ll merely be left with an adam here. That ‘s the solid motivation. If I do it to the left side, I have to do it to the right-hand english. These cancel out, and I get x is peer to 78 divided by 0.15. now, we have to figure 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 it ‘s going to be some decimal total. It ‘s going to be larger than 78. But let ‘s figure out what it ends up being, so let ‘s throw some zeroes out there. It ‘s not going to be a unharmed numeral. And we ‘re dividing it by 0.15. immediately, to simplify things, let’s multiply both this numerator and this denominator by 100, and that ‘s thus that 0.15 becomes 15. thus 0.15 times 100 is 15. We ‘re just moving the decimal to the justly. Let me put that in a newfangled color. Right there, that ‘s where our decimals goes. Let me erase the other one, so we do n’t get confused. If we did that for the 15, we besides have to do that for the 78. so if you move the decimal fraction two to the right, one, two, it becomes 7,800. then one way to think about it, 78 divided by 0.15 is the lapp thing as 7,800 divided by 15, multiplying the numerator and the denominator by 100. So lease ‘s visualize out what this is. 15 does not go into 7, So you could do it zero times and you can do all that, or you can precisely say, OK, that ‘s not going to give us anything. thus then how many times does 15 go into 78 ? So lashkar-e-taiba ‘s think about it. 15 goes into 60 four times. 15 times 5 is 75. That looks about right, so we say five 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 minus 75 five is 3. Bring down a nothing. 15 goes into 30 precisely two times. 2 times 15 is 30. Subtract. No end. Bring down the next zero. We ‘re silent to the leave of the decimal point. The decimal sharpen is right over here. If we write it up here, which we should, it ‘s correct over there, so we have one more identify to go. then we bring down this next zero. 15 goes into 0 zero times. 0 times 15 is 0. Subtract. No end. so 78 divided by 0.15 is precisely 520. so ten is adequate to 520. so 78 is 15 % of 520. And if we want to use some of the terminology that you might see in a mathematics class, the 15 % is obviously the percentage. 520, or what issue before we figured out it was 520, that ‘s what we ‘re taking the share of. This is sometimes referred to as the basis. And then when you take some share of the root, you get what ‘s sometimes referred to as the sum. so in this circumstance, 78 would be the amount. You could view it as the come is the percentage of the base, but we were able to figure that out. It ‘s nice to know those, if that ‘s the terminology you use in your class. But the authoritative matter is to be able just answer this motion. And it makes sense, because 15 % is a very small share. If 78 is a small percentage of some issue, that means that number has to be pretty boastfully, and our answer gels with that. This looks about correctly. 78 is precisely 15 % of 520.

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