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78 is 15% of what number?

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So there's some unknown number out there, and if we take 15%

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of that number, we will get 78.

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So let's just call that unknown number x.

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And we know that if we take 15% of x, so multiply x by

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15%, we will get 78.

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And now we just literally have to solve for x.

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Now, 15% mathematically, you can deal directly with

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percentages, but it's much easier if it's

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written as a decimal.

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And we know that 15% is the same thing as 15 per 100.

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That's literally per cent.

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Cent means 100, which is the same thing as 0.15.

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This is literally 15 hundredths.

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So we could rewrite this as 0.15 times some unknown

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number, times x, is equal to 78.

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And now we can divide both sides of this equation by 0.15

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to solve for x.

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So you divide the left side by 0.15, and I'm literally

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picking 0.15 to divide both sides because that's what I

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have out here in front of the x.

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So if I'm multiplying something by 0.15 and then I

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divided by 0.15, I'll just be left with an x here.

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That's the whole motivation.

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If I do it to the left-hand side, I have to do it to the

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right-hand side.

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These cancel out, and I get x is equal to

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78 divided by 0.15.

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Now, we have to figure out what that is.

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If we had a calculator, pretty straightforward, but let's

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actually work it out.

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So we have 78 divided by, and it's going to be

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some decimal number.

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It's going to be larger than 78.

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But let's figure out what it ends up being, so let's throw

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some zeroes out there.

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It's not going to be a whole number.

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And we're dividing it by 0.15.

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Now, to simplify things, let's multiply both this numerator

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and this denominator by 100, and that's so that 0.15

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becomes 15.

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So 0.15 times 100 is 15.

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We're just moving the decimal to the right.

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Let me put that in a new color.

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Right there, that's where our decimals goes.

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Let me erase the other one, so we don't get confused.

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If we did that for the 15, we also have to do

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that for the 78.

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So if you move the decimal two to the right, one, two, it

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becomes 7,800.

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So one way to think about it, 78 divided by 0.15 is the same

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thing as 7,800 divided by 15, multiplying the numerator and

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the denominator by 100.

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So let's figure out what this is.

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15 does not go into 7, So you could do it zero times and you

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can do all that, or you can just say, OK, that's not going

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to give us anything.

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So then how many times does 15 go into 78?

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So let's think about it.

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15 goes into 60 four times.

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15 times 5 is 75.

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That looks about right, so we say five times.

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5 times 15.

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5 times 5 is 25.

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Put the 2 up there.

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5 times 1 is 5, plus 2 is 7.

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75, you subtract.

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78 minus 75 five is 3.

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Bring down a zero.

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15 goes into 30 exactly two times.

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2 times 15 is 30.

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Subtract.

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No remainder.

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Bring down the next zero.

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We're still to the left of the decimal point.

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The decimal point is right over here.

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If we write it up here, which we should, it's right over

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there, so we have one more place to go.

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So we bring down this next zero.

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15 goes into 0 zero times.

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0 times 15 is 0.

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Subtract.

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No remainder.

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So 78 divided by 0.15 is exactly 520.

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So x is equal to 520.

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So 78 is 15% of 520.

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And if we want to use some of the terminology that you might

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see in a math class, the 15% is obviously the percent.

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520, or what number before we figured out it was 520, that's

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what we're taking the percentage of.

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This is sometimes referred to as the base.

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And then when you take some percentage of the base, you

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get what's sometimes referred to as the amount.

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So in this circumstance, 78 would be the amount.

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You could view it as the amount is the percentage of

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the base, but we were able to figure that out.

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It's nice to know those, if that's the terminology you use

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in your class.

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But the important thing is to be able

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just answer this question.

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And it makes sense, because 15% is a very small

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percentage.

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If 78 is a small percentage of some number, that means that

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number has to be pretty big, and our answer gels with that.

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This looks about right.

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78 is exactly 15% of 520.

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