Percent word problems
Solving Percent Problems 3 Solving Percent Problems 3
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- 78 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 multiply x 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 same thing as 15 per 100.
- That's literally per cent.
- Cent means 100, which is the same thing as 0.15.
- This is literally 15 hundredths.
- So we could rewrite this as 0.15 times some unknown
- number, times x, 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
- divided 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.
- These cancel out, and I get x is equal 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 number.
- 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 whole number.
- And we're dividing it by 0.15.
- Now, 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 to the right.
- Let me put that in a new color.
- Right there, that's where our decimals goes.
- Let me erase the other one, so we don't get confused.
- If we did that for the 15, we also have to do
- that for the 78.
- So if you move the decimal two to the right, one, two, it
- becomes 7,800.
- So one way to think about it, 78 divided by 0.15 is the same
- thing as 7,800 divided by 15, multiplying the numerator and
- the denominator by 100.
- So let's figure 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 just say, OK, 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.
- 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 zero.
- 15 goes into 30 exactly two 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.
- 0 times 15 is 0.
- Subtract.
- No remainder.
- So 78 divided by 0.15 is exactly 520.
- So x is equal to 520.
- So 78 is 15% 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.
- 520, or 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.
- And then when you take some percentage of the base, you
- get what's sometimes referred 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 the terminology you use
- in your class.
- But the important thing is to be able
- just answer this question.
- And it makes sense, because 15% is a very small
- percentage.
- If 78 is a small percentage of some number, that means that
- number has to be pretty big, and our answer gels with that.
- This looks about right.
- 78 is exactly 15% of 520.
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