Percentages | Worked example

- [Instructor] We are asked if 35% of a certain number is 14, what is 170% of that number? Alright, pause this video and see if you can work through this. Okay, now let's do it together. And, it's important to realize that there's many different ways to approach this type of question. One way you could do it is you could try to parse out what the words are saying and try to write an algebraic equation that represents that and then try to solve that. So let's try to do that. So they're saying if 35% of a number, and 35%, remember, percent literally means per hundred. So another way to think of 35% is it's 35 over 100, or, you could view it as, 35 hundredths. And so when they say 35 hundredths or 35% of a certain number. So that's what they want us to figure out. So let's just call this certain number, let's just call that n. So they're talking about 35% of a certain number. So when they're saying of a number, one way to think about it is that you're multiplying 35% times that number. So we could write it like this. We could say 35% which is the same thing as 35 hundredths of a number, so that means 0.35 times that number, is, so you should view is as equal to, is equal to 14, what is 170% of that number? So this way what we could do is we could try to figure out what that number is first and then figure out what 170% of it is. So, how do we figure out this number? Well, we just want to solve for n here. So let's divide both sides by the coefficient on end, by the 0.35. And so we're going to get n is equal to 14 over 0.35. Now, many of you might be able to do this on paper or even potentially in your head, but on the PRAXIS you are allowed to use a calculator. And so we could get a calculator out just so that we remind ourselves that we can do that. So we have 14 divided by 0.35 is equal to 40. So that certain number is equal to 40. We figured that out. But we're not done yet. They're not asking us what that certain number is. They're asking us what is 170% of that number? So just to remind ourselves, 170% that is the same thing as 170 over 100. 170 per 100. Percent. Which is the same thing as 1.70. And then 1.70 of that number. Remember, of that number means times that number. So it's really 1.70 times 40. That is what they're asking for. And so, let's get our calculator back. We have our 40 here, so let's just multiply it times 1.7, and we get 68. 68. And we are done. Now, I mentioned there's many ways that you could approach something like this. You could actually try to set up some type of a proportion. You could say that, if 35% is to 14 as 170% is to the thing you are trying to figure out. But this might be a little bit more complicated for some of you. And this gets a little bit more algebraically complicated. And essentially this is trying to solve everything in one step. So, I would suggest going this way. Just really parse out what they're trying to say and write that English in Math. Solve for the certain number, which we are just calling n in this case, and then figure out what 170% of that number is which is just multiplying that number times 1.7 which is 68.