# Video: AQA GCSE Mathematics Higher Tier Pack 5 • Paper 1 • Question 26

25% of a number is 45. Work out the number.

02:07

### Video Transcript

25 percent of a number is 45. Work out the number.

Well, there’s a couple of methods you can use to solve this. So I’m gonna show you both of them. One) To check the other. So first of all, what we’re gonna do is let the number be 𝑥 because we’re told that 25 percent of a number is 45. So therefore, we know that 25 percent of 𝑥 is going to be 45. Well, 25 percent is equal to 0.25 if it’s written as a decimal or a quarter if it’s written as fraction. And this is one of the ones that we should know.

So therefore, we can say that a quarter 𝑥 is equal to 45. And that’s because if we have 25 percent of something, this is the same of a quarter of something. And if we say a quarter of, that’s like a quarter multiplied. So we’ve got a quarter multiplied by 𝑥 is equal to 45. So therefore, we can multiply each side of the equation by four cause if we want a whole 𝑥 and we’ve got a quarter 𝑥, we multiply it by four to get that whole 𝑥. So therefore, we get 𝑥 is equal to 180 and that’s because four multiplied by 45 is 180. We can work this out. Probably, the most simple way of doing that would be double 45 to give us 90 and then double 90 to give us 180. So therefore, we can say that the number is 180.

Now like I said, we’re gonna check this just with another method. Well, if we know that 25 percent is equal to 45, then if we double this, we get 50 percent. So 50 percent will be equal to 90 and that’s because if you double 45, you get 90. And then, if we’ve got 50 percent, we want to double this to get 100 percent. So therefore, we can say that 100 percent is gonna be equal to 180. And that’s because if we double 90, we get 180. So that’s the same answer as we got before.

So we can say that if 25 percent of a number is 45, the number must be 180.