# Video: Pack 4 • Paper 3 • Question 5

Pack 4 • Paper 3 • Question 5

01:58

### Video Transcript

The ratio of the number of sport books to the number of animal books in a library is two to three. There are 39 animal books in the library. How many sport books are there in the library?

We’ll consider two different approaches that we could use to answer this question. The first is a scaling-up approach. We’re told that the number of animal books in the library is 39 and we want to work out the number of sport books. We want to scale the ratio of two to three up to an equivalent ratio of something — the number of sports books — to 39.

To do so, we just need to work out what we’ve multiplied three by to get to 39. Three is multiplied by 13 to give 39. To scale up the other side of the ratio, we, therefore, need to multiply two by 13, which gives 26. This is the number of sports books in the library. Now, I said we’re going to consider two approaches to this question. That’s our first approach.

And our second approach involves scaling back down to work out what one part of the ratio is equal to. We know that three parts of the ratio is equivalent to 39 books. So to find out what one part of the ratio is equal to, we can divide by three. One part is equal to 13 books. The number of sports books in the library is two parts of the ratio. So we now need to multiply it by two. 13 multiplied by two is 26. So we have the same answer as before.

Both of these approaches are equally valid. We can either scale the ratio up from a ratio of two to three to a ratio of 26 to 39 or we can scale back to working out what one part is equal to and then scaling up to finding two parts.