Orange squash is made by mixing water and orange cordial in the ratio nine to two. Wendy has 800 millilitres of water and 170 millilitres of orange cordial. What is the maximum amount of orange squash that Wendy can make?
This word “maximum” in the question suggests that Wendy will probably have either some water or some orange cordial left over. She won’t be able to use all of them because the amounts of water and orange cordial that she has are probably not in the correct ratio of nine to two. But we don’t know starting off whether she’ll be limited by the amount of water or the amount of orange cordial that she has.
We start off by noting that, in order to make orange squash, Wendy needs to use water and orange cordial in the ratio nine to two. We can simplify this ratio by dividing both sides by two, giving a ratio of nine over two to one. This tells us that, for every one millilitre of orange cordial that Wendy uses, she needs to use nine over two or 4.5 millilitres of water. Let’s see if Wendy has enough water to use all 170 millilitres of her orange cordial.
To scale up on the right of this ratio from one to 170, we need to multiply by 170. So we also need to do the same on the left-hand side. We have the ratio 170 multiplied by nine over two to 170. And using a calculator, we can simplify the calculation on the left to 765. So to use all 170 millilitres of her orange cordial, Wendy will need to add 765 millilitres of water. This is fine because Wendy has enough. She has 800 millilitres of water. So she can use 765 millilitres of it and she’ll still have some left over.
To find the maximum amount of orange squash that Wendy can make then, we need to add the 765 millilitres of water and the 170 millilitres of orange cordial together. This gives 935. So we found that the maximum amount of orange squash that Wendy can make is 935 millilitres. She does have some water left over. But as she’s used all of her orange cordial, she can’t make any more orange squash.