There are between 10 and 20 litres of drink for a party. The drink is made by mixing one-litre cartons of orange juice and one-litre cartons of pineapple juice in the ratio three to five. How much drink is there in total?
We’re told in the question that we always mix whole one-litre cartons of orange juice with whole one-litre cartons of pineapple juice. And the ratio of the two flavours of juice is always three to five. Suppose then that we just made the smallest amount of this drink possible. That would be three litres of orange juice and five litres of pineapple juice, which would give us a total of eight litres of drink.
However, the question tells us that there are between 10 and 20 litres of drink made for this party. And eight litres is less than 10. We therefore need to scale this ratio up so that we have a total amount of drink which is between 10 and 20 litres. Let’s try scaling up by multiplying both sides of this ratio by a factor of two. Remember, whatever we do to one side of the ratio, we must also do to the other so that the quantities remain in the same proportions.
Three multiplied by two is six. And five multiplied by two is 10. So our scaled-up ratio is six to 10. This means we’d use six litres of orange juice and 10 litres of pineapple juice. And the sum of these is 16. 16 litres is between 10 and 20 litres. So this is a possibility for the total amount of drink made. But let’s just check that there aren’t any others.
If, instead, we’d scaled up by the next smallest integer, so that’s multiplying both sides of the ratio by three this time, we’d have the ratio nine to 15. However, the sum of nine and 15 would be 24, meaning we’d have 24 litres of the drink. And as this is greater than 20, this can’t be the correct amount of drink. So we can conclude that there are 16 litres of drink made for this party.
Once we had noted that the total number of parts in our ratio was eight, we could also have got to this answer by listing out the beginning of our eight times table. 16 is the only number in the eight times table which is between 10 and 20. So again this confirms that the total amount of drink made for the party is 16 litres.