RATIOS worked example

a)
The recipe tells us for every 500g of flour we need 125g of butter.
Therefore we can start by writing the ratio 500 : 125
We want to find this ratio in its simplest form
We do this by finding the greatest common divisor of 500 and 125, and dividing both sides by this number
gcd(500,125) = 125
Therefore the ratio is = 4:1

b)
The ratio of sugar to water is 125 : 100
gcd(125,100) = 25
We divide both sides of the ratio by 25 to get = 5 : 4

c)
Tom has 2 bags of flour, each with 150g of flour. So overall he has 300g of flour
This question has a hidden ratio. To find out how many cookies this amount of flour will produce, we want to look at the ratio of flour to cookies
The recipe says 500g of flour makes 30 cookies.
So the ratio is 500 : 30
We reduce this ratio to its simplest form by dividing by the greatest common divisor
gcd(500,30) = 10
Therefore we have = 50 : 3
So every 50g of flour makes 3 cookies.
Tom has 300g of flour. 50×6 = 300
We multiply both sides of the ratio by 6 to give us:
50×6 : 3×6 = 300 : 18
So for every 300g of flour, Tom will make 18 cookies

d)
Again this question is a hidden ratio question. We want to find the ratio of sugar to cookies.
125g of sugar makes 30 cookies, so we have the ratio 125 : 30
We need to reduce this to it’s simplest form to be more useful.
gcd(125,30) = 5
Divide the ratio through by 5 gives us = 25 : 6
This tells us that 25g of sugar produces 6 cookies.
We want to find out how much sugar is need for 12 cookies. 12 = 6 × 2
We multiply both sides of the ratio by 2 to get 50 : 12
Therefore, Tom needs 50g of sugar to bake 12 cookies

e)
From part (b) we know that the ratio of sugar to water is 5 : 4
Tom has 3kg of sugar and 2.5kg of water.
To fins out which will run out first, we can suppose Tom uses all the sugar and then find out how much water we would need. From this we can work out if we have too little water (water runs out first) or excess water (sugar runs out first)
3000 = 600 × 5 so we need to multiply both sides of the ratio by 600
4 × 600 = 2400 so we get a ratio of 3000 : 2400
This means that for 3kg of sugar, Tom needs 2.4kg of water.
Since Tom has 2.5 kg of water, Tom havs water left over
Tom will run out of sugar first