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A recipe is an example of direct proportion. When you double the amount of cakes you make you double the amount of each ingredient that you use. The ingredients are always in the same ratio.

Example 1: Here is a recipe to make 30 cookies

Cookie Recipe

150g Butter
180g Sugar
225g Flour
210g Chocolate Chips

Work out how much of each ingredient is needed to make 20 cookies

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There are lots of ways to answer questions like this.
We could work out the amount of each ingredient needed for each cookie by dividing by 30 (30 ÷ 30 = 1), and then multiply by 20 for 20 cookies.

Another option is to start by working out the amounts needed for 10 cookies.
We can work out the amounts needed for 10 cookies by dividing by 3
30 cookies ÷ 3 = 10 cookies

For 10 cookies we need:
Butter: 150g ÷ 3 = 50g
Sugar: 180g ÷ 3 = 60g
Flour: 225g ÷ 3 = 75g
Chocolate Chips: 210g ÷ 3 = 70g

We can now either take the amount for 10 cookies away from the amount for 30 cookies
or we can double the amount for 10 cookies to get 20 cookies

For 20 cookies we need:
Butter: 50g × 2 = 100g
Sugar: 60g × 2 = 120g
Flour: 75g × 2 = 150g
Chocolate Chips: 70g × 2 = 140g

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Example 2: Here is a recipe to make 12 flapjacks

Flapjack Recipe

240g Butter
80g Sugar
400g Oats
4 tbsp Honey

Work out how much of each ingredient is needed to make 30 flapjacks

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Again there are lots of ways to approach this question.

One way is to halve the recipe. This will give us the amounts for 6 flapjacks. We can then multiply by 5 (6 × 5 = 30).

For 6 flapjacks we need:
Butter: 240g ÷ 2 = 120g
Sugar: 80g ÷ 2 = 40g
Oats: 400g ÷ 2 = 200g
Honey: 4tbsp ÷ 2 = 2tbsp

We can now multiply the amounts needed for 6 flapjacks by 5 to get the amounts for 30 flapjacks.

For 30 flapjacks we need:
Butter: 120g × 5 = 600g
Sugar: 40g × 5 = 200g
Oats: 200g × 5 = 1000g
Honey: 2tbsp × 5 = 10tbsp

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