Ratios in Cake Making

Some of the children enjoy making mudcakes following a recipe. They discovered that the consistency of these cakes can be changed by adding more of one type of ingredient. In the image below, you can see the children making their mudcakes.

When following a recipe, the children are following a ratio of the ingredients to each other. Making half of a batch of a recipe is also a ratio of the full recipe. Imagine a standard recipe requires 150 grams of flour and 120 grams of butter to make 6 cupcakes. If you only wanted to make 3 cupcakes, you would need to halve the amount of each ingredient. This would leave 75 grams of flour and 60 grams of butter. The ratio of flour to butter remains the same no matter how many cupcakes you make (there are \(1.25\) grams of flour for every gram of butter). We can visualise the ratios used in the table below. If the children changed the ratio of water in their mud cake recipe, they realised the consistency of the mud cake would change.

	Flour	Butter
6 cakes	150g	120g
3 cakes	75g	60g