Final answer:
To calculate the amount of oatmeal needed in a recipe that requires 18 cups of total ingredients and has a ratio of 4:2 (oatmeal to raisins), simplify the ratio to 2:1, divide the total cups by the sum of the parts, and multiply by the oatmeal parts to find that 12 cups of oatmeal are needed.
Step-by-step explanation:
The ratio of oatmeal to raisins in the cookies is given as 4 to 2, which can be simplified to 2 to 1 because we can divide both sides by 2. To determine how many cups of oatmeal are needed in a large batch that requires 18 cups of ingredients, we need to find out how many parts of the total are oatmeal.
First, we combine the parts of oatmeal and raisins: 2 parts oatmeal + 1 part raisins = 3 parts total. Next, we divide the total number of cups (18) by the total number of parts (3) to find out how much one part is: 18 cups ÷ 3 parts = 6 cups per part.
Since oatmeal makes up 2 parts, we multiply the cups per part by the number of oatmeal parts: 6 cups per part × 2 parts = 12 cups of oatmeal needed for the recipe.