Final answer:
To find out how many cups of sugar are needed for 12 cups of flour, a proportion based on the original recipe is used. By cross-multiplying the proportion (4 cups of flour per 2 cups of sugar), it is determined that 6 cups of sugar are needed for 12 cups of flour.
Step-by-step explanation:
To determine how many cups of sugar are needed if you have 12 cups of flour, you should use a simple proportion based on the original recipe. The recipe needs 4 cups of flour and 2 cups of sugar to make one cake. If you have 12 cups of flour, you can set up a proportion where 4 cups of flour corresponds to 2 cups of sugar.
4 cups of flour / 2 cups of sugar = 12 cups of flour / x cups of sugar
Cross-multiplying to solve for x, you get:
So, you would need 6 cups of sugar for 12 cups of flour.