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------------------------------------------------ A recipe calls for 5 cups of sugar for every 2 tablespoons of vanilla. How many cups of sugar are needed for each teaspoon of vanilla?

To find out how many cups of sugar are needed for each teaspoon of vanilla, the given ratio of 5 cups of sugar to 2 tablespoons of vanilla is converted to teaspoons. Since 1 tablespoon equals 3 teaspoons, 2 tablespoons are 6 teaspoons. Thus, for each teaspoon of vanilla, 5/6 cups of sugar are required.

Explanation:

The student is asking how many cups of sugar are needed for each teaspoon of vanilla according to a recipe. The original recipe calls for 5 cups of sugar for every 2 tablespoons of vanilla. We need to convert tablespoons to teaspoons, knowing that 1 tablespoon equals 3 teaspoons. So, 2 tablespoons of vanilla equal 6 teaspoons.

Now, we can set up a ratio to find out how much sugar is required for 1 teaspoon of vanilla:

5 cups of sugar / 6 teaspoons of vanilla = x cups of sugar / 1 teaspoon of vanilla
5/6 cups of sugar = x cups of sugar
x = 5/6 cups of sugar per teaspoon of vanilla

Therefore, you would need 5/6 cups of sugar for each teaspoon of vanilla.