Deepak is making a large amount of trail mix. He uses 2 cups of raisins in a single batch, which makes 7 cups. If he uses 14 1/4 cups of other ingredients, how many cups of raisins will he use?

5 7/10 cups of raisins

Step-by-step explanation:

We assume that the total volume made equals the sum of the volumes of the individual ingredients.

He uses 2 cups of raisins and makes 7 cups of trail mix. That mean the amount of other ingredients is 7 cups - 2 cups = 5 cups.

He uses 2 cups raisins and 5 cups of other ingredients.

When he uses 14 1/4 cups of other ingredients instead of only 5 cups, he is multiplying the recipe to make it bigger.

Now we calculate how many times he is multiplying the recipe by.

14 1/4 divided by 5 = (14 1/4) / 5 = (57/4) / 5 = 57/4 * 1/5 = 57/20

He is making 57/20 times the original recipe.

Since he is making 57/20 times the recipe, he needs 57/20 times 2 cups of raisins.

Now we calculate what 57/20 times 2 cups of raisins is.

57/20 * 2 = (57 * 2) / 10 = (57 * 2) / (10 * 2) = 57/10 = 5 7/10

Answer: 5 7/10 cups of raisins