Question

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?

Answer 1

Deepak will use approximately 5.42 cups of raisins for his trail mix when combining them with 14 1/4 cups of other ingredients, based on the ratio of 2 cups of raisins to 7 cups of trail mix per batch.

Step-by-step explanation:

To solve how many cups of raisins Deepak will use, we first need to understand the ratio of raisins to the total amount of trail mix per batch. In this case, it's given that 2 cups of raisins are used for every 7 cups of trail mix.

Next, we are informed that Deepak uses 14 1/4 cups of other ingredients. Since the total batch is made up of both raisins and other ingredients, we add the 2 cups of raisins to the 'other ingredients' to find the total amount of trail mix per batch, which is 7 cups. Now we need to find how many batches are made with 14 1/4 cups of other ingredients. To find this, we divide 14 1/4 cups by 5 1/4 cups (the amount of other ingredients per batch, which is 7 cups minus 2 cups of raisins).

14 1/4 cups ÷ 5 1/4 cups = 2.71 batches (approximately).

Now that we know how many batches Deepak can make, we multiply this by the amount of raisins per batch to find the total cups of raisins needed.

2.71 batches x 2 cups of raisins per batch = 5.42 cups of raisins (approximately).

So, Deepak will use approximately 5.42 cups of raisins for the mix with the given quantities of other ingredients.

Answer 2

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