Question

A recipe for sparkling grape juice calls for 112 quarts of sparkling water and 34 quart of grape juice. How much grape juice would you need to mix with 154 quarts of sparkling water?

Answer 1

To mix with 154 quarts of sparkling water, you would need approximately 50 quarts of grape juice according to the ratio provided in the original recipe.

Step-by-step explanation:

To determine the amount of grape juice needed when you have 154 quarts of water, we need to establish the ratio of grape juice to sparkling water in the original recipe. Here, for 112 quarts of water, 34 quarts of grape juice are used, which simplifies to approximately 3.29 quarts of water for every 1 quart of grape juice.

Using this ratio, we can set up a proportion to find out how much grape juice is needed for 154 quarts of water:

112 quarts water / 34 quarts grape juice = 154 quarts water / x quarts grape juice

Now, cross-multiply to solve for x:

112x = 34 × 154

x = (34 × 154) / 112

x ≈ 50 quarts of grape juice

So, you would need approximately 50 quarts of grape juice to mix with 154 quarts of sparkling water, according to the original recipe's ratio.