Calculating the Amount of Sparkling Water

Oct 13, 2025 by windailys.com 78 views

**A Recipe for Sparkling Grape Juice: Calculating the Perfect Mix**

Understanding the Recipe

A recipe for sparkling grape juice calls for a specific amount of sparkling water and grape juice. The recipe requires $1 \frac{1}{2}$ quarts of sparkling water and $\frac{3}{4}$ quart of grape juice. In this article, we will explore how to calculate the amount of sparkling water needed to mix with a given amount of grape juice.

Calculating the Amount of Sparkling Water

a. How much sparkling water would you need to mix with 9 quarts of grape juice?

To calculate the amount of sparkling water needed, we can use a simple ratio. The recipe calls for $1 \frac{1}{2}$ quarts of sparkling water for every $\frac{3}{4}$ quart of grape juice. We can set up a proportion to find the amount of sparkling water needed for 9 quarts of grape juice.

Let's start by converting the mixed number $1 \frac{1}{2}$ to an improper fraction. We can do this by multiplying the whole number part (1) by the denominator (2) and then adding the numerator (1).

$1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}$

Now we can set up the proportion:

$\frac{\frac{3}{2}}{\frac{3}{4}} = \frac{x}{9}$

To solve for x, we can cross-multiply:

$\frac{3}{2} \times 9 = \frac{3}{4} \times x$

$13.5 = \frac{3}{4} \times x$

Now we can multiply both sides by $\frac{4}{3}$ to solve for x:

$x = 13.5 \times \frac{4}{3}$

$x = 18$

So, we would need 18 quarts of sparkling water to mix with 9 quarts of grape juice.

b. How much grape juice would you need to mix with 12 quarts of sparkling water?

To calculate the amount of grape juice needed, we can use the same ratio as before. We can set up a proportion to find the amount of grape juice needed for 12 quarts of sparkling water.

Let's start by setting up the proportion:

$\frac{\frac{3}{4}}{\frac{3}{2}} = \frac{y}{12}$

To solve for y, we can cross-multiply:

$\frac{3}{4} \times 12 = \frac{3}{2} \times y$

$9 = \frac{3}{2} \times y$

Now we can multiply both sides by $\frac{2}{3}$ to solve for y:

$y = 9 \times \frac{2}{3}$

$y = 6$

So, we would need 6 quarts of grape juice to mix with 12 quarts of sparkling water.

Conclusion

In this article, we explored how to calculate the amount of sparkling water and grape juice needed for a recipe. We used a simple ratio to set up proportions and solve for the unknown values. By following these steps, you can easily calculate the perfect mix for your sparkling grape juice recipe.

Frequently Asked Questions

Q: What is the ratio of sparkling water to grape juice in the recipe?

A: The ratio of sparkling water to grape juice is $\frac{3}{2}$ to $\frac{3}{4}$ , or 1.5 to 0.75.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and then add the numerator.

Q: How do I set up a proportion to solve for an unknown value?

A: To set up a proportion, write the ratio of the known values as a fraction and then set it equal to the ratio of the unknown values.

Q: How do I solve for an unknown value in a proportion?

A: To solve for an unknown value in a proportion, cross-multiply and then solve for the unknown value.

Q: What is the amount of sparkling water needed to mix with 9 quarts of grape juice?

A: The amount of sparkling water needed to mix with 9 quarts of grape juice is 18 quarts.

Q: What is the amount of grape juice needed to mix with 12 quarts of sparkling water?

A: The amount of grape juice needed to mix with 12 quarts of sparkling water is 6 quarts.