A fruit drink recipe takes a mixture of 1/5 cup of carrot juice to 3/5 cup of apple juice.

For A, how many cups of carrot juice are used for 1 cup of apple juice?

For B, how many cups of fruit drink is made with 1 cup of apple juice?

Let's break the problem down step by step.

### For A: 
We are asked how many cups of carrot juice are used for 1 cup of apple juice.

- The ratio of carrot juice to apple juice in the recipe is \( \frac{1}{5} \) cup of carrot juice to \( \frac{3}{5} \) cup of apple juice.
  
To find how much carrot juice is used for 1 cup of apple juice, we set up a proportion:

\[
\frac{1}{5} \text{ cup of carrot juice} : \frac{3}{5} \text{ cup of apple juice} = x \text{ cups of carrot juice} : 1 \text{ cup of apple juice}
\]

Solving for \( x \):
\[
x = \frac{1}{5} \div \frac{3}{5} = \frac{1}{5} \times \frac{5}{3} = \frac{1}{3}
\]

So, for every 1 cup of apple juice, \( \frac{1}{3} \) cup of carrot juice is used.

### For B:
We are asked how many cups of fruit drink are made with 1 cup of apple juice.

From A, we know that 1 cup of apple juice requires \( \frac{1}{3} \) cup of carrot juice. Therefore, the total amount of fruit drink is:

\[
1 \text{ cup of apple juice} + \frac{1}{3} \text{ cup of carrot juice} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \text{ cups of fruit drink}.
\]

Thus, with 1 cup of apple juice, \( \frac{4}{3} \) cups of fruit drink are made.

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Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. What is the total volume of fruit drink made with 2 cups of apple juice?
2. How would the ratio change if 2/5 cup of carrot juice were used instead?
3. How many cups of carrot juice are needed for 5 cups of apple juice?
4. What is the percentage of apple juice in the fruit drink?
5. How can we scale the recipe to make 10 cups of fruit drink?

**Tip**: When working with ratios and proportions, setting up a clear proportion can simplify the process of finding unknown quantities!

A fruit drink recipe takes a mixture of 1/5 cup of carrot juice to 3/5 cup of apple juice. For A, how many cups of carrot juice are used for 1 cup of apple juice? For B, how many cups of fruit drink are made with 1 cup of apple juice?

Learn how to determine the amount of carrot juice needed for 1 cup of apple juice in a fruit drink recipe. This problem covers ratios and proportions and is ideal for students in Grades 6-8. Explore a step-by-step solution using fractions and proportionality concepts.

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