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The image presents a problem involving the mixing of cranberry juice and apple juice. Lin’s favorite blend is represented by the ratio of cranberry juice to apple juice, shown on the double number line: 9 fluid ounces of cranberry juice to 21 fluid ounces of apple juice.

### To find smaller or larger batches that maintain the same ratio:

1. **Determine the ratio**: 
   The ratio of cranberry juice to apple juice is:
   \[
   \frac{9}{21} = \frac{3}{7}
   \]
   So, Lin's favorite juice blend has a ratio of **3 parts cranberry juice to 7 parts apple juice**.

2. **Smaller Batches**:
   To find smaller batches, scale the ratio down:
   - One possible smaller batch would be multiplying the ratio by \(1\), so the next point is \( \frac{3 \times 1}{7 \times 1} = 3 \) fluid ounces cranberry juice and \(7\) fluid ounces apple juice.

3. **Larger Batches**:
   To find larger batches, scale the ratio up:
   - Multiplying the ratio by \(2\), for example, results in \( \frac{3 \times 2}{7 \times 2} = 6 \) fluid ounces cranberry juice and \(14\) fluid ounces apple juice.

Thus, the diagram can be filled with these points:
- Smaller batch: \(3 \) fluid ounces cranberry juice and \(7 \) fluid ounces apple juice.
- Larger batch: \(6 \) fluid ounces cranberry juice and \(14 \) fluid ounces apple juice.
   
Would you like further details or assistance on this problem?

### Related Questions:
1. What other ratios would maintain the same proportion?
2. How would you verify the consistency of the ratios in real-world mixing?
3. Can this ratio be used to determine amounts for much larger blends, such as 45 ounces of cranberry juice?
4. What is the simplest way to scale a recipe up or down while preserving the ratio?
5. How can ratios be applied in different contexts, such as cooking or chemistry?

**Tip**: When working with ratios, multiplying both parts of the ratio by the same number will maintain the relationship!

Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. Complete the diagram to show smaller and larger batches that would taste the same as Lin’s favorite blend.

Learn how to solve a problem involving the mixing of cranberry juice and apple juice using ratios and proportions. This solution walks through scaling the blend up and down while maintaining the same taste ratio. Suitable for students in Grades 5-7.

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