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Let's break down the ratios of orange juice to pineapple juice in each recipe to determine which two will taste the same and which one will taste different.

1. **Recipe 1**: Mix 4 cups of orange juice with 6 cups of pineapple juice.
   - Ratio: \( \frac{4}{6} = \frac{2}{3} \)

2. **Recipe 2**: Mix 6 cups of orange juice with 9 cups of pineapple juice.
   - Ratio: \( \frac{6}{9} = \frac{2}{3} \)

3. **Recipe 3**: Mix 9 cups of orange juice with 12 cups of pineapple juice.
   - Ratio: \( \frac{9}{12} = \frac{3}{4} \)

Now, comparing the ratios:
- Recipe 1 and Recipe 2 have the same ratio, \( \frac{2}{3} \).
- Recipe 3 has a different ratio, \( \frac{3}{4} \).

Thus, **Recipes 1 and 2 will taste the same**, while **Recipe 3 will taste different**.

The correct answer is **A**: Recipes 1 and 2 will taste the same, and Recipe 3 will taste different.

Would you like further details or have any questions? Here are some related questions to deepen your understanding:

1. How can you compare ratios more efficiently?
2. What does it mean for two mixtures to have the same ratio?
3. How can simplifying ratios help in real-world applications like cooking?
4. What is the mathematical process of simplifying a fraction or ratio?
5. What are some examples of ratios in daily life besides cooking?

**Tip**: Always simplify ratios to their lowest terms for easy comparison.

Here are three different recipes for Orangey-Pineapple Juice. Two of these mixtures taste the same, and one tastes different.

Recipe 1: Mix 4 cups of orange juice with 6 cups of pineapple juice.
Recipe 2: Mix 6 cups of orange juice with 9 cups of pineapple juice.
Recipe 3: Mix 9 cups of orange juice with 12 cups of pineapple juice.

Which two recipes will taste the same, and which one will taste different?

Learn how to compare ratios using a real-world example of mixing orange juice and pineapple juice in different proportions. This problem helps students in Grades 5-7 understand how simplifying ratios can reveal which mixtures taste the same.

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