Determine if each situation represents a proportional relationships. Explain your reasoning - A specific shade of orange paint calls for 2 parts yellow and 3 parts red. Katie uses 3 cups of yellow paint and 4 cups of red paint to make orange paint

To determine if the situation represents a proportional relationship, we need to compare the ratios of yellow to red paint in both the original recipe and Katie's mixture.

### Original Recipe:
- **Yellow:** 2 parts
- **Red:** 3 parts
- **Ratio (Yellow to Red):** \( \frac{2}{3} \)

### Katie's Mixture:
- **Yellow:** 3 cups
- **Red:** 4 cups
- **Ratio (Yellow to Red):** \( \frac{3}{4} \)

### Comparison:
- The original ratio is \( \frac{2}{3} \).
- Katie's ratio is \( \frac{3}{4} \).

Since \( \frac{2}{3} \) is not equal to \( \frac{3}{4} \), the two ratios are different.

### Conclusion:
Katie's mixture does **not** represent a proportional relationship to the original recipe. A proportional relationship would require that the ratio of yellow to red paint in Katie's mixture be the same as the original recipe's ratio, which is not the case here.

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Would you like more details or have any questions?

Here are 5 related questions to consider:

1. What would the amount of red paint be if Katie used 3 cups of yellow paint and maintained a proportional relationship?
2. How many cups of yellow paint would Katie need to use 4 cups of red paint in a proportional relationship?
3. If Katie wanted to make a larger batch using the same ratio as the original recipe, how much of each color would she need for 10 parts red?
4. Can you calculate the missing quantity if the total amount of orange paint made by Katie was 7 cups?
5. What is the significance of maintaining proportional relationships in recipes or mixtures?

**Tip:** When working with ratios, always ensure to compare them in their simplest form to check for proportionality.

Explore whether a mixture of 3 cups of yellow paint and 4 cups of red paint forms a proportional relationship with a recipe requiring 2 parts yellow and 3 parts red paint. Compare ratios and learn how to determine proportionality in ratios. Suitable for Grades 6-8.

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