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To determine which mixture is a lighter shade of purple, we need to analyze the ratios of purple paint to white paint in each mixture. The more white paint relative to purple, the lighter the shade of purple will be.

- **Mixture A**: 5 cups of purple paint and 2 cups of white paint.
  - The ratio of purple to white = \( \frac{5}{2} \).

- **Mixture B**: 15 cups of purple paint and 8 cups of white paint.
  - The ratio of purple to white = \( \frac{15}{8} \).

Now, let's compare the ratios:

- \( \frac{5}{2} = 2.5 \)
- \( \frac{15}{8} = 1.875 \)

A smaller ratio means there is more white paint in comparison to purple, which leads to a lighter shade of purple.

Since \( 1.875 \) (Mixture B) is less than \( 2.5 \) (Mixture A), **Mixture B** has a higher proportion of white paint and will be a lighter shade of purple.

### Answer: Mixture B is the lighter shade of purple because it has a lower ratio of purple to white paint.

Would you like more details or have any other questions? Here are some related questions for further practice:

1. How would the color change if we added more white paint to Mixture A?
2. What would the ratio of purple to white be if we mixed both Mixture A and B together?
3. How do the proportions affect the darkness of a color in general?
4. If you wanted to make Mixture B darker, how much purple paint would you need to add?
5. Can we achieve a specific shade by mixing these two mixtures? How would you calculate that?

**Tip**: To compare ratios easily, divide both the numerator and denominator in each mixture to get their decimal form. This helps in determining which is larger or smaller!

Which mixture is a lighter shade of purple? Explain your reasoning. Mixture A: 5 cups of purple paint and 2 cups of white paint. Mixture B: 15 cups of purple paint and 8 cups of white paint.

Learn how to determine which mixture of purple and white paint results in a lighter shade by comparing the ratios. Mixture A has 5 cups of purple and 2 cups of white paint, while Mixture B has 15 cups of purple and 8 cups of white paint. This lesson covers ratios and proportions, suitable for students in Grades 5-7.

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