- Analyze the ratios by dividing the amount of blue paint by the amount of white paint for each mixture: \(R_A = \frac{5}{12}\), \(R_B = \frac{6}{6} = 1\), and \(R_D = \frac{5}{6}\).
- Compare the numerical values: \(1 > \frac{5}{6} > \frac{5}{12}\).
- Identify that Mixture B has the highest value.
- The correct option is \(\boxed{b}\).
Explanation
- Understanding the Problem and Data Analysis
We are tasked with identifying which paint mixture has the highest ratio of blue paint to white paint among the given options: Mixture A, Mixture B, and Mixture D. The ratio for each mixture is defined as the amount of blue paint divided by the amount of white paint. Let the ratio for each mixture be denoted by \(R\). The table provides the amounts of blue and white paint for all mixtures, allowing us to calculate these ratios directly.
- Calculating the Ratios for Each Mixture
We calculate the ratios for the relevant mixtures provided in the options:
- For Mixture A: There are 5 cups of blue paint and 12 cups of white paint. Thus, the ratio is \(R_A = \frac{5}{12} \approx 0.417\).
- For Mixture B: There are 6 cups of blue paint and 6 cups of white paint. Thus, the ratio is \(R_B = \frac{6}{6} = 1\).
- For Mixture D: There are 5 cups of blue paint and 6 cups of white paint. Thus, the ratio is \(R_D = \frac{5}{6} \approx 0.833\).
- Comparison and Conclusion
Comparing the ratios calculated:
- \(R_A = \frac{5}{12}\)
- \(R_B = 1\)
- \(R_D = \frac{5}{6}\)
Since \(1 > \frac{5}{6} > \frac{5}{12}\), it is clear that Mixture B has the highest ratio of blue paint to white paint. Comparing the given options, we find that the highest ratio belongs to Mixture B.
Examples
In interior design, mixing paint colors to achieve a specific shade often requires precise ratios. For example, if you want a vibrant blue tint for a bedroom, you need to know which mixture of base paint and white paint will give you the most intense blue color. Calculating these ratios allows you to make informed decisions about your supplies, ensuring you achieve the exact color you envision without wasting paint. Understanding these proportions is a foundational skill in both DIY projects and professional painting.