In art class students are mixing black and white paint to make gray paint. Nathaniel mixes 2 cups of black paint and 5 cups of white paint. Tanisha mixes 1 cup of black paint and 2 cups of white paint. Use Nathaniel and Tanisha’s percent of black paint to determine whose gray paint will be darker.

Answer 1

To determine whose gray paint will be darker, we need to calculate the percentage of black paint in each person's mixture.

Nathaniel's mixture:

• Black paint: 2 cups
• White paint: 5 cups
• Total paint = 2 cups (black) + 5 cups (white) = 7 cups

Percentage of black paint in Nathaniel's mixture: \[ \text{Percentage of black} = \left( \frac{\text{Black paint}}{\text{Total paint}} \right) \times 100 = \left( \frac{2}{7} \right) \times 100 \approx 28.57% \]

Tanisha's mixture:

• Black paint: 1 cup
• White paint: 2 cups
• Total paint = 1 cup (black) + 2 cups (white) = 3 cups

Percentage of black paint in Tanisha's mixture: \[ \text{Percentage of black} = \left( \frac{\text{Black paint}}{\text{Total paint}} \right) \times 100 = \left( \frac{1}{3} \right) \times 100 \approx 33.33% \]

Comparison:

• Nathaniel's mixture: approximately 28.57% black paint
• Tanisha's mixture: approximately 33.33% black paint

Since Tanisha has a higher percentage of black paint in her mixture than Nathaniel, Tanisha's gray paint will be darker.