Question

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.