In art class students are mixing black and white paint to make gray paint. Allison mixes 1 cup of black paint and 2 cups of white paint. Alexander mixes 6 cups of black paint and 11 cups of white paint. Use Allison and Alexander’s percent of white paint to determine whose gray paint will be lighter.

Question

Answer
Attempt 1 out of 2

Allison percent of white paint (to nearest whole number) =
%
Alexander percent of white paint (to nearest whole number) =
%

Answer 1

To determine whose gray paint will be lighter, we need to calculate the percent of white paint in both Allison's and Alexander's mixes.

Allison's Mix:

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

Percentage of white paint in Allison's mix: \[ \text{Percent of white paint} = \left( \frac{\text{White Paint}}{\text{Total Paint}} \right) \times 100 \] \[ \text{Percent of white paint} = \left( \frac{2}{3} \right) \times 100 \approx 66.67% \] Rounded to the nearest whole number, Allison's percent of white paint is 67%.

Alexander's Mix:

• Black paint: 6 cups
• White paint: 11 cups
• Total paint = 6 cups (black) + 11 cups (white) = 17 cups

Percentage of white paint in Alexander's mix: \[ \text{Percent of white paint} = \left( \frac{\text{White Paint}}{\text{Total Paint}} \right) \times 100 \] \[ \text{Percent of white paint} = \left( \frac{11}{17} \right) \times 100 \approx 64.71% \] Rounded to the nearest whole number, Alexander's percent of white paint is 65%.

Final Answers:

• Allison percent of white paint (to nearest whole number) = 67%
• Alexander percent of white paint (to nearest whole number) = 65%

Since Allison's gray paint has a higher percent of white paint (67%) compared to Alexander's (65%), Allison's gray paint will be lighter.