In art class students are mixing black and white paint to make gray paint. Yusuf mixes 1 cup of black paint and 2 cups of white paint. Samantha mixes 3 cups of black paint and 4 cups of white paint. Use Yusuf and Samantha’s percent of black paint to determine whose gray paint will be darker.

Question

Answer
Attempt 1 out of 2

Yusuf percent of black paint (to nearest whole number) =
%
Samantha percent of black paint (to nearest whole number) =
%

Answer 1

To find the percentage of black paint in the mixtures made by Yusuf and Samantha, we can use the formula:

\[ \text{Percent of black paint} = \left( \frac{\text{cups of black paint}}{\text{total cups of paint}} \right) \times 100 \]

Yusuf's Mixture:

Yusuf mixes:

• 1 cup of black paint
• 2 cups of white paint

Total cups of paint = 1 cup (black) + 2 cups (white) = 3 cups

Now we calculate the percentage of black paint:

\[ \text{Percent of black paint (Yusuf)} = \left( \frac{1}{3} \right) \times 100 \approx 33.33% \]

Rounded to the nearest whole number, Yusuf's percent of black paint is approximately 33%.

Samantha's Mixture:

Samantha mixes:

• 3 cups of black paint
• 4 cups of white paint

Total cups of paint = 3 cups (black) + 4 cups (white) = 7 cups

Now we calculate the percentage of black paint:

\[ \text{Percent of black paint (Samantha)} = \left( \frac{3}{7} \right) \times 100 \approx 42.86% \]

Rounded to the nearest whole number, Samantha's percent of black paint is approximately 43%.

Conclusion:

• Yusuf's percent of black paint = 33%
• Samantha's percent of black paint = 43%

Since Samantha has a higher percentage of black paint in her mixture, her gray paint will be darker.