To determine how much violet paint is produced when 6 liters of red paint is used, we need to follow these steps:
1. Understand the ratio: The ratio of red paint to blue paint in the mixture is 3:4. This means for every 3 parts of red paint, there are 4 parts of blue paint.
2. Determine the amount of blue paint needed: Since 6 liters of red paint is used, which corresponds to the '3 parts' in the ratio, we need to find out how much blue paint (representing the '4 parts') is required.
- If 3 parts correspond to 6 liters of red paint, then 1 part corresponds to [tex]\(\frac{6}{3} = 2\)[/tex] liters.
- Thus, 4 parts of blue paint would correspond to [tex]\(4 \times 2 = 8\)[/tex] liters.
3. Calculate the total amount of violet paint: The total amount of violet paint produced is simply the sum of the red and blue paint used.
- Red paint used: 6 liters
- Blue paint used: 8 liters
- Total violet paint: [tex]\(6 + 8 = 14\)[/tex] liters
Therefore, when 6 liters of red paint is used, the total amount of violet paint produced is 14 liters.
The correct option is [tex]\( 14 \)[/tex] liters.
