To determine how much red paint is needed, we start by looking at the ratio of red to blue paint, which is 3:4. This means that for every 3 parts of red paint, there are 4 parts of blue paint.
Given that we are using 6 liters of blue paint, we can set up a proportion to find the amount of red paint needed. In this situation, let’s define the amount of red paint as R.
The ratio tells us that:
- Red paint = 3 parts
- Blue paint = 4 parts
From the ratio, we can express these parts in terms of a common multiplier:
- Red paint = 3x
- Blue paint = 4x
Since we know the amount of blue paint (6 liters), we can substitute this into the equation:
4x = 6
Now, solving for x, we divide both sides by 4:
x = 6 / 4 = 1.5
Now that we have the value of x, we can find the amount of red paint:
Red paint = 3x = 3 * 1.5 = 4.5 liters
Therefore, 4.5 liters of red paint are needed to mix with 6 liters of blue paint to maintain the purple paint ratio of 3:4.