While mixing a light green paint, Luke mixes 35% blue paint and the rest is yellow. The green paint fills up two fifths of a litre container. Still thinking it needs to be a lighter green how much more yellow paint must be added to make the yellow paint 75% of the green paint?
consider the amount of yellow paint.
If x liters of pure yellow are added, we need
.65 * 2/5 + x = .75(2/5 + x)
so now just solve for x
To find out how much more yellow paint needs to be added to make the yellow paint 75% of the green paint, we need to follow these steps:
Step 1: Calculate the amount of blue paint in the green mixture.
The green paint occupies two-fifths of a litre container. Since 35% of the mixture is blue, we can calculate the amount of blue paint as follows:
Blue paint = 35% * (2/5) L = 0.35 * (2/5) L = 0.14 L
Step 2: Calculate the amount of green paint in the mixture.
As the green paint fills two-fifths of the container, we've already determined that it is 0.4 L. So, the amount of green paint is:
Green paint = 2/5 L = 0.4 L
Step 3: Calculate the amount of yellow paint in the mixture.
Since the green and blue paints account for the entire mixture, the amount of yellow paint can be found by subtracting the amount of blue and green paints from the total volume of mixture:
Total mixture volume = 2/5 L
Yellow paint = Total mixture volume - (Green paint + Blue paint)
Yellow paint = (2/5) L - (0.4 L + 0.14 L)
Yellow paint = 0.46 L
Step 4: Determine the desired amount of yellow paint.
To make the yellow paint 75% of the green paint, we need to calculate 75% of the amount of green paint:
Desired yellow paint = 75% * Green paint
Desired yellow paint = 75% * 0.4 L = 0.75 * 0.4 L = 0.3 L
Step 5: Find out how much more yellow paint needs to be added.
To determine how much more yellow paint needs to be added, we subtract the current amount of yellow paint from the desired amount:
Additional yellow paint = Desired yellow paint - Current yellow paint
Additional yellow paint = 0.3 L - 0.46 L
Additional yellow paint = -0.16 L
Based on the calculations, it appears that there is an excess of yellow paint in the mixture, as we have -0.16 L for the additional yellow paint. This means there is already more yellow than needed to make it 75% of the green paint.