Answer:
You would need 18 litres more of white paint to create Citron Green paint.
Step-by-step explanation:
Given the Green Apple paint contains 24 litres of green paint in a 2:1 ratio with white paint, we can conclude the mixture contains 12 litres of white paint because 24 / 2 = 12.
In a Citron Green paint mixture, the current paint mixture would contain 24 litres of green paint in a 4:5 ratio with white paint. This would mean there are 30 litres of white paint in this mixture.
24 / 4 = 6
5 x 6 = 30
To make Citron Green paint, you would need 18 litres more of white paint.
30 - 12 = 18
The amount of white paint that needs to be added is required.
He needs to add 75 liters of white paint.
Let x be amount of green paint
y be amount of white paint.
Amount of apple green paint is 90 L, so
[tex]x+y=90[/tex]
The ratio of green to white paint is 2:1, so
[tex]\dfrac{x}{y}=\dfrac{2}{1}[/tex]
Rearranging the equation
[tex]x=2y[/tex]
Substituting in the first equation
[tex]2y+y=90\\\Rightarrow y=\dfrac{90}{3}\\\Rightarrow y=30\ \text{L}[/tex]
Amount of white paint is 30 L.
Amount of green paint is [tex]x=2y=2\times 30=60\ \text{L}[/tex]
Amount of green paint added to the apple green paint is 24 L.
Amount of green paint in the mixture is 60+24 = 84 L.
Let the amount of white paint to be added in the mixture be y.
This will be added to the 30 L of white paint in the original mixture.
The ratio of green:white = 4:5, so
[tex]\dfrac{84}{y+30}=\dfrac{4}{5}\\\Rightarrow \dfrac{84\times 5}{4}=y+30\\\Rightarrow 105=y+30\\\Rightarrow y=105-30=75[/tex]
The amount of white paint to be added is 75 L.
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