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14 liter of Forset green have 8 liter of blue and 6 liter of yellow
Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is

Blue/yellow =8/(6+x) = ¾
Solving this we get x =14/3 and answer is 5
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In 14 litres of forest green there are 8L of Blue and 6L of Yellow. To convert this to Verdant green(whose ratio of mixture is 4 parts of yellow and 3 parts of blue paint)

8/(6+x) = 3/4
==> x = 14/3

But i do not find that in the choices.
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soundofmusic is correct.

In forest green, the ratio of Blue:Yellow is 4:3. If I have 14 lts of this paint, it means I have 8 lts of Blue in it and 6 litres of Yellow in it.

To make it Verdant Green I need to add Yellow because it has Blue:Yellow ratio of 3:4. If x lts is the amount of Yellow I need to add,
\(\frac{8}{{6 + x}} = \frac{3}{4}\)
\(x = \frac{14}{3} = 4 \frac{2}{3}\)

The answer is not there in the options.
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Can we solve this algebraically, the thought of using ratios never occurred to me (for mixtures), I was trying to solve it algebraically and then it went downhill from there. :(
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At a certain paint store forest green is made by mixing 4parts of blue and 3 parts of yellow paint. verdant green is made by 4 parts of yellow and 3 parts of blue paint. how many litres of yellow paint must be added to 14litres of forest green to change it to verdant green?
a)10 3/2 b)11 3/2 c)14 3/4 d)15 5/6 e) 18 2/3

You can use mixtures formula.

Method 2: We need to mix 14 litres of forest green(3/7 parts yellow) with yellow paint to give us verdant green (4/7 parts yellow).

Using mixtures formula:
Lets say we need x litres of yellow paint. This entire x will be yellow paint so fraction is 1.

\(\frac{(3/7)*14 + 1*x}{14 + x} = \frac{4}{7}\)

x = 14/3 litres
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let y=liters of yellow to be added
(3/7)(14)+y=(4/7)(14+y)
3y=14
y=14/3 liters
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samrand
At a certain paint store "forest green"is made by mixing 4 parts blue paint with 3 parts yellow paint."Verdant green"is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 14 liters of "forest green"to change it to "Verdant green"?

A. 2
B. 13/6
C. 3
D. 4
E. 14/3

We are given that we have 14 liters of forest green, which has the ratio of blue : yellow = 4x : 3x. Thus:

7x = 14

x = 2

So, we have 8 liters of blue and 6 liters of yellow. We can let y = the additional liters of yellow paint added to the 14 liters of forest green to change it to Verdant green and we can create the following equation:

(6 + y)/8 = 4/3

32 = 3(6 + y)

32 = 18 + 3y

14 = 3y

14/3 = y

Answer: E
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samrand
At a certain paint store "forest green"is made by mixing 4 parts blue paint with 3 parts yellow paint."Verdant green"is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 14 liters of "forest green"to change it to "Verdant green"?

A. 2
B. 13/6
C. 3
D. 4
E. 14/3

Hello chetan2u, Gladiator59, generis

My question is on the blue font specifically

Should one assume that

- Blue paint to yellow paint for Forest green is 4x to 3x
whereas
- Blue paint to yellow paint for Verdant green is 3y : 4y

marking Blue paint to yellow paint for Verdant green as 3x : 4x WOULD BE WRONG

as the ratio's maybe different

Please let me know if my assumption is accurate
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At a certain paint store "forest green"is made by mixing 4 parts blue paint with 3 parts yellow paint."Verdant green"is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 14 liters of "forest green"to change it to "Verdant green"?

A. 2
B. 13/6
C. 3
D. 4
E. 14/3
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samrand
At a certain paint store "forest green"is made by mixing 4 parts blue paint with 3 parts yellow paint."Verdant green"is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 14 liters of "forest green"to change it to "Verdant green"?

A. 2
B. 13/6
C. 3
D. 4
E. 14/3

Hello chetan2u, Gladiator59, generis

My question is on the blue font specifically

Should one assume that

- Blue paint to yellow paint for Forest green is 4x to 3x
whereas
- Blue paint to yellow paint for Verdant green is 3y : 4y

marking Blue paint to yellow paint for Verdant green as 3x : 4x WOULD BE WRONG

as the ratio's maybe different

Please let me know if my assumption is accurate

Yes, both are different ratios and you cannot take same common ratio as x
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Forest Green
Blue : Yellow = 4: 3
14 litters= Blue : Yellow 8: 6

Verdant Green
Blue : Yellow 3:4

Let’s consider that X amount of yellow needs to be added

8/(6+X) = 3/4
=18+3X = 32
X=14/3

Posted from my mobile device
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We know 14 liters of forest green consists of 8 blue, 6 yellow.

The ratio of verdant green is 4 yellow : 3 blue.

That means in our 14 liters of forest green, we need to add more yellow to get the 3/4 blue ratio.

We can make the equation:

8 / (6+x) = 3/4
18 + 3x = 32
3x = 14
x = 14/3
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