14 liters of "forest green" contain 8 liters of blue paint. in order to transform it into "verdant green" blue paint should become 3/7 of total paint volume (now it's 4/7)

Let's suppose we add x liters of yellow paint. Then

\(\frac{8}{14+x}=\frac{3}{7}\)

\(56=42+3x\)

\(x=\frac{14}{3}\)

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.

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.

Hi All,

This question is essentially just about ratios and the average formula. You can actually do the math in a few different ways, but sometimes it's easiest to just break simple calculations down into their components:

We're told that we have 14 liters of "forest green" paint. Forest green paint is 4 parts blue paint and 3 parts yellow paint. With this information, we know that the 14 liters we currently have is....

14 liters of forest green = 8 liters blue paint + 6 liters yellow paint

"Verdant green" paint is 3 parts blue paint and 4 parts yellow paint. We're asked how many liters of YELLOW paint must be ADDED to the 14 liters of forest green paint to convert that paint into verdant green paint.

Since Verdant green paint uses the ratio of blue to yellow as B/Y = 3/4, we can use the current amount of blue paint that we have to figure out how much TOTAL yellow paint we need.

With 8 liters of blue, we can solve for TOTAL yellow:

8/Y = 3/4
3Y = 32
Y = 10 2/3 liters of TOTAL yellow paint are needed....

We currently have 6 liters of yellow paint, so we need....

10 2/3 - 6 = 4 2/3 MORE yellow paint.

Final Answer:

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Rich
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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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