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At a certain paint store "forest green"is made by mixing 4 p

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At a certain paint store "forest green"is made by mixing 4 p  [#permalink]

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New post 15 Jan 2010, 12:57
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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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Re: How to solve ?  [#permalink]

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New post Updated on: 15 Jan 2010, 14:12
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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

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

\(56=42+3x\)

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

Originally posted by shalva on 15 Jan 2010, 14:07.
Last edited by shalva on 15 Jan 2010, 14:12, edited 1 time in total.
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Re: How to solve ?  [#permalink]

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New post 15 Jan 2010, 14:12
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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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Re: At a certain paint store "forest green" is made by mixing 4 parts blue  [#permalink]

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New post 18 Nov 2010, 21:49
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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Re: At a certain paint store "forest green" is made by mixing 4 parts blue  [#permalink]

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New post 20 Nov 2010, 11:25
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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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Re: At a certain paint store "forest green" is made by mixing 4 parts blue  [#permalink]

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New post 22 Nov 2010, 09:04
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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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Re: At a certain paint store "forest green" is made by mixing 4 parts blue  [#permalink]

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New post 22 Nov 2010, 10:15
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tejhpamarthi wrote:
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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Re: At a certain paint store "forest green"is made by mixing 4 p  [#permalink]

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New post 25 Apr 2015, 16:15
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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.

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Re: At a certain paint store "forest green"is made by mixing 4 p  [#permalink]

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New post 18 Jan 2016, 14:18
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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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Re: At a certain paint store "forest green"is made by mixing 4 p  [#permalink]

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New post 14 Jul 2017, 09:38
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samrand wrote:
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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Re: At a certain paint store "forest green"is made by mixing 4 p  [#permalink]

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