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A solution is 90% glycerin. If there are 4 gallons of the solution, ho

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Bunuel
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A solution is 90% glycerin. If there are 4 gallons of the solution, ho [#permalink] New post   04 Dec 2020, 06:30
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A solution is 90% glycerin. If there are 4 gallons of the solution, how much water, in gallons must be added to make a 75% glycerin solution?

A. 1.8
B. 1.4
C. 1.2
D. 1.0
E. 0.8
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Bunuel
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Re: A solution is 90% glycerin. If there are 4 gallons of the solution, ho [#permalink] New post   07 Dec 2020, 06:30
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Bunuel wrote:
A solution is 90% glycerin. If there are 4 gallons of the solution, how much water, in gallons must be added to make a 75% glycerin solution?

A. 1.8
B. 1.4
C. 1.2
D. 1.0
E. 0.8


In 4 gallons of the solution there are \(0.9*4=3.6\) gallons of glycerin. We want to add \(w\) gallons of water to 4 gallons of solution so that these 3.6 gallons of glycerin to be 75% of new solution: \(0.9*4=0.75(4+w)\) --> \(w=0.8\)

Answer: E.
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A solution is 90% glycerin. If there are 4 gallons of the solution, ho [#permalink] New post   04 Dec 2020, 09:23
IMO E

Given the ratio of G:W in the solution which is 4 gallons, try to form the equation in terms of the quantity which needs to be found out instead of the quantity that is given - it makes calculations simpler and faster.

We know that the percentage of water in the original solution is 10%, hence we can calculate the volume.
Assuming 'x' gallons of water needs addition.
Then,

2/5 + x=1/4(4+x)

x-x/4=1-2/5

3x/4=3/5

x=0.8
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Re: A solution is 90% glycerin. If there are 4 gallons of the solution, ho [#permalink] New post   05 Dec 2020, 03:59
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Bunuel wrote:
A solution is 90% glycerin. If there are 4 gallons of the solution, how much water, in gallons must be added to make a 75% glycerin solution?

A. 1.8
B. 1.4
C. 1.2
D. 1.0
E. 0.8




4 gallons of 90% glycerine contains 0.9 * 4 = 3.6 gallons of glycerine and 0.4 gallons of water.

Let us add x gallons of water to make it a 75% glycerine (25% water solution)

Therefore \(\frac{3.6}{0.4 + x} = \frac{75}{25}\)

3.6 = 3(0.4 + x)

3x = 2.4

x = 0.8


Option E

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Re: A solution is 90% glycerin. If there are 4 gallons of the solution, ho [#permalink] New post   07 Dec 2020, 09:07
Answer is E.

90% of the solution is Glycerin.
Hence Glycerin=0.9*4=3.6

Since the amount of Glycerin won't change
Let "s" be the Total weight of the new solution
\(3.6=0.75*s\)
\(s=4.8\)

We know out of the 4.8, 3.6 is glycerin.
Hence the amount of water in the new solution is 1.2
Therefore the amount added is \(1.2-0.4=0.8\)
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Re: A solution is 90% glycerin. If there are 4 gallons of the solution, ho [#permalink] New post   07 Dec 2020, 09:08
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Given: A solution is 90% glycerin.
Asked: If there are 4 gallons of the solution, how much water, in gallons must be added to make a 75% glycerin solution?

Attachment:
Screenshot 2020-12-07 at 9.38.05 PM.png
Screenshot 2020-12-07 at 9.38.05 PM.png [ 29.76 KiB | Viewed 6147 times ]


IMO E
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Re: A solution is 90% glycerin. If there are 4 gallons of the solution, ho [#permalink] New post   01 Sep 2021, 01:36
kinshook

Can you explain how you came to this line "4:4/5=.8 gallons"

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Re: A solution is 90% glycerin. If there are 4 gallons of the solution, ho [#permalink]
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