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How many gallons of water must be mixed with 1 gallon of a

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How many gallons of water must be mixed with 1 gallon of a [#permalink]

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The below questions were taken from two paper tests, i know the answer however wanted to see if anyone could solve based on the attached "Mixture Problems Made Easy"

The attached works great for mixture problems

How many gallons of water must be mixed with 1 gallon of a 15% salt solution To obtain a 10% salt solution

A. 5
B. 67
C. 1.00
D. 1.50
E. 2.00

[Reveal] Spoiler:
OA: A



One fourth of a solution that was 10% sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?

A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

[Reveal] Spoiler:
OA: A



for this problem based on the attached method, which this problem and the one below appear,

i understand how to get (x-16):6
but how do i get to 3:1 (since 1/4th was taken out) how is this calculated?
then solving for x give me 34 but how do i solve for x?

OPEN DISCUSSION OF THE FIRST QUESTION IS HERE: https://gmatclub.com/forum/how-many-gal ... 02888.html

OPEN DISCUSSION OF THE SECOND QUESTION IS HERE: https://gmatclub.com/forum/one-fourth-o ... 49134.html

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Mixture Problems Made Easy.pdf [53.94 KiB]
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Last edited by jsphcal on 29 Mar 2012, 22:50, edited 3 times in total.
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Re: How many gallons of water must be mixed with 1 gallon of a [#permalink]

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New post 23 Mar 2012, 19:09
also if one could elaborate on both questions and answers based on attachments,
would be greatly appreciated since the attached doesnt provide an answer for the

15% salt added to 5 liters of solution 8% salt, resulting in 10% salt solution

Last edited by jsphcal on 29 Mar 2012, 22:58, edited 1 time in total.
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Re: How many gallons of water must be mixed with 1 gallon of a [#permalink]

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New post 24 Mar 2012, 01:42
How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution
A. 5
B. 67
C. 1.00
D. 1.50
E. 2.00

Since we are adding pure water then the amount of salt in both solutions will be the same, so 0.15*1=0.1*(1+x) --> x=0.5.

Answer: A.

One fourth of a solution that was 10% sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

This is a weighted average question.

Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.

Answer: A.

P.S. Please post one question per topic.
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Re: How many gallons of water must be mixed with 1 gallon of a [#permalink]

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New post 25 Mar 2012, 10:39
Ans : A

Total Solution = x

Sugar contain = 10% (x)

1/4 (x) is replaced with new solution with y% sugar

y% [(1/4)(x)]

New Solution contain 16% sugar 16%(x)

Remaining solution + replaced solution = new sugar
[ 10/100[(3/4)(x)] ] + y% [(1/4)(x)] = [16/100](x)
3/40(x) + xy/400 = 16x/100
xy/400 = 16x/100 -3x/40
xy/400 = 340x/4000
y = 34%
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Re: How many gallons of water must be mixed with 1 gallon of a [#permalink]

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New post 26 Mar 2012, 07:40
Bunuel wrote:
How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution
A. 5
B. 67
C. 1.00
D. 1.50
E. 2.00

Since we are adding pure water then the amount of salt in both solutions will be the same, so 0.15*1=0.1*(1+x) --> x=0.5.

Answer: A.

One fourth of a solution that was 10% sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

This is a weighted average question.

Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.

Answer: A.

P.S. Please post one question per topic.



Bunuel,

thanks for your help.

and in the future i will only post one question at a time, thank you.
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Re: How many gallons of water must be mixed with 1 gallon of a [#permalink]

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New post 05 Apr 2012, 06:07
Bunuel wrote:
How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution
A. 5
B. 67
C. 1.00
D. 1.50
E. 2.00

Since we are adding pure water then the amount of salt in both solutions will be the same, so 0.15*1=0.1*(1+x) --> x=0.5.

Answer: A.

One fourth of a solution that was 10% sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

This is a weighted average question.

Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.

Answer: A.

P.S. Please post one question per topic.



Dear Bunnel,

Is my approach right to solve such problems??

I use weighted average formula-

V1/V2= (C2-C3)/( C3-C1)

1/X= (0-10)/(10-15)

1/x=2
X=0.5

:?:
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Re: How many gallons of water must be mixed with 1 gallon of a [#permalink]

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Re: How many gallons of water must be mixed with 1 gallon of a [#permalink]

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New post 08 Jan 2018, 20:59
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Re: How many gallons of water must be mixed with 1 gallon of a [#permalink]

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New post 08 Jan 2018, 22:16
Re: How many gallons of water must be mixed with 1 gallon of a   [#permalink] 08 Jan 2018, 22:16
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