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How many gallons of water must be mixed with 1 gallon of a 15% salt so

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Joined: 19 Dec 2009
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How many gallons of water must be mixed with 1 gallon of a 15% salt so [#permalink]

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New post 15 Oct 2010, 10:20
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How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution?

A. 0.50
B. 0.67
C. 1.00
D. 1.50
E. 2.00
[Reveal] Spoiler: OA
3 KUDOS received
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Posts: 227
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Re: How many gallons of water must be mixed with 1 gallon of a 15% salt so [#permalink]

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New post 15 Oct 2010, 22:56
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rtaha2412 wrote:
Does anyone have a good strategy to solving solutions problems?

Question

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

A 0.50
b 0.67
c 1.00
d 1.50
e. 2.00


you are having 1 gallon of a 15% salt solution means you are having (15/100)*1 gallon of salt.

Now consider you are using x gallons of water and making it to (x+1) gallon of solution.now the salt content(15/100) will be the 10% of total solution.
Hence (10/100)(x+1)=15/100

Solving we get x=0.5 gallon.Answer is A.

Consider KUDOS if it is helpful to u.Thanks.
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Re: How many gallons of water must be mixed with 1 gallon of a 15% salt so [#permalink]

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New post 29 Nov 2016, 07:16
rtaha2412 wrote:
How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution?

A. 0.50
B. 0.67
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.
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Re: How many gallons of water must be mixed with 1 gallon of a 15% salt so [#permalink]

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New post 29 May 2017, 20:21
Since we are adding pure water

I got the equation

x + .85 = .9 (1 + x)

x - 1/1 of x i.e. only water being added.
.85 - .85 gallons of water
.9 = the resultant percentage of water + salt.

Solve for it to get .50 Gallons.
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Re: How many gallons of water must be mixed with 1 gallon of a 15% salt so [#permalink]

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New post 30 May 2017, 10:27
rtaha2412 wrote:
How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution?

A. 0.50
B. 0.67
C. 1.00
D. 1.50
E. 2.00


let w=gallons of water to be mixed
.85+w=.9(1+w)
w=.5 gallons
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How many gallons of water must be mixed with 1 gallon of a 15% salt so [#permalink]

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New post 02 Jun 2017, 16:46
rtaha2412 wrote:
How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution?

A. 0.50
B. 0.67
C. 1.00
D. 1.50
E. 2.00


Let x = the number of gallons of water to be added

(concentration of A)*(Volume of A) + (concentration of B)* (Volume of B) = (desired concentration in resultant mixture)*(Volume of resultant mixture = A + B)

Water has a salt concentration of 0

(.15)*(1) + (0)(x) = (.10) (1 + x)

.15 = .10 + .10x

.05 = .10 x

\(\frac{.05}{.10}\) = .50

Answer A
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Re: How many gallons of water must be mixed with 1 gallon of a 15% salt so [#permalink]

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New post 17 Jun 2017, 03:27
How can this be solved by the mixture chart method?
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How many gallons of water must be mixed with 1 gallon of a 15% salt so [#permalink]

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New post 17 Jun 2017, 03:58
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TheMastermind wrote:
How can this be solved by the mixture chart method?


Since pure water contains 0% salt
the mixture chart will be as follows :

0(Pure water) - - - - - 15(Salt Solution)
- - - - - - - - - - - 10 - - - - - - - - - - - - -
5 - - - - - - - - - - - - - - - - - - - - - - - 10

This in in proportion 1 : 2
Since we are mixing 1 gallon of 15% salt solution, which is twice the portion of pure water,
we will be adding 0.5 gallon of pure water(Option A)

Hope this helps
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How many gallons of water must be mixed with 1 gallon of a 15% salt so   [#permalink] 17 Jun 2017, 03:58
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