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John has 3 solutions: a 12% saline solution, a 8% vinegar solution, an

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John has 3 solutions: a 12% saline solution, a 8% vinegar solution, an [#permalink]

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New post 19 Mar 2017, 07:10
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John has 3 solutions: a 12% saline solution, a 8% vinegar solution, and a 15% alcohol solution. He mixes 3 liters of the alcohol solution with 3 liters of the vinegar solution. What is the minimum amount of the saline solution he must add if the resulting mixture must be at least 2% saline solution?

A. 7.1 liters
B. 3 liters
C. 2.4 liters
D. 1.2 liters
E. 1.1 liters

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Re: John has 3 solutions: a 12% saline solution, a 8% vinegar solution, an [#permalink]

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New post 19 Mar 2017, 11:29
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Bunuel wrote:
John has 3 solutions: a 12% saline solution, a 8% vinegar solution, and a 15% alcohol solution. He mixes 3 liters of the alcohol solution with 3 liters of the vinegar solution. What is the minimum amount of the saline solution he must add if the resulting mixture must be at least 2% saline solution?

A. 7.1 liters
B. 3 liters
C. 2.4 liters
D. 1.2 liters
E. 1.1 liters


let x=minimum liters of saline solution needed
.12x=.02(6+x)
x=1.2 liters
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Re: John has 3 solutions: a 12% saline solution, a 8% vinegar solution, an [#permalink]

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New post 20 Mar 2017, 02:02
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Bunuel wrote:
John has 3 solutions: a 12% saline solution, a 8% vinegar solution, and a 15% alcohol solution. He mixes 3 liters of the alcohol solution with 3 liters of the vinegar solution. What is the minimum amount of the saline solution he must add if the resulting mixture must be at least 2% saline solution?

A. 7.1 liters
B. 3 liters
C. 2.4 liters
D. 1.2 liters
E. 1.1 liters


let the saline solution he adds be x

saline content = 0.12x
saline content required = 0.02(3+3+x) = 0.02(6+x)
equating these two, we get
0.12x = 0.02*(6+x)
or 0.1x = 0.12
or x = 1.2

option D
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Re: John has 3 solutions: a 12% saline solution, a 8% vinegar solution, an [#permalink]

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New post 08 Jul 2018, 23:19
Bunuel wrote:
John has 3 solutions: a 12% saline solution, a 8% vinegar solution, and a 15% alcohol solution. He mixes 3 liters of the alcohol solution with 3 liters of the vinegar solution. What is the minimum amount of the saline solution he must add if the resulting mixture must be at least 2% saline solution?

A. 7.1 liters
B. 3 liters
C. 2.4 liters
D. 1.2 liters
E. 1.1 liters



Let X be the amount of Saline Solution, that needs to be added.

We have Total amount of Final Solution = 3 + 3 + X = 6 + X liters

For the final solution to be 2% Saline, we need 2% of (6 + X) = 12% of X

Hence 2*(6+X) = 12*X

Solving we, get X = 1.2 liters


Answer D.



Thanks,
GyM
Re: John has 3 solutions: a 12% saline solution, a 8% vinegar solution, an   [#permalink] 08 Jul 2018, 23:19
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