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How many gallons of a 7% saline solution must be added to 4 gallons of
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15 Sep 2021, 09:35
15 Sep 2021, 09:35
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How many gallons of a 7% saline solution must be added to 4 gallons of a 25% saline solution so that the resulting mixture is a 15% saline solution?
A. 1
B. 4
C. 5
D. 9
E. 10
A. 1
B. 4
C. 5
D. 9
E. 10
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Re: How many gallons of a 7% saline solution must be added to 4 gallons of
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15 Sep 2021, 10:00
15 Sep 2021, 10:00
1
Carcass wrote:
How many gallons of a 7% saline solution must be added to 4 gallons of a 25% saline solution so that the resulting mixture is a 15% saline solution?
A. 1
B. 4
C. 5
D. 9
E. 10
A. 1
B. 4
C. 5
D. 9
E. 10
This question nicely illustrates how the GRE test-makers reward students for taking their understanding of a concept to use some number sense (rather than follow a formula).
We have 4 gallons of a 25% saline solution to start
First recognize that, IF we were to add an EQUAL volume of 7% saline solution to the 4 gallons of 25% saline solution, then the salinity of the resulting mixture would be the AVERAGE of the two solutions.
That is, if we add 4 gallons of 7% saline solution to the 4 gallons of 25% saline solution, the resulting solution will be 16% saline, since (7% + 25%)/2 = 16%.
This 16% solution is VERY CLOSE to our goal of having a 15% solution.
To get down to 15%, we must add more than 4 gallons of the weaker (less saline) solution.
However, since adding 4 gallons of the 7% solution bought us VERY CLOSE to our goal of having a 15% solution, we only need to add a LITTLE MORE THAN 4 gallons of 7% solution to reach the goal salinity of 15%.
Since only one answer choice (C) is a little more than 4, we can conclude that 5 is the correct answer.
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Re: How many gallons of a 7% saline solution must be added to 4 gallons of
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28 Sep 2022, 14:54
28 Sep 2022, 14:54
1
Let Y be gallons needed to be added to 7% saline solution.
0.07Y + 4(0.25) = 0.15(4 + Y)
0.07Y + 1 = 0.6 + 0.15Y
-0.08Y = -0.4
Y = 5
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0.07Y + 4(0.25) = 0.15(4 + Y)
0.07Y + 1 = 0.6 + 0.15Y
-0.08Y = -0.4
Y = 5
Posted from my mobile device
