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19 Nov 2018, 09:24
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A
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A 5-liter jug contains 4 liters of a saltwater solution that is 15 percent salt. If 1.5 liters of the solution spills out of the jug, and the jug is then filled to capacity with water, approximately what percent of the resulting solution in the jug is salt?
(A) \(7\frac{1}{2}\)%
(B) \(9\frac{3}{8}\)%
(C) \(10\frac{1}{2}\)%
(D) \(12\)%
(E) \(15\)%
(A) \(7\frac{1}{2}\)%
(B) \(9\frac{3}{8}\)%
(C) \(10\frac{1}{2}\)%
(D) \(12\)%
(E) \(15\)%
19 Nov 2018, 10:30
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HKD1710
-----------ASIDE------------
IMPORTANT CONCEPT: If EQUAL VOLUMES of 2 solutions are combined, the concentration of the resulting mixture will be the AVERAGE of the 2 solutions.
Example: If 3 liters of a 10% alcohol solution are combined with 3 liters of a 30% alcohol solution, the resulting solution will be 20% alcohol.
Likewise, if 11 liters of 6% alcohol solution are combined with 11 liters of a 7% alcohol solution, the resulting solution will be 6.5% alcohol.
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Once we pour out 1.5 liters, we're left with 2.5 liters of 15% salt solution
Since the jug holds 5 liters, we then add 2.5 liters of water (aka a 0% salt solution)
Since we're combining EQUAL VOLUMES of 15% and 0% solutions, the salt content of the resulting solution will equal the average of 15% and 0%
(15 + 0)/2 = 7.5
So, the resulting solution will be 7.5% salt.
Answer: A
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19 Nov 2018, 11:47
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dave13
but what if volumes of mixtures aren't equal ? any advice is appreciated Thanks, Dave!
If the volumes aren't equal, you can use the Weighted Averages formula (discussed in the video), or you might be able to use the answer choices to your advantage.
For example, let's say that we're adding 3 liters of 0% salt solution to 2.5 liters of 22% salt solution, and the answer choices are:
A) 10%
B) 11%
C) 13%
D) 14%
E) 17%
We know that, if we were adding EQUAL volumes of the two solutions, then the resulting solution would be 11% (since 11% is the AVERAGE of 0% and 22%)
Since we're actually add more 0% solution, then the resulting solution will be LESS THAN 11% salt.
Since answer choice A is the only answer that is less than 11%, the correct answer must be A
Cheers,
Brent
