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23 May 2018, 07:01
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E
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Difficulty:
75%
(hard)
Question Stats:
60% (02:33) correct
40%
(02:23)
wrong
based on 660
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Solution X is 30% alcohol by volume, solution Y is 10% alcohol by volume, and solution Z is 40% alcohol by volume. If 41 gallons of solution X, 20 gallons of solution Y, and 20 gallons of solution Z are combined, which of the following best approximates the percentage of alcohol in the resulting mixture?
A) 20.13
B) 24.91
C) 25.07
D) 27.46
E) 27.53
A) 20.13
B) 24.91
C) 25.07
D) 27.46
E) 27.53
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25 May 2018, 12:59
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We can avoid tedious calculations by creating this mixture in parts
First combine 20 gallons of solution Y (10% alcohol) with 20 gallons of solution Z (40% alcohol)
Since we have EQUAL volumes of each solution, the percentage of alcohol in the resulting mixture will be the AVERAGE of the two concentrations.
So, concentration of alcohol in new mixture = (10% + 40%)/2 = 25%
So, now have 40 gallons of a solution that's 25% alcohol.
Next, add 41 gallons of solution X (30% alcohol) to this 40-gallon mixture (25% alcohol)
KEY POINT: If we were to add 40 gallons of solution X (30% alcohol) to the 40-gallon mixture (25% alcohol), then we'd have EQUAL volumes of each solution.
In this case the percentage of alcohol in the resulting mixture WOULD equal the AVERAGE of the two concentrations.
So, the concentration of alcohol in new mixture WOULD equal (30% + 25%)/2 = 27.5%
In reality we have 41 gallons of solution X (30%).
Since the volume of solution X (30%) is greater than the volume of the existing solution (25%), the concentration will be closer to 30% than it is to 25%
So, the concentration of the final solution will be a bit more than 27.5%
Answer: E
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23 May 2018, 19:17
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41 gallons of solution X contains --> 41 * 0.3 = 12.3 gallons of alcohol
20 gallons of solution Y contains --> 20 * 0.1 = 2 gallons of alcohol
20 gallons of solution Z contains --> 20 * 0.4 = 8 gallons of alcohol
Percentage of alcohol in the resulting mixture = (12.3 + 2 + 8)/81 = 223/810 = 0.275x * 100 = 27.5x
Answer: E
20 gallons of solution Y contains --> 20 * 0.1 = 2 gallons of alcohol
20 gallons of solution Z contains --> 20 * 0.4 = 8 gallons of alcohol
Percentage of alcohol in the resulting mixture = (12.3 + 2 + 8)/81 = 223/810 = 0.275x * 100 = 27.5x
Answer: E
