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30 Jun 2017, 03:34
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
80% (01:46) correct
20%
(02:02)
wrong
based on 485
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How many liters of pure alcohol must be added to a 90-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?
(A) 4.5
(B) 5.0
(C) 5.5
(D) 6.0
(E) 6.5
(A) 4.5
(B) 5.0
(C) 5.5
(D) 6.0
(E) 6.5
30 Jun 2017, 06:38
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Bunuel
Weighted average, one formula **
Let \(x\) = amount of alcohol to be added
\((.20)90 + (1)x = .25 (90 + x)\)
\(18 + x = 22.5 + .25x\)
\(.75x = 4.5\)
\(\frac{3}{4}x=\frac{9}{2}\)
\(x=\frac{9}{2}*\frac{4}{3}\)
\(x = 6\)
Answer D
**
This weighted average method uses these variables:
A = 90 L of solution that is 20% alcohol
B = \(x\) (above) = Amount (volume) of pure alcohol to be added
(A+B) = total volume of resultant solution
% = concentration of alcohol
-- A, % alcohol = .20
-- B, % alcohol = 1
(Concentration of pure alcohol, B, is 100%, which in decimal form = 1)
-- (A+B), % alcohol? 25% = .25 (For the resultant solution, use the desired concentration)
Use this formula:
(% of A)*(Vol of A) + (% of B)*(Vol of B) = (Desired % of (A+B))*(Vol of A+B)
30 Jun 2017, 06:33
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The amount of alcohol in the 90% solution is 90*\(\frac{1}{5}\)=18 litres
We need to add some solution of pure alcohol to make the total alcohol 25% of the solution
We can use answer choices as it is easier
From D, if we add 6 litres alcohol to the solution, total alcohol will become 18+6=24 litres
Alcohol percent = \(\frac{24}{(90+6)}\) = \(\frac{24}{96}\) = \(\frac{1}{4}\) = 25%
This fits the question, so D is the answer.
We need to add some solution of pure alcohol to make the total alcohol 25% of the solution
We can use answer choices as it is easier
From D, if we add 6 litres alcohol to the solution, total alcohol will become 18+6=24 litres
Alcohol percent = \(\frac{24}{(90+6)}\) = \(\frac{24}{96}\) = \(\frac{1}{4}\) = 25%
This fits the question, so D is the answer.
- D! 
