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16 Sep 2014, 00:56
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Two different acid solutions were combined to create a 10-liter mixture. The first solution contained 0.8 liters of acid, while the second solution contained 0.6 liters of acid. If the concentration of acid in the first solution was twice that of the second solution, what was the volume of the first solution?
A. 3.0 liters
B. 3.2 liters
C. 3.6 liters
D. 4.0 liters
E. 4.2 liters
A. 3.0 liters
B. 3.2 liters
C. 3.6 liters
D. 4.0 liters
E. 4.2 liters
16 Sep 2014, 00:56
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Official Solution:
Two different acid solutions were combined to create a 10-liter mixture. The first solution contained 0.8 liters of acid, while the second solution contained 0.6 liters of acid. If the concentration of acid in the first solution was twice that of the second solution, what was the volume of the first solution?
A. 3.0 liters
B. 3.2 liters
C. 3.6 liters
D. 4.0 liters
E. 4.2 liters
Let \(x\) be the volume of the first solution. Since the total volume is 10 liters, the volume of the second solution is \(10-x\). Using the given information, we form the equation \(\frac{0.8}{x} = 2*\frac{0.6}{10 - x}\), representing the acid concentration in the first solution being twice that in the second solution. Solving for \(x\), we find the volume of the first solution to be \(x = 4\) liters.
Answer: D
Two different acid solutions were combined to create a 10-liter mixture. The first solution contained 0.8 liters of acid, while the second solution contained 0.6 liters of acid. If the concentration of acid in the first solution was twice that of the second solution, what was the volume of the first solution?
A. 3.0 liters
B. 3.2 liters
C. 3.6 liters
D. 4.0 liters
E. 4.2 liters
Let \(x\) be the volume of the first solution. Since the total volume is 10 liters, the volume of the second solution is \(10-x\). Using the given information, we form the equation \(\frac{0.8}{x} = 2*\frac{0.6}{10 - x}\), representing the acid concentration in the first solution being twice that in the second solution. Solving for \(x\), we find the volume of the first solution to be \(x = 4\) liters.
Answer: D
General Discussion
25 Jun 2017, 00:48
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I used an another method which works.
Solution A1 (0.8 litres)
Solution A2 (0.6 litres)
A1+A2=10
(0.8/A1)=2*(0.6/A2)
Therefore A2=1.5A1
A1+1.5A1 =10
A1= 10/2.5 = 4 litres.
Solution A1 (0.8 litres)
Solution A2 (0.6 litres)
A1+A2=10
(0.8/A1)=2*(0.6/A2)
Therefore A2=1.5A1
A1+1.5A1 =10
A1= 10/2.5 = 4 litres.
