ccassel wrote:How would you explain the answer to this question?
How many liters of pure alcohol must be added to a 100-liter solution that is 20% alcohol in order to produce a solution that is 25% alcohol?
A. 7/2
B. 5
C. 20/3
D. 8
E. 39/4
Answer is C
The 100-liter solution contains 20 liters of alcohol.
We can plug in the answers, which represent the amount of pure alcohol that needs to be added.
Answer choice C: 20/3 of pure alcohol.
Total alcohol = 20 + 20/3 = 80/3 liters.
Total solution = 100 + 20/3 = 320/3 liters.
Alcohol/total = (80/3)/(320/3) = 1/4 = 25%.
Success!
The correct answer is
C.
Another easy approach:
The 100-liter solution contains 20 liters alcohol, 80 liters non-alcohol.
The 80 liters of non-alcohol is not changing.
Since the final mixture must be 25% alcohol, the 80 liters of non-alochol must be 75% of the final mixture.
80 = .75x
x = 80/.75 = 320/3 liters.
Since the final mixture must be 320/3 liters, the amount of alcohol that must be added to the 100-liter solution = 320/3 - 100 = 20/3 liters.
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