moonshine has 50 liters of a 70% alcohol solution.how many liters of pure alcohol must be added to obtain an 80% alcohol solution?
The alcohol content is .7*50=35 liters.
Then, adding alcohol...
35+V=.80*(50+V)
solve for V, volume alcohol added
To solve for the volume of pure alcohol that must be added, we can use the equation:
35 + V = 0.8 * (50 + V)
where V represents the volume of pure alcohol to be added.
Let's solve it step by step:
1. Distribute 0.8 to both terms within the parentheses on the right side of the equation:
35 + V = 40 + 0.8V
2. Simplify the equation by combining like terms:
V - 0.8V = 40 - 35
0.2V = 5
3. Divide both sides of the equation by 0.2 to isolate V:
V = 5 / 0.2
V = 25
Therefore, you need to add 25 liters of pure alcohol to obtain an 80% alcohol solution.