You have 8 liters of a 60% alcohol solution. How many liters of water should be added to make a 35% alcohol solution?.
amount of water to be added --- x L
.6(8) + 0x = .35(8+x)
4.8 = 2.8 + .35x
.35x = 2
x = appr 5.71 L
To solve this problem, we need to calculate the amount of water that needs to be added to the existing solution.
Step 1: Determine the amount of alcohol in the existing solution:
Since the solution is 60% alcohol, the amount of alcohol in it can be calculated as:
Alcohol (in liters) = 60/100 * 8 liters = 4.8 liters
Step 2: Determine the final volume of the solution:
To find out the total volume of the final solution, we need to divide the amount of alcohol by the desired alcohol percentage:
Total volume of the final solution = Alcohol / Desired alcohol percentage
Total volume = 4.8 / 35/100 = 13.7143 liters
Step 3: Calculate the amount of water needed:
The amount of water that needs to be added is the difference between the total volume of the final solution and the volume of the existing solution:
Water needed = Total volume of the final solution - Existing volume of the alcohol solution
Water needed = 13.7143 liters - 8 liters = 5.7143 liters
Therefore, you need to add approximately 5.7143 liters of water to the existing 8 liters of a 60% alcohol solution to obtain a final solution with a 35% alcohol concentration.