How many liters of water should be evaporated from 110 liters of a 12% saline solution so that the solution that remains is a 20% saline solution?
The amount of salt stays the same
.20(110-x) = .12x
times 100
20(110-x) = 12x
2200 - 20x = 12x
2200 = 32x
x = 68.75
To solve this problem, we need to determine the amount of water that needs to be evaporated from the initial solution.
Step 1: Calculate the amount of saline in the initial solution
The 12% saline solution means that there are 12 liters of saline in every 100 liters of the solution. Since we have 110 liters of the initial solution, we can calculate the amount of saline as follows:
Amount of saline = (12 / 100) * 110
Amount of saline = 13.2 liters
Step 2: Determine the amount of water in the initial solution
To find the amount of water in the initial solution, we can subtract the amount of saline from the total volume of the solution:
Amount of water = Total volume of solution - Amount of saline
Amount of water = 110 - 13.2
Amount of water = 96.8 liters
Step 3: Calculate the amount of water that needs to be evaporated
Let's assume that x liters of water need to be evaporated from the solution to obtain a 20% saline solution.
Amount of water remaining = Amount of water - x
Amount of water remaining = 96.8 - x
Now, since the saline concentration is 20%, the amount of saline in the remaining solution can be calculated as:
Amount of saline remaining = (20 / 100) * (110 - x)
Step 4: Set up the equation
Since the amount of saline remaining should be equal to the amount of saline in the initial solution, we can set up the equation:
13.2 = (20 / 100) * (110 - x)
Step 5: Solve the equation
Let's solve the equation to find the value of x:
13.2 = (20 / 100) * (110 - x)
13.2 = (1/5) * (110 - x)
66 = 110 - x
x = 110 - 66
x = 44
Step 6: Interpret the result
The calculations show that 44 liters of water should be evaporated from the initial 110 liters of the 12% saline solution to obtain a 20% saline solution.