It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 60 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength?
let the amount to be drained be x l
then
.2(60-x) + 1.0(x) = .4(60)
2(60-x) + 10x = 4(60)
etc.
I got x = 15
To determine how many liters of the 20% antifreeze solution should be drained and replaced with 100% antifreeze, we can follow these steps:
Step 1: Calculate the amount of antifreeze in the current solution:
The 20% antifreeze solution contains 20% of antifreeze in every liter.
So, the amount of antifreeze in the 60 liters of the 20% solution is (20/100) * 60 = 12 liters of antifreeze.
Step 2: Set up the equation for the desired concentration:
Let x be the amount of 20% antifreeze solution to be replaced with 100% antifreeze.
The remaining amount of the 20% solution will be (60 - x) liters.
So, the amount of antifreeze in the remaining solution will be 0.20 * (60 - x) liters.
The amount of antifreeze in the 100% antifreeze solution will be x liters.
Step 3: Set up the equation for the desired strength:
The total volume of the mixture after draining and adding the antifreeze should still be 60 liters.
The desired concentration is 40%, so the total amount of antifreeze should be 0.40 * 60 liters.
Equating the amount of antifreeze in the mixture:
12 - 0.20x + x = 0.40 * 60
Simplifying the equation:
12 + 0.80x = 24
Step 4: Solve for x:
0.80x = 24 - 12
0.80x = 12
x = 12 / 0.80
x = 15
Therefore, 15 liters of the 20% antifreeze solution should be drained and replaced with 15 liters of 100% antifreeze to achieve the desired 40% strength.
To find out how many liters of the 20% solution should be drained and replaced with 100% antifreeze, we can follow these steps:
Step 1: Determine the desired amount of antifreeze in the final solution
Since the desired strength is a 40% antifreeze solution, this means that 40% of the final solution should be antifreeze. Therefore, the desired amount of antifreeze can be calculated as 40% of the total volume.
Desired amount of antifreeze = 40% * Total volume
Step 2: Calculate the volume of antifreeze in the initial solution
The initial solution has 60 liters of 20% antifreeze solution. To find the volume of antifreeze in this solution, we can multiply the volume of the solution by the concentration of antifreeze.
Volume of antifreeze in initial solution = 60 liters * 20%
Step 3: Determine the volume of antifreeze that needs to be added
The volume of antifreeze that needs to be added to achieve the desired concentration can be calculated by subtracting the volume of antifreeze in the initial solution from the desired amount of antifreeze.
Volume of antifreeze to be added = Desired amount of antifreeze - Volume of antifreeze in initial solution
Step 4: Calculate the volume of the 20% solution that needs to be drained
Since we need to replace a certain volume of the 20% solution with the 100% antifreeze, the volume of the 20% solution that needs to be drained can be determined by dividing the volume of antifreeze to be added by the concentration of antifreeze in the initial solution.
Volume of 20% solution to be drained = Volume of antifreeze to be added / Concentration of antifreeze in initial solution
Now, let's calculate the values:
Desired amount of antifreeze = 40% * Total volume
Desired amount of antifreeze = (40/100) * Total volume
Desired amount of antifreeze = 2/5 * Total volume
Volume of antifreeze in initial solution = 60 liters * 20%
Volume of antifreeze in initial solution = 60 liters * (20/100)
Volume of antifreeze in initial solution = 12 liters
Volume of antifreeze to be added = Desired amount of antifreeze - Volume of antifreeze in initial solution
Volume of antifreeze to be added = (2/5 * Total volume) - 12 liters
Volume of 20% solution to be drained = Volume of antifreeze to be added / Concentration of antifreeze in initial solution
Volume of 20% solution to be drained = [(2/5 * Total volume) - 12 liters] / (20/100)
Volume of 20% solution to be drained = [(2/5 * Total volume) - 12 liters] * (100/20)
Volume of 20% solution to be drained = [(2/5 * Total volume) - 12 liters] * 5
Volume of 20% solution to be drained = 2 * Total volume - 60 liters
Thus, the number of liters of the 20% solution that should be drained and replaced with 100% antifreeze to get the desired strength is 2 * Total volume - 60 liters.