How many liters of a 30% saline solution must be added to 4 liters of a 15% saline solution to obtain a 25% saline solution?
Question
How many liters of a 30% saline solution must be added to 4 liters of a 15% saline solution to obtain a 25% saline solution?
Solution
Let's denote the amount of the 30% saline solution that needs to be added as x liters.
The total amount of salt in the final solution is the sum of the salt in the 15% solution and the salt in the 30% solution.
In the 4 liters of 15% solution, there are 0.15 * 4 = 0.6 liters of salt.
In the x liters of 30% solution, there are 0.30 * x liters of salt.
The final solution has a volume of 4 + x liters and is 25% salt, so it contains 0.25 * (4 + x) liters of salt.
Setting these two expressions for the total amount of salt equal to each other gives us the equation:
0.6 + 0.30x = 0.25 * (4 + x)
Solving this equation for x gives us the amount of the 30% solution that needs to be added.
First, distribute the 0.25 to get:
0.6 + 0.30x = 1 + 0.25x
Then, subtract 0.25x from both sides to get:
0.05x = 0.4
Finally, divide both sides by 0.05 to solve for x:
x = 0.4 / 0.05 = 8 liters
So, 8 liters of the 30% saline solution must be added to the 4 liters of the 15% saline solution to obtain a 25% saline solution.
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