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?

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.