How many ml of a 20% solution should be added to 50 ml of a 40% solution to obtain a 25% solution?

To determine how many milliliters of a 20% solution need to be added to 50 ml of a 40% solution to create a 25% solution, we begin by setting up an equation based on the concentrations and the volumes.

Let ( x ) be the volume of the 20% solution to be added. The total volume after adding ( x ) ml of the 20% solution will be ( 50 + x ) ml. The final solution needs to have a concentration of 25%, so we set up the equation balancing the total amount of active ingredient before and after mixing.

The total amount of active ingredient in the original solutions can be calculated as follows:

1. The amount of active ingredient in the 40% solution:

[

0.40 \times 50 = 20 \text{ ml}

]

2. The amount of active ingredient in the 20% solution:

[

0.20 \times x

]

Now, the total amount of active ingredient in the final solution will be:

[

20 + 0.20x

]

To find the concentration of the final mixture, we need to set up the