We can start by using the concept of percentage concentration, which states that the percentage of alcohol in a solution is equal to the number of milliliters of alcohol in the solution divided by the number of milliliters of the solution, multiplied by 100.
Let's call the number of milliliters of Solution B that Linda uses x.
We know that:
Solution A is 50% alcohol, so it contains 50/100 = 0.5 = 1/2 of alcohol.
Solution B is 10% alcohol, so it contains 10/100 = 0.1 = 1/10 of alcohol.
The resulting mixture is a 20% alcohol solution.
Linda uses 400 milliliters of Solution A.
We can set up an equation using the percentage concentration concept and the information provided:
(400 * 1/2) + (x * 1/10) = (x + 400) * (20/100)
Solving for x:
200 + x/10 = (x + 400) * 0.2
x/10 = (x + 400) * 0.2 - 200
x/10 = x * 0.2 + 80
9x/10 = x * 0.2 + 80
9x = x*2 + 800
x = 800/8 = 100
So, Linda uses 100 milliliters of Solution B to make the resulting mixture a 20% alcohol solution.