A farmer needs a 50% solution of alcohol. How many liters of pure alcohol must the farmer addto 10 liters of 40% alcohol to get the proper solution?

To solve this problem, we can use the concept of mixtures and solutions.

Step 1: Identify the initial and final concentrations of alcohol.

The initial concentration of alcohol is 40% and the farmer needs a 50% solution.

Step 2: Let's denote the amount of pure alcohol to be added as 'x' liters.

Step 3: Write an equation that represents the total amount of pure alcohol in the final solution.

The total amount of pure alcohol in the final solution is the sum of the pure alcohol in the initial solution and the pure alcohol added.

So, 0.40 * 10 (from the 40% solution) + x (the pure alcohol added) = 0.50 * (10 + x) (the final solution)

Step 4: Solve the equation for 'x'.

4 + x = 5 + 0.5x

0.5x = 1

x = 2

So, the farmer needs to add 2 liters of pure alcohol to the 10 liters of 40% alcohol solution to get a 50% alcohol solution.