how many liters of water must be added to 30 liters of a 20% alcohol solution to dilute it to a 15% solution?

To solve this problem, we can use a simple formula to find the amount of water that needs to be added.

Step 1: Convert the concentrations to decimal form.
20% alcohol solution = 0.20
15% alcohol solution = 0.15

Step 2: Set up the equation using the formula:
(concentration of solution 1) * (volume of solution 1) = (concentration of solution 2) * (volume of solution 2)

Here, the volume of solution 1 is 30 liters and the volume of solution 2 is 30 liters + the volume of water to be added.

(0.20) * (30) = (0.15) * (30 + x)

Step 3: Solve the equation for x (the volume of water to be added).

6 = 4.5 + 0.15x
1.5 = 0.15x

Step 4: Solve for x by dividing both sides of the equation by 0.15.

x = 1.5 รท 0.15
x = 10

Therefore, 10 liters of water must be added to 30 liters of a 20% alcohol solution to dilute it to a 15% solution.