Let x be the amount of 18% alcohol solution needed, and y be the amount of water needed to make 10 liters of a 12% alcohol solution.
The concentration of the alcohol in the 18% solution is 18%, which means that it contains 18 mL of alcohol per 100 mL of solution.
The concentration of the alcohol in the final 12% solution is 12%, which means that it contains 12 mL of alcohol per 100 mL of solution.
To find the amount of alcohol in the final solution, we can use the equation:
0.12(10) = 0.18x
where 0.12(10) is the total amount of alcohol needed in the final solution, and 0.18x is the amount of alcohol in the 18% solution.
Simplifying this equation, we get:
x = 6.67
This means that we need 6.67 liters of the 18% alcohol solution.
To find the amount of water needed, we can subtract the amount of the 18% alcohol solution from the total volume:
y = 10 - 6.67
y = 3.33
Therefore, we need 6.67 liters of the 18% alcohol solution and 3.33 liters of water to make 10 liters of a 12% alcohol solution.