To determine the amount of water that needs to be added to the 50 gallons of a 12% alcohol solution to obtain an 8% alcohol solution, we can set up a proportion based on the alcohol content. Here's how we can calculate it:
Let "x" represent the amount of water to be added (in gallons).
Alcohol in the original solution: 12% of 50 gallons = 0.12 * 50 = 6 gallons (since 12% of 50 is 6).
Alcohol in the final solution: 8% of (50 + x) gallons.
We can set up the proportion:
6 gallons / 50 gallons = 8% / 100%
Now, we can cross-multiply and solve for "x":
6 gallons * 100% = 8% * (50 + x) gallons
600 gallons = 4 (50 + x) gallons
600 = 200 + 4x
4x = 600 - 200
4x = 400
x = 400 / 4
x = 100
Therefore, 100 gallons of water must be added to the 50 gallons of a 12% alcohol solution to obtain a solution with 8% alcohol.