how many gallons of a 12% indicator solution must be mixed with a 20% indicator solution to get 10 gallons of a 14% solution
To determine the number of gallons of a 12% indicator solution needed, we can use the following equation:
(12% solution volume) + (20% solution volume) = 10 gallons
Let x represent the number of gallons of the 12% solution. Since we know that the total volume must be 10 gallons, we can express the volume of the 20% solution as (10 - x) gallons.
Now, let's apply the percentages to set up our equation:
0.12x + 0.20(10 - x) = 0.14(10)
Simplifying this equation step by step:
0.12x + 2 - 0.20x = 1.4
Combining like terms:
-0.08x + 2 = 1.4
Subtracting 2 from both sides:
-0.08x = -0.6
Dividing by -0.08:
x = 7.5
Therefore, you would need 7.5 gallons of the 12% indicator solution and (10 - 7.5) = 2.5 gallons of the 20% indicator solution to obtain 10 gallons of a 14% solution.