We have to find the volume of each solution to make 16 gallons of a blend of 13% disinfectant solution.
Solution A has 11% disinfectant, while Solution B has 19% disinfectant.
We can call A and B to the volume of each respective solution.
The total volume (16 gallons) is made only from solutions A and B, so the sum of their volumes is equal to the total volume.
Then, we can write:
We can repeat this analyisis but only with the volume of pure disinfectant.
The total volume will be 0.13*16 = 2.08 gallons.
This will be made of the volume of disinfectant of solution A, which is 0.11*A, and the volume of disinfectant of solution B, which is 0.19*B.
Then, we can write:
We can now use the first equation to express B in function of A:
We can then replace B in the second equation and solve for A as:
Now, we can calculate B as:
Answer:
Volume of 11% disinfectant solution = 12 gallons.
Volume of 19% disinfectant solution = 4 gallons.