To solve for the amount of 63% chlorine solution and 12% chlorine solution needed, we can use the equation:
m1 * v1 * c1 = m2 * v2 * c2
where m1, m2 are the masses of the solutions, v1, v2 are the volumes of the solutions, and c1, c2 are their concentrations.
Let's call the volume of the 63% solution "x". The volume of the 12% solution is (3876 - x) ml.
We can now use the equation to find the value of x:
63 * x * 1 = 15 * 3876 * 1
And:
12 * (3876 - x) * 1 = 15 * 3876 * 1
Now we have a system of two equations:
63x = 5.8364 * 3876
And:
12 * 3876 - 12x = 5.8364 * 3876
We can now solve for x:
63x = 22,719.68
x = 361.5 ml
So, 361.5 ml of the 63% solution and 3876 - 361.5 = 3514.5 ml of the 12% solution must be mixed to produce 3876 ml of 15% solution.