50 quarts of 60% solution and 50 quarts of 40% solution.
You want a total of 100 quarts, so we'll use the following expressions
x = amount of 60% solution
(100 - x) = amount of 40% solution.
The total amount of alcohol will be
0.6x + 0.4(100-x)
We want the final result to be 100 quarts of 50% solution, so we express that as
0.5 * 100
Now we set them equal to each other, and solve for x
0.6x + 0.4(100-x) = 0.5 * 100
Distribute the .4
0.6x + 0.4*100 - 0.4x = 0.5 * 100
0.6x + 40 - 0.4x = 50
Subtract 40 from both sides and combine the x terms
0.2x = 10
Divide both sides by 0.2
x = 50
Now we know we need 50 quarts of the 60% solution. And we need (100 - 50) = 50 quarts of the 40% solution as well.
