How much of a 50% alcohol solution should we mix with 10 gallons of a 35% solution to get a 40% solution?

Solution

Let x is the amount of 50% solution which we need.  It means that there will be gallons of the 40% solution once we're done mixing the two.

Following is the basic work equation for this problem.

Now, plug in the volumes & solve for x.

0.5x + 0.35 (10) =0.4 ( x + 10)

0.5x + 3.5 + 0.4x + 4

0.1x + 0.5

x =0.5/0.1 = 5 gallons

Thus, we required 5 gallons of the 50% solution to get a 40% solution.