Question

How many gallons of 15% iodine solution should be mixed with 40% iodine solution to make 100 gallons of a 20% solution?

Answer 1

the amount of iodine in the mixture is the sum of all the iodine in the parts:

.20*100 = .15x + .40(100-x)
20 = .15x + 40 - .40x
.25x = 20
x = 80

So, mix 80 gals of 15% with 20 gals of 40%

Note that 20% is 1/5 of the way from 15% to 40%, so 1/5 of the mixture is the 40% solution.