A 90% KCN solution is diluted with water to make a solution of 60% acid. When 3 gallons of water is added to dilute it again, the solution becomes 40% acid.
a. how much water was added to the solution on the first instance?
b. what was the original volume of the 90% acid solution?
K = the amount of KCN
w = the amount of water
a = amount of water added
K = 2 / 5
w = 18 / 5
a = 2
You should be able to answer a and b now.
By the way, KCN is the salt of a strong base KOH and a weak acid HCN therefore is it a base not an acid.
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.