Question 714695
You ask, what would be the formula!  Very good question.  Let's solve the problem purely symbolically!


P = current percentage concentration of alcohol, 10%
T = target percentage that we want, 8%
M = volume of solution or mixture currently, 40 gallons
w = how many gallons of water to add (volume) to reach T; UNKNOWN


ONE equation to relate the percentages used in the description of the problem:
(Amount of Alcohol)/(Amount of Solution)=(Percent Alcohol)


{{{highlight(M*P/(M+w)=T)}}}, Our fundamental equation.  We will keep the next few steps in symbols, variables only.


{{{MP=T(M+w)}}}
{{{MP=TM+Tw}}}
{{{TM+Tw=MP}}}
{{{Tw=MP-TM}}}
{{{w=(MP-MT)/T}}}, a reasonable form already
{{{highlight(w=M(P-T)/T)}}}, Our fundamental formula for how much water to add, as gallons volume