Question 27003
There's a little trick that is the key. Once you get it, it's hard to forget.
If I've got 100 gallons total, and it's divided into two parts, then
I can call those two parts S and (100 - S) where S is an unknown.
The rest is easy.
You've got a 12% solution and a 20% solution to start with
Ask yourself how much alcohol are in those solutions?
(12%)*(S) + (20%)*(100 - S)
What do you want that much alcohol to equal?
You want it to equal (18%)*(100), the final concentration
(12%)*(S) + (20%)*(100 - S) = (18%)*(100)
{{{(.12 * S) + .2 * (100 - S) = 18}}}
{{{(.12 * S) + 20 - (.2 * S) = 18}}}
{{{(-.08 * S) = -2}}}
{{{S = 25}}}
check
.12*25 + .2(100 - 25) = 18
3 + 15 = 18
It checks