Question 147290
Let {{{x}}}= amount of 30% solution to be drained and replaced with 
70% solution
Currently, how much chemical is in the 30% solution?
{{{.3*80 = 24}}} gallons
How much chemical will be in the amount drained off?
{{{.3x}}}
Then how much chemical will be in the solution that is put back in?
{{{.7x}}}
In words:
(amount of chemical I end up with) / (amount of solution I end up with) =
final strength of solution
{{{(24 - .3x + .7x) / (80 - x + x) = .4}}}
{{{(24 + .4x) / 80 = .4}}}
{{{24 + .4x = .4*80}}}
{{{24 + .4x = 32}}}
{{{.4x = 8}}}
{{{x = 20}}}
20 gallons must be drained off and replaced with 70% solution
check answer:
{{{(24 + .4x) / 80 = .4}}}
{{{24 + .4*20) / 80 = .4}}}
{{{24 + 8) / 80 = .4}}}
{{{32/80 = .4}}}
{{{32 = 32}}}
OK