Question 127817
We want to end up with a 10 liters of 40% solution.  That means that of the 10 liters, 4 liters are the chemical, and the rest is something else.  To make this mixture, we want to mix x liters of 75% solution with enough 25% solution to make the full 10 liters.  So the amount of 25% solution must be {{{10-x}}} liters.


The 75% solution has {{{.75x}}} liters of chemical, and the 25% solution has {{{.25(10-x)}}} liters of chemical.  These two quantities must add up to the 4 liters that make up the amount of chemical in the final solution (geez, that sounds ominous!).


So:

{{{.75x+.25(10-x)=4}}}


{{{.75x-.25x+2.5=4}}}


{{{.5x=4-2.5=1.5}}}


{{{x=3}}}


So there are 3 liters of 75% solution, meaning that there are 7 liters of 25% solution.


Check:

{{{3*.75=2.25}}}
{{{7*.25=1.75}}}


{{{2.25+1.75=4}}}