Question 581857
In words:
( liters of acid you end up with ) / ( liters of total solution you end up with ) = 15%
A point of confusion might be that the acid is mixed with something to make
a solution, but they don't tell you what that something is. It really doesn't matter.
Just think of it as water. So 12% acid solution is 12% acid and 88% water.
---------------
Let {{{ a }}} = liters of 12% solution needed
Let {{{ b }}} = liters of 20% solution needed
given:
{{{ .12a }}} = liters of acid in 12% solution
{{{ .2b }}} = liters of acid in 20% solution
--------------------------------
(1) {{{ a + b = 4 }}}
(2) {{{ ( .12a + .2b ) / 4 = .15 }}} 
-------------------------
This is 2 equations with 2 unknowns, so it's solvable
(2) {{{ .12a + .2b = .15*4 }}}
(2) {{{ .12a + .2b = .6 }}}
(2) {{{ 12a + 20b = 60 }}}
(2) {{{ 3a + 5b = 15 }}}
Multiply both sides of (1) by {{{3}}} and
subtract (1) from (2)
(2) {{{ 3a + 5b = 15 }}}
(1) {{{ -3a - 3b = -12 }}}
{{{ 2b = 3 }}}
{{{ b = 1.5 }}}
and, since
(1) {{{ a + b = 4 }}}
(1) {{{ a + 1.5 = 4 }}}
(1) {{{ a = 2.5 }}}
-------------
2.5 liters of 12% solution are needed
1.5 liters of 20% solution are needed
check answer:
(2) {{{ ( .12*2.5 + .2*1.5 ) / 4 = .15 }}} 
(2) {{{ ( .3 + .3 ) / 4 = .15 }}}
(2) {{{ .6/4 = .15 }}}
(2) {{{ .6 = .15*4 }}}
(2) {{{ .6 = .6 }}}
OK