Question 432534
Let {{{a}}} = liters of 25% acid to be used
Let {{{b}}} = liters of 50% acid to be used
In words:
( acid in solution)/(total solution) = 40%
given:
{{{.25a}}} = acid in 25% solution
{{{.5b}}} = acid in 50% solution
{{{ a + b = 10 }}}
----------------
(1) {{{ (.25a + .5b) / 10 = .4 }}}
(2) {{{a + b = 10 }}}
From (1):
(1) {{{ .25a + .5b = 4 }}}
(1) {{{ 25a + 50b = 400 }}}
Multiply both sides of (2) by {{{25}}}
and subtract (2) from (1)
(1) {{{ 25a + 50b = 400 }}}
(2) {{{-25a - 25b = 250 }}}
{{{ 25b = 150 }}}
{{{ b = 6 }}}
and
(2) {{{a + b = 10 }}}
{{{ a = 10 - 6 }}}  
{{{ a = 4 }}}
4 liters of 25% acid must be used
6 liters of 50% acid must be used
check:
(1) {{{ (.25a + .5b) / 10 = .4 }}}
(1) {{{ (.25*4 + .5*6) / 10 = .4 }}}
(1) {{{ ( 1 + 3)/10 = .4 }}}
(1) {{{ 4 = .4*10 }}}
(1) {{{ 4 = 4 }}}