Question 451165
Let {{{a}}} = liters of 25% solution needed
Let {{{b}}} = liters of 50% solution needed
given:
(1) {{{ a + b = 10 }}} liters
(2) {{{ (.25a + .5b) / 10 = .4 }}} 
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(2) {{{ .25a + .5b = 4 }}}
(2) {{{ 25a + 50b = 400 }}}
Multiply both sides of (1) by {{{25}}} and
subtract (1) from (2)
(2) {{{ 25a + 50b = 400 }}}
(1) {{{ -25a - 25b = -250 }}}
{{{ 25b = 150 }}}
{{{ b = 6 }}}
and, since
(1) {{{ a + b = 10 }}}
{{{ a = 4 }}}
4 liters of 25% solution are needed
6 liters of 50% solution are needed
check:
(2) {{{ (.25a + .5b) / 10 = .4 }}} 
(2) {{{ (.25*4 + .5*6) / 10 = .4 }}} 
(2) {{{ (1 + 3)/10 = .4 }}}
(2) {{{ 4/10 = .4 }}}
OK