Question 409134
Let {{{a}}} = liters of 50% solution needed
Let {{{b}}} = liters of 25% solution needed
given:
(1) {{{a + b = 250}}}
{{{.5a + .25b}}} = liters of salt in final solution
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In words:
(liters of salt) / (liters of total solution) = 40%
{{{(.5a + .25b) / 250 = .4}}}
{{{.5a + .25b = .4*250}}}
{{{.5a + .25b = 100}}}
(2) {{{50a + 25b = 10000}}} 
Multiply both sides of (1) by {{{25}}}, and
subtract from (2)
(2) {{{50a + 25b = 10000}}} 
(1) {{{-25a - 25b = -6250}}}
{{{25a = 3750}}}
{{{a = 150}}}
and, since
{{{a + b = 250}}}
{{{b = 250 - 150}}}
{{{b = 100}}}
150 liters of 50% solution and 100 liters of 25% solution are needed
check answer:
{{{(.5a + .25b) / 250 = .4}}}
{{{(.5*150 + .25*100) / 250 = .4}}}
{{{(75 + 25)/250 = .4}}}
{{{100 = .4*250}}}
{{{100 = 100}}}
OK