Question 810099
Let {{{ a }}} = liters of 10% solution needed
Let {{{ b }}} = liters of 40% solution needed
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(1) {{{ a + b = 30 }}} liters
(2) {{{ ( .1a + .4b ) / 30 = .2 }}}
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(2) {{{ .1a + .4b = 6 }}}
(2) {{{ a + 4b = 60 }}}
Subtract (1) from (2)
(2) {{{ a + 4b = 60 }}}
(1) {{{ -a - b = -30 }}}
{{{ 3b = 30 }}}
{{{ b = 10 }}}
and, since
(1) {{{ a + b = 30 }}} 
(1) {{{ a = 20 }}}
20 liters of 10% solution is needed
10 liters of 40% solution is needed
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check answer:
(2) {{{ ( .1a + .4b ) / 30 = .2 }}}
(2) {{{ ( .1*20 + .4*10 ) / 30 = .2 }}}
(2) {{{ ( 2 + 4 ) / 30 = .2 }}}
(2) {{{ 6/30 = .2 }}}
(2) {{{ 6 = .2*30 }}}
(2) {{{ 6 = 6 }}}
OK