Question 1041870
Let {{{ a }}} = liters of 15% solution needed
Let {{{ b }}} = liters of 35% solution needed
Let {{{ c }}} = liters of 80% solution needed
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(1) {{{ a + b + c = 100 }}}
(2) {{{ c = 2b }}}
(3) {{{ ( .15a + .35b + .8c ) / 100 = .3 }}}
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(3) {{{ .15a + .35b + .8c = 30 }}}
(3) {{{ 15a + 35b + 80c  3000 }}}
(3) {{{ 3a + 7b + 16c = 600 }}}
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Multiply both sides of (1) by {{{ 3 }}} and
subtract (1) from (3)
(3) {{{ 3a + 7b + 16c = 600 }}}
(1) {{{ -3a - 3b - 3c = -300 }}}
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{{{ 4b + 13c = 300 }}}
Substitute (2) into this result
{{{ 4b + 13*(2b) = 300 }}}
{{{ 4b + 26b = 300 }}}
{{{ 30b = 300 }}}
{{{ b = 10 }}}
and
(2) {{{ c = 2b }}}
(2) {{{ c = 2*10 }}} 
(2) {{{ c = 20 }}}
and
(1) {{{ a + 10 + 20 = 100 }}}
(1) {{{ a = 100 - 30 }}}
(1) {{{ a = 70 }}}
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70 liters of 15% solution is needed
10 liters of 35% solution is needed
20 liters of 80% solution is needed
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check:
(3) {{{ ( .15a + .35b + .8c ) / 100 = .3 }}}
(3) {{{ ( .15*70 + .35*10 + .8*20 ) / 100 = .3 }}}
(3) {{{ ( 10.5 + 3.5 + 16 ) / 100 = .3 }}}
(3) {{{ 10.5 + 3.5 + 16 = 30 }}}
(3) {{{ 30 = 30 }}}
OK