Question 802380
Let {{{ a }}} = liters of 60% alcohol solution needed
Let {{{ b }}} = liters of 30% alcohol solution needed
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(1) {{{ a + b = 12 }}}
(2) {{{ ( .6a + .3b ) / 12 = .4 }}}
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(2) {{{ .6a + .3b = 4.8 }}}
(2) {{{ 6a + 3b = 48 }}}
(2) {{{ 2a + b = 16 }}}
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Subtract (1) from (2)
(2) {{{ 2a + b = 16 }}}
(1) {{{ -a - b = -12 }}}
{{{ a = 4 }}}
and, since
(1) {{{ 4 + b = 12 }}}
(1) {{{ b = 8 }}}
4 liters of 60% alcohol solution are needed
8 liters of 30% alcohol solution are needed
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check:
(2) {{{ ( .6a + .3b ) / 12 = .4 }}}
(2) {{{ ( .6*4 + .3*8 ) / 12 = .4 }}}
(2) {{{ ( 2.4 + 2.4 ) / 12 = .4 }}}
(2) {{{ 4.8/12 = .4 }}}
(2) {{{ 4.8 = 4.8 }}}
OK