Question 1032038
Let {{{ a }}} = liters of alcohol in the 
initial mixture
Let {{{ w }}} = liters of water in the
initial mixture
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(1) {{{ a/w = 12/5 }}}
(2) {{{ a / ( w + 14 ) = 4/3 }}}
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(1) {{{ 5a = 12w }}}
(1) {{{ 5a - 12w  = 0 }}}
and
(2) {{{ 3a = 4*( w + 14 ) }}}
(2) {{{ 3a = 4w + 56 }}}
(2) {{{ 3a - 4w = 56 }}}
(2) {{{ 9a - 12w = 168 }}}
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Subtract (1) from (2)
(2) {{{ 9a - 12w = 168 }}}
(1) {{{ -5a + 12w  = 0 }}}
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{{{ 4a  = 168 }}}
{{{ a = 42 }}}
and
(1) {{{ 5a = 12w }}}
(1) {{{ w = (5/12)*a }}}
(1) {{{ w = (5/12)*42 }}}
(1) {{{ w = 17.5 }}}
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There are 42 liters of alcohol in the mixture
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check:
(1) {{{ a/w = 12/5 }}}
(1) {{{ a/w = 2.4 }}}
(1) {{{ 42/17.5 = 2.4 }}}
(1) {{{ 2.4 = 2.4 }}}
OK
(2) {{{ a / ( w + 14 ) = 4/3 }}}
(2) {{{ 42 / ( 17.5 + 14 ) = 4/3 }}}
(2) {{{ 42 / 31.5 = 4/3 }}}
(2) {{{ 4/3 = 4/3 }}}
OK