Question 475288
Let {{{a}}} = liters of water to be added to mixture
Let {{{b}}} = liters of milk in 30 liter mixture
Let {{{c}}} = liters of water in 30 liter mixture
given:
(1) {{{ b + c  = 30 }}}
(2) {{{ b/c = 7/3 }}}
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Multiply both sides of (2) by {{{3c}}}
(2) {{{ 3b = 7c }}}
(2) {{{ b = (7/3)*c }}}
Substitute (2) into (1)
(1) {{{ (7/3)*c + c = 30 }}}
(1) {{{ 7c + 3c = 90 }}}
(1) {{{ 10c = 90 }}
(1) {{{ c = 9 }}}
and
(1) {{{ b + c = 30 }}}
(1) {{{ b + 9 = 30 }}}
(1) {{{ b = 21 }}}
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In words:
(liters of water in final mixture) / (total liters of final mixture) = 40%
{{{ ( a + 9 ) / ( a + 30 ) = .4 }}}
{{{ a + 9 = .4*(a + 30) }}}
{{{ a + 9 = .4a + 12 }}}
{{{ .6a = 3 }}}
{{{ a = 5 }}}
5 liters of water need to be added to the 30 liter mixture