Question 570856
Let {{{ a }}} = liters of 30% solution needed
Let {{{ b }}} = liters of 60% solution needed
given:
(1) {{{ a + b = 90 }}}
(2) {{{ ( .3a + .6b ) / 90 = .5 }}}
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(2) {{{ .3a + .6b = .5*90 }}}
(2) {{{ .3a + .6b = 45 }}}
(2) {{{ 3a + 6b = 450 }}}
Multiply both sides of (1) by {{{ 3 }}}
and subtract (1) from (2)
(2) {{{ 3a + 6b = 450 }}}
(1) {{{ -3a - 3b = -270 }}}
{{{ 3b = 180 }}}
{{{  b = 60 }}}
and, since
(1) {{{ a + b = 90 }}}
(1) {{{ a + 60 = 90 }}}
(1) {{{ a = 30 }}}
30 liters of 30% solution are needed
60 liters of 60% solution are needed
check:
(2) {{{ ( .3a + .6b ) / 90 = .5 }}}
(2) {{{ ( .3*30 + .6*60 ) / 90 = .5 }}}
(2) {{{ ( 9 + 36 ) / 90 = .5 }}}
(2) {{{ 45/90 = .5 }}}
(2) {{{ 45 = 45 }}}
OK