Question 798711
Let {{{ a }}} = liters of 75% solution needed
Let {{{ b }}} = liters of 25% solution needed
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(1) {{{ a + b = 30 }}}
(2) {{{ ( .75a + .25b ) / 30 = .45 }}}
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(2) {{{ .75a + .25b = .45*30 }}}
(2) {{{ .75a + .25b = 13.5 }}}
(2) {{{ 75a + 25b = 1350 }}}
Multiply both sides of (1) by {{{ 25 }}} and
subtract (1) from (2)
(2) {{{ 75a + 25b = 1350 }}}
(1) {{{ -25a - 25b = -750 }}}
{{{ 50a = 600 }}}
{{{ a = 12 }}}
and, since
(1) {{{ a + b = 30 }}}
(1) {{{ b = 18 }}}
12 liters of 75% solution are needed
18 liters of 25% solution are needed
check:
(2) {{{ ( .75a + .25b ) / 30 = .45 }}}
(2) {{{ ( .75*12 + .25*18 ) / 30 = .45 }}}
(2) {{{ ( 9 + 4.5 ) / 30 = .45 }}}
(2) {{{ 13.5 = .45*30 }}}
(2) {{{ 13.5 = 13.5 }}}