Question 880752
Let {{{ a }}} = liters of 50% solution needed
Let {{{ b }}} = liters of 40% solution needed
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(1) {{{ a + b = 50 }}}
(2) {{{ ( .5a + .4b ) / 50 = .46 }}}
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(2) {{{ .5a + .4b = .46*50 }}}
(2) {{{ .5a + .4b = 23 }}}
(2) {{{ 5a + 4b = 230 }}}
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Multiply both sides of (1) by {{{ 4 }}}
and subtract (1) from (2)
(2) {{{ 5a + 4b = 230 }}}
(1) {{{ -4a - 4b = -200 }}}
{{{ a = 30 }}}
and, since
(1) {{{ a + b = 50 }}}
(1) {{{ b = 20 }}}
30 liters of 50% solution is needed
20 liters of 40% solution is needed
check:
(2) {{{ ( .5*30 + .4*20 ) / 50 = .46 }}}
(2) {{{ ( 15 + 8 ) / 50 = .46 }}}
(2) {{{ 23 = .46*50 }}}
(2) {{{ 23 = 23 }}}
OK