Question 1104555
Let {{{ a }}} = liters of 20% solution needed
Let {{{ b }}} = liters of 50% solution needed
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(1) {{{ a + b = 12 }}}
(2) {{{ ( .2a + .5b ) / 12 = .4 }}}
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(2) {{{ .2a + .5b = 4.8 }}}
(2) {{{ 2a + 5b = 48 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
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(2) {{{ 2a + 5b = 48 }}}
(1) {{{ -2a - 2b = -24 }}}
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{{{ 3b = 24 }}}
{{{ b = 8 }}}
and
(1) {{{ a + 8 = 12 }}}
(1) {{{ a = 4 }}}
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4 liters of 20% solution are needed
8 liters of 50% solution are needed
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check:
(2) {{{ ( .2a + .5b ) / 12 = .4 }}}
(2) {{{ ( .2*4 + .5*8 ) / 12 = .4 }}}
(2) {{{ ( .8 + 4 ) / 12 = .4 }}}
(2) {{{ 4.8 = .4*12 }}}
(2) {{{ 4.8 = 4.8 }}}
OK