Question 1026009
Let {{{ a }}} = quarts of 30% solution needed
Let {{{ b }}} = quarts of 70% solution needed
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(1) {{{ a + b = 20 }}}
(2) {{{ ( .3a + .7b ) / 20 = .4 }}}
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(2) {{{ .3a + .7b = 8 }}}
(2) {{{ 3a + 7b = 80 }}}
Multiply both sides of (1) by {{{ 3 }}}
and subtract (1) from (2)
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(2) {{{ 3a + 7b = 80 }}}
(1) {{{ -3a - 3b = -60 }}}
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{{{ 4b = 20 }}}
{{{ b = 5 }}}
and
(1) {{{ a +5 = 20 }}}
(1) {{{ a = 15 }}}
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15 quarts of 30% solution is needed
5 quarts of 70% solution is needed
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check:
(2) {{{ ( .3a + .7b ) / 20 = .4 }}}
(2) {{{ ( .3*15 + .7*5 ) / 20 = .4 }}}
(2) {{{ ( 4.5 + 3.5 ) / 20 = .4 }}}
(2) {{{ 8/20 = .4 }}}
(2) {{{ 8 = 8 }}}
OK