Question 1144648
Let {{{ a }}} = gallons of 40% solution needed
Let {{{ b }}} = gallons of 80% solution needed
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(1) {{{ ( .4a + .8b ) / 40 = .5 }}}
(2) {{{ a + b = 40 }}}
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(1) {{{ .4a + .8b = 20 }}}
(1) {{{ 4a + 8b = 200 }}}
(1) {{{ a + 2b = 50 }}} subtract (2) from (1)
(2) {{{ -a - b = 40 }}}
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{{{ b = 10 }}}
and
(2) {{{ a + 10 = 40 }}}
(2) {{{ a = 30 }}}
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30 gallons of 40% solution and 10 gallons of 
80% solution are needed
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check:
(1) {{{ ( .4a + .8b ) / 40 = .5 }}}
(1) {{{ ( .4*30 + .8*10 ) / 40 = .5 }}}
(1) {{{ ( 12 + 8 ) / 40 = .5 }}}
(1) {{{ 20/40 = .5 }}}
(1) {{{ 20 = 20 }}}
OK