Question 939413
Let {{{ a }}} = kg of $.80/kg coffee needed
Let {{{ b }}} = kg of $1.20/kg coffee needed
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(1) {{{ a + b = 70 }}}
(2) {{{ ( .8a + 1.2b ) / 70 = 1.08 }}}
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(2) {{{ .8a + 1.2b = 1.08*70 }}}
(2) {{{ .8a + 1.2b = 75.6 }}}
(2) {{{ 8a + 12b = 756 }}}
(2) {{{ 2a + 3b = 189 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2a + 3b = 189 }}}
(1) {{{ -2a - 2b = -140 }}}
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{{{ b = 49 }}}
and
(1) {{{ a + b = 70 }}}
(1) {{{ a = 21 }}}
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21 kg of $.80/kg coffee are needed
49 kg of $1.20/kg coffee are needed
check:
(2) {{{ ( .8*21 + 1.2*49 ) / 70 = 1.08 }}}
(2) {{{ ( 16.8 + 58.8 ) / 70 = 1.08 }}}
(2) {{{ 75.6 = 75.6 }}}
OK