Question 1054026
Let {{{ a }}} = pounds of $9.10/lb coffee needed
Let {{{ b }}} = pounds of $13.70/lb coffee needed
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(1) {{{ a + b = 70 }}}
(2) {{{ ( 9.1a + 13.7b ) / 70 = 13.57 }}}
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(2) {{{ 9.1a + 13.7b = 13.57*70 }}}
(2) {{{ 9.1a + 13.7b = 949.9 }}}
(2) {{{ 91a + 137b = 9499 }}}
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Multiply both sides of (1) by {{{ 91 }}}
and subtract (1) from (2)
(2) {{{ 91a + 137b = 9499 }}}
(1) {{{ -91a - 91b = -6370 }}}
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{{{ 46b = 3129 }}}
{{{ b = 68.022 }}}
and
(1) {{{ a + b = 70 }}}
(1) {{{ a + 68.022 = 70 }}}
(1) {{{ a = 1.978 }}}
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They need 1.978 pounds of Queen City Coffee
They need 68.022 pounds of Organic Free Trade Coffee
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check:
(2) {{{ ( 9.1a + 13.7b ) / 70 = 13.57 }}}
(2) {{{ ( 9.1*1.978 + 13.7*68.022 ) / 70 = 13.57 }}}
(2) {{{ ( 18 + 931.9 ) / 70 = 13.57 }}}
(2) {{{ 949.9 / 70 = 13.57 }}}
(2) {{{ 949.9 = 949.9 }}}
OK
Hope I got it