Question 1033350
Let {{{ a }}} = pounds of Rift Valley coffee
blend needed
Let {{{ b }}} = pounds of Mexican Shade Grown
coffee needed
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(1) {{{ a + b = 20 }}}
(2) {{{ ( 8a + 10.4b ) / 20 = 8.12 }}}
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(2) {{{ 8a + 10.4b = 162.4 }}}
(2) {{{ 80a + 104b = 1624 }}}
(2) {{{ 10a + 13b = 203 }}}
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Multiply both sides of (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 10a + 13b = 203 }}}
(1) {{{ -10a - 10b = -200 }}}
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{{{ 3b = 3 }}}
{{{ b = 1 }}}
and
(1) {{{ a + 1 = 20 }}}
(1) {{{ a = 19 }}}
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19 pounds of Rift Valley coffee
blend are needed
1 pound of Mexican Shade Grown
coffee is needed
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check:
(2) {{{ ( 8a + 10.4b ) / 20 = 8.12 }}}
(2) {{{ ( 8*19 + 10.4*1 ) / 20 = 8.12 }}}
(2) {{{ ( 152 + 10.4 ) / 20 = 8.12 }}}
(2) {{{ 162.4 = 20*8.12 }}}
(2) {{{ 162.4 = 162.4 }}}
OK