Question 1074468
Let {{{ a }}} = pounds of AFR coffee needed
Let {{{ b }}} = pounds of HPB coffee needed
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(1) {{{ a + b = 20 }}}
(2) {{{ ( 9a + 8b ) / 20 = 8.4 }}}
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(2) {{{ 9a + 8b = 168 }}}
Multiply both sides of (1) by {{{ 8 }}}
and subtract (1) from (2)
(2) {{{ 9a + 8b = 168 }}}
(1) {{{ -8a - 8b = -160 }}}
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{{{ a = 8 }}}
and
(1) {{{ 8 + b = 20 }}}
(1) {{{ b = 12 }}}
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8 pounds of AFR coffee are needed
12 pounds of HPB coffee are needed
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check:
(2) {{{ ( 9a + 8b ) / 20 = 8.4 }}}
(2) {{{ ( 9*8 + 8*12 ) / 20 = 8.4 }}}
(2) {{{ ( 72 + 96 ) / 20 = 8.4 }}}
(2) {{{ 168 = 8.4*20 }}}
(2) {{{ 168 = 168 }}}
OK