Question 683962
Let {{{ a }}} = pounds of coffee A needed
Let {{{ b }}} = pounds of coffee B needed
Let {{{ c }}} = pounds of coffee C needed
given:
(1) {{{ c = 2a }}}
(2) {{{ a + b + c = 55 }}}
(3) {{{ ( 15.21a + 12.99b + 10.19c ) / 55 = 12.61 }}}
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Multiply both sides of (3) by {{{ 100 }}}
(3) {{{ ( 1521a + 1299b + 1019c ) / 55 = 1261 }}}
(3) {{{  1521a + 1299b + 1019c  = 69355 }}}
Multiply both sides of (2) by {{{ 1019 }}} and
subtract (2) from (3)
(3) {{{ 1521a + 1299b + 1019c =  69355 }}}
(2) {{{  -1019a - 1019b - 1019c = -56045 }}}
{{{ 502a + 280b = 13310 }}}
{{{ 280b = 13310 - 502a }}}
{{{ b = 1331/28 - ( 251/140 )*a }}}
Plug this into (2)
(2) {{{ a + b + c = 55 }}}
(2) {{{ a + 1331/28 - ( 251/140 )*a + 2a = 55 }}}
(2) {{{ 3a - ( 251/140 )*a  = 55 -  1331/28 }}}
(2) {{{ a*( 3 - 1.7929 ) = 55 - 47.5357 }}}
(2) {{{ 1.2071a = 7.4643 }}}
(2) {{{ a = 6.1837 }}}
and, since
(1) {{{ c = 2a }}}
(1) {{{ c = 2*6.1837 }}}
(1) {{{ c = 12.3673 }}}
and
(2) {{{ a + b + c = 55 }}}
(2) {{{ 6.1837 + b + 12.3673 = 55 }}}
(2) {{{ b = 55 - 6.1837 - 12.3673 }}}
(2) {{{ b = 55 - 18.5510 }}}
(2) {{{ b = 36.449 }}}
6.1837 pounds of coffee A are needed
36.449 pounds of coffee B are needed
12.3673 pounds of coffee C are needed
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check:
(2) {{{ a + b + c = 55 }}}
(2) {{{ 6.1837 + 36.449 + 12.3673 = 55 }}}
(2) {{{ 55 = 55 }}}
and
(3) {{{ ( 15.21a + 12.99b + 10.19c ) / 55 = 12.61 }}}
(3) {{{ ( 15.21*6.1837 + 12.99*36.449 + 10.19*12.3673 ) / 55 = 12.61 }}}
(3) {{{  94.0541 + 473.4725 + 126.0228 = 55*12.61 }}}
(3) {{{ 693.5494 = 693.55 }}}
close enough