Question 776068
Let {{{ a }}} = pounds of  31 cents/pound feed needed
Let {{{ b }}} = pounds of 77 cents/pound feed needed
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(1) {{{ a + b = 27 }}}
(2) {{{ ( 31a + 77b ) / 27 = 46 }}} ( in terms of cents )
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(2) {{{ 31a + 77b = 1242 }}}
Multiply both sides of (1) by {{{ 31 }}}
and subtract (1) from (2)
(2) {{{ 31a + 77b = 1242 }}}
(1) {{{ -31a - 31b = -837 }}}
{{{ 46b = 405 }}}
{{{ b = 8.804 }}}
and
(1) {{{ a + b = 27 }}}
(1) {{{ a = 18.196 }}}
18.196 pounds of cheaper seed are needed
check:
(2) {{{ ( 31a + 77b ) / 27 = 46 }}} 
(2) {{{ ( 31*18.196 + 77*8.804 ) / 27 = 46 }}} 
(2) {{{ ( 564.076 + 677.908 ) / 27 = 46 }}}
(2) {{{ 1241.984 = 27*46 }}}
(2) {{{ 1241.984 = 1242 }}}
close enough