Question 567119
Let {{{ a }}} = pounds of birdseed needed
Let {{{ b }}} = pounds of sunflower seeds needed
given:
(1) {{{ a + b = 40 }}}
(2) {{{ ( .59a + .89b ) / 40 = .76 }}}
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(2) {{{ .59a + .89b = .76*40 }}}
(2) {{{ .59a + .89b = 30.4 }}}
(2) {{{ 59a + 89b = 3040 }}}
Multiply both sides of (1) by {{{ 59 }}}
and subtract (1) from (2)
(2) {{{ 59a + 89b = 3040 }}}
(1) {{{ -59a - 59b = -2360 }}}
{{{ 30b = 680 }}}
{{{ b = 22.667 }}}
and
(1) {{{ a + 22.667 = 40 }}}
(1) {{{ a = 17. 333 }}}
17 and 1/3 pounds of birdseed are needed
22 and 2/3 pounds of sunflower seed are needed
check answer:
(2) {{{ ( .59*17.333 + .89*22.667 ) / 40 = .76 }}} 
(2) {{{ ( 10.22666 + 20.17333 ) / 40 = .76 }}}
(2) {{{ 30.40003 = .76*40 }}}
(2) {{{ 30.40003 = 30.4 }}}
close enough, error due to rounding off