Question 839264
Let {{{ a }}} = bushels of soybeans needed
Let {{{ b }}} = bushels of wheat needed
{{{ 8.5a }}} = cost of {{{ a }}} bushels of soybeans
{{{ 4.5b }}} = cost of {{{ b }}} bushels of wheat
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(1) {{{ a + b = 800 }}}
(2) {{{ ( 8.5a + 4.5b ) / 800 = 5.5 }}}
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(2) {{{ 8.5a + 4.5b = 5.5*800 }}}
(2) {{{ 8.5a + 4.5b = 4400 }}}
(2) {{{ 85a + 45b = 44000 }}}
(2) {{{ 17a + 9b = 8800 }}}
Multiply both sides of (1) by {{{ 9 }}}
and subtract (1) from (2)
(2) {{{ 17a + 9b = 8800 }}}
(1) {{{ -9a - 9b = -7200 }}}
{{{ 8a = 1600 }}}
{{{ a = 200 }}}
and, since
(1) {{{ a + b = 800 }}}
(1) {{{ 200 + b = 800 }}}
(1) {{{ b = 600 }}}
200 bushels of soybeans are needed
600 bushels of wheat are needed
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check:
(2) {{{ ( 8.5a + 4.5b ) / 800 = 5.5 }}}
(2) {{{ ( 8.5*200 + 4.5*600 ) / 800 = 5.5 }}}
(2) {{{ ( 1700 + 2700 ) / 800 = 5.5 }}}
(2) {{{ 4400 = 5.5*800 }}}
(2) {{{ 4400 = 4400 }}}
OK