Question 631963
Let {{{ a }}} = pounds of soybean meal needed
Let {{{ b }}} = pounds of cornmeal needed
{{{ .14a }}} = pounds of protein in soybean meal needed
{{{ .07b }}} = pounds of protein in cornmeal needed
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(1) {{{ a + b = 280 }}}
(2) {{{ ( .14a + .07b ) / 280 = .12 }}}
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(2) {{{ .14a + .07b = .12*280 }}}
(2) {{{ .14a + .07b = 33.6 }}}
(2) {{{ 14a + 7b = 3360 }}}
(2) {{{ 2a + b = 480 }}}
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Subtract (1) from (2)
(2) {{{ 2a + b = 480 }}}
(1) {{{ -a - b = -280 }}}
{{{ a = 200 }}}
and, since
(1) {{{ a + b = 280 }}}
(1) {{{ 200 + b = 280 }}}
(1) {{{ b = 80 }}}
200 pounds of soybean meal are needed
80 pounds of cornmeal are needed
check:
(2) {{{ ( .14a + .07b ) / 280 = .12 }}}
(2) {{{ ( .14*200 + .07*80 ) / 280 = .12 }}}
(2) {{{ ( 28 + 5.6 ) / 280 = .12 }}}
(2) {{{ 33.6 = .12*280 }}}
(2) {{{ 33.6 = 33.6 }}}
OK