Question 477048
Let {{{a}}} = pounds of soybean meal needed
Let {{{b}}} = pounds of cornmeal needed
In words:
(total pounds of protein in final mixture) / (total pounds in final mixture) = 13%
given:
{{{ .16a }}} = pounds of protein in soybean meal
{{{ .08b }}} = pounds of protein in cornmeal
(1) {{{ a + b = 320 }}}
(2) {{{ ( .16a + .08b ) / 320 = .13 }}}
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Multiply both sides of (2) by {{{ 320 }}}
(2) {{{ .16a + .08b = 41.6 }}}
Multiply both sides by {{{ 100 }}}
(2) {{{ 16a + 8b = 4160 }}}
Divide both sides by {{{8}}}
(2) {{{ 2a + b = 520 }}}
Subtract (1) from (2)
(2) {{{ 2a + b = 520 }}}
(1) {{{ -a - b = -320 }}}
{{{ a = 200 }}}
and, since
(1) {{{ a + b = 320 }}}
(1) {{{ 200 + b = 320 }}}
(1) {{{ b = 120 }}}
200 pounds of soybean meal and 120 pounds 
of cornmeal need to be mixed
check answer:
(2) {{{ ( .16a + .08b ) / 320 = .13 }}}
(2) {{{ ( .16*200 + .08*120 ) / 320 = .13 }}}
(2) {{{ ( 32 + 9.6 ) / 320 = .13 }}}
(2) {{{ 41.6 / 320 = .13 }}}
(2) {{{ 41.6 = 41.6 }}}
OK