Question 329365
In words:
(pounds of protein in final mixture)/(pounds of final mixture) = 10%
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Let {{{c}}} = pounds of cornmeal in final mixture
Let {{{s}}} = pounds of soybean meal in final mixture
given:
{{{.14s}}} = pounds of protein in soybean meal
{{{.07c}}} = pounds of protein in corn meal
(1) {{{s + c = 280}}}
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{{{(.14s + .07c)/280 = .1}}}
{{{.14s + .07c = 28}}}
(2) {{{14s + 7c = 2800}}}
Multiply both sides of (1) by {{{7}}} and
subtract from (2)
(2) {{{14s + 7c = 2800}}}
(1) {{{-7s - 7c = 1960}}}
{{{7s = 840}}}
{{{s = 120}}}
And, since
(1) {{{s + c = 280}}}
{{{120 + c = 280}}}
{{{c = 160}}}
160 pounds of cornmeal and 
120 pounds of soybean meal are needed
check:
{{{(.14s + .07c)/280 = .1}}}
{{{(.14*120 + .07*160)/280 = .1}}}
{{{(16.8 + 11.2)/280 = .1}}}
{{{28/280 = .1}}}
{{{.1 = .1}}}
OK