Question 185934
Let {{{s}}}= pounds of soybean meal needed
Let {{{c}}}= pounds of cornmeal needed
given:
{{{.16s}}}= pounds of protein in soybean meal needed
{{{.08c}}}= pounds of protein in cornmeal needed
{{{320}}}= pounds of final mixture
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(1) {{{(.16s + .08c)/320 = .1}}}
(2) {{{s + c = 320}}}
Multiply both sides of (1) by {{{320}}}
(1) {{{.16s + .08c = .1*320}}}
(1) {{{.16s + .08c = 32}}}
Multiply both sides of (2) by {{{.08}}}
(2) {{{.08s + .08c = 25.6}}}
Subtract (2) from (1)
(1) {{{.16s + .08c = 32}}}
(2) {{{-.08s - .08c = -25.6}}}
(3) {{{.08s = 6.4}}}
(3) {{{s = 80}}}
and
(2) {{{s + c = 320}}}
(2) {{{80 + c = 320}}}
(2) {{{c = 240}}}
80 pounds of soybean meal and 240 pounds of cornmeal
are needed
check:
(1) {{{(.16*80 + .08*240)/320 = .1}}}
(1) {{{(12.8 + 19.2)/320 = .1}}}
(1) {{{32/320 = .1}}}
(1) {{{.1 = .1}}}
OK