Question 174118
{{{.05x + .25y = 66}}}
{{{.15x + .05y = 72}}}
What I would do is multiply both equations by
{{{100}}} to get rid of all decimals
(1) {{{5x + 25y = 6600}}}
(2) {{{15x + 5y = 7200}}}
Now multiply (2) by {{{5}}} and subtract (1) from it
(2) {{{75x + 25y = 36000}}}
(1) {{{5x + 25y = 6600}}}
(3) {{{70x = 29400}}}
{{{x = 420}}}
Substitute this into ((1) or (2)
(1) {{{5x + 25y = 6600}}}
{{{5*420 + 25y = 6600}}}
{{{2100 + 25y = 6600}}}
{{{25y = 4500}}}
{{{y = 180}}}
The answer is {{{x = 420}}} and {{{y = 180}}}
check:
(2) {{{15x + 5y = 7200}}}
{{{15*420 + 5*180 = 7200}}}
{{{6300 + 900 = 7200}}}
{{{7200 = 7200}}}
OK
---------------------------
Let {{{c}}}= pounds of cornmeal reeded
Let {{{s}}}= pounds of soybeans needed
Given is
{{{c + s = 360}}} lbs
In words:
(pounds of protein from soybeans) + (pounds of protein from cornmeal)
divided by (total pounds of mixture) = % protein in mixture
{{{(.18s + .09c) / 360 = .17}}}
multiply both sides by {{{360}}}
{{{.18s + .09c = 61.2}}}
Multiply both sides by {{{100}}}
(1) {{{18s + 9c = 6120}}} and, given is
(2) {{{s + c = 360}}}
Multiply (2) by {{{18}}} and subtract (1) from (2) 
(1) {{{18s + 9c = 6120}}} 
(2) {{{18s + 18c = 6480}}}
(3) {{{9c = 360}}}
{{{c = 40}}} and,since
{{{s + c = 360}}}
{{{s + 40 = 360}}}
{{{s = 320}}}
40 pounds of cornmeal and 320 pound of soybeans are needed
check:
(1) {{{18s + 9c = 6120}}}
{{{18*320 + 9*40 = 6120}}}
{{{5760 + 360 = 6120}}}
{{{6120 = 6120}}}
OK