Question 146587
let x= # of pounds of soybean meal and y=# of pounds of cornmeal 


Since we want a 320 mixture, this means that we have the first equation: 

{{{x+y=320}}}



Also, because we want a "320-lb mixture that is 14% protein" from the mixture of 
soybean meal that is 16% protein and "cornmeal that is 8% protein, we have the second equation:


{{{0.16x+0.08y=320(0.14)}}}



{{{0.16x+0.08y=44.8}}} Multiply



{{{10(0.16x+0.08y)=10(44.8)}}} Multiply both sides by 10 to remove the decimals



{{{16x+8y=4480}}} Distribute 



So we have the new system of equations:

{{{system(x+y=320,16x+8y=4480)}}}





{{{x+y=320}}} Start with the first equation



{{{y=320-x}}}  Subtract {{{x}}} from both sides



{{{y=-x+320}}} Rearrange the equation




---------------------


Since {{{y=-x+320}}}, we can now replace each {{{y}}} in the second equation with {{{-x+320}}} to solve for {{{x}}}




{{{16x+8highlight((-x+320))=4480}}} Plug in {{{y=-x+320}}} into the first equation. In other words, replace each {{{y}}} with {{{-x+320}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{16x+(8)(-1)x+(8)(320)=4480}}} Distribute {{{8}}} to {{{-x+320}}}



{{{16x-8x+2560=4480}}} Multiply



{{{8x+2560=4480}}} Combine like terms on the left side



{{{8x=4480-2560}}}Subtract 2560 from both sides



{{{8x=1920}}} Combine like terms on the right side



{{{x=(1920)/(8)}}} Divide both sides by 8 to isolate x




{{{x=240}}} Divide






-----------------First Answer------------------------------



So the first part of our answer is: {{{x=240}}}










Since we know that {{{x=240}}} we can plug it into the equation {{{y=-x+320}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-x+320}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-(240)+320}}} Plug in {{{x=240}}}



{{{y=-240+320}}} Multiply



{{{y=80}}} Combine like terms 




-----------------Second Answer------------------------------



So the second part of our answer is: {{{y=80}}}










-----------------Summary------------------------------


So our answers are:


{{{x=240}}} and {{{y=80}}}


which form the ordered pair *[Tex \LARGE \left(240,80\right)] 




So there are 240 pounds of Soybean meal and 80 pounds of cornmeal