Question 146767
let x= # of pounds of soybean meal and y=# of pounds of cornmeal 


Since we want a 360 mixture, this means that we have the first equation: 

{{{x+y=360}}}



Also, because we want a "360-lb mixture that is 12% protein" from the mixture of 
soybean meal that is 18% protein and cornmeal that is 9% protein, we have the second equation:


{{{0.18x+0.09y=360(0.12)}}}



{{{0.18x+0.09y=43.2}}} Multiply



{{{10(0.18x+0.09y)=10(43.2)}}} Multiply both sides by 10 to remove the decimals



{{{18x+9y=4320}}} Distribute 



So we have the new system of equations:

{{{system(x+y=360,18x+9y=4320)}}}




{{{x+y=360}}} Start with the first equation



{{{y=360-x}}}  Subtract {{{x}}} from both sides



{{{y=-x+360}}} Rearrange the equation



{{{y=(-x+360)/(1)}}} Divide both sides by {{{1}}}



{{{y=((-1)/(1))x+(360)/(1)}}} Break up the fraction



{{{y=-x+360}}} Reduce




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


Since {{{y=-x+360}}}, we can now replace each {{{y}}} in the second equation with {{{-x+360}}} to solve for {{{x}}}




{{{18x+9highlight((-x+360))=4320}}} Plug in {{{y=-x+360}}} into the first equation. In other words, replace each {{{y}}} with {{{-x+360}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{18x+(9)(-1)x+(9)(360)=4320}}} Distribute {{{9}}} to {{{-x+360}}}



{{{18x-9x+3240=4320}}} Multiply



{{{9x+3240=4320}}} Combine like terms on the left side



{{{9x=4320-3240}}}Subtract 3240 from both sides



{{{9x=1080}}} Combine like terms on the right side



{{{x=(1080)/(9)}}} Divide both sides by 9 to isolate x




{{{x=120}}} Divide






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



So the first part of our answer is: {{{x=120}}}










Since we know that {{{x=120}}} we can plug it into the equation {{{y=-x+360}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-x+360}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-(120)+360}}} Plug in {{{x=120}}}



{{{y=-120+360}}} Multiply



{{{y=240}}} Combine like terms 




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



So the second part of our answer is: {{{y=240}}}










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


So our answers are:


{{{x=120}}} and {{{y=240}}}


which form the ordered pair *[Tex \LARGE \left(120,240\right)] 




So 120 pounds of soybean meal and 240 pounds of cornmeal are needed for the mixture.