SOLUTION: Soybean meal is 18% protein and cornmeal is 9% protein. How many pounds of each mixture should be mixed together in order to get 360lb mixture that is 12% protein?

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Question 146767: Soybean meal is 18% protein and cornmeal is 9% protein. How many pounds of each mixture should be mixed together in order to get 360lb mixture that is 12% protein?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2By=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%2B0.09y=360%280.12%29


0.18x%2B0.09y=43.2 Multiply


10%280.18x%2B0.09y%29=10%2843.2%29 Multiply both sides by 10 to remove the decimals


18x%2B9y=4320 Distribute


So we have the new system of equations:
system%28x%2By=360%2C18x%2B9y=4320%29



x%2By=360 Start with the first equation


y=360-x Subtract x from both sides


y=-x%2B360 Rearrange the equation


y=%28-x%2B360%29%2F%281%29 Divide both sides by 1


y=%28%28-1%29%2F%281%29%29x%2B%28360%29%2F%281%29 Break up the fraction


y=-x%2B360 Reduce



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

Since y=-x%2B360, we can now replace each y in the second equation with -x%2B360 to solve for x



18x%2B9highlight%28%28-x%2B360%29%29=4320 Plug in y=-x%2B360 into the first equation. In other words, replace each y with -x%2B360. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



18x%2B%289%29%28-1%29x%2B%289%29%28360%29=4320 Distribute 9 to -x%2B360


18x-9x%2B3240=4320 Multiply


9x%2B3240=4320 Combine like terms on the left side


9x=4320-3240Subtract 3240 from both sides


9x=1080 Combine like terms on the right side


x=%281080%29%2F%289%29 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%2B360 (remember we previously solved for y in the first equation).



y=-x%2B360 Start with the equation where y was previously isolated.


y=-%28120%29%2B360 Plug in x=120


y=-120%2B360 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



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