SOLUTION: Soybean meal is 16% protein; cornmela is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 14% protein? How many pounds of the

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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:



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:




Multiply


Multiply both sides by 10 to remove the decimals


Distribute


So we have the new system of equations:





Start with the first equation


Subtract from both sides


Rearrange the equation



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

Since , we can now replace each in the second equation with to solve for



Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.



Distribute to


Multiply


Combine like terms on the left side


Subtract 2560 from both sides


Combine like terms on the right side


Divide both sides by 8 to isolate x



Divide





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


So the first part of our answer is:









Since we know that we can plug it into the equation (remember we previously solved for in the first equation).



Start with the equation where was previously isolated.


Plug in


Multiply


Combine like terms



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


So the second part of our answer is:









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

So our answers are:

and

which form the ordered pair



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