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?

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) (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:

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:

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

Divide both sides by

Break up the fraction

Reduce

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

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 3240 from both sides

Combine like terms on the right side

Divide both sides by 9 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 120 pounds of soybean meal and 240 pounds of cornmeal are needed for the mixture.

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