soybean meal is 16% and corn meal is 9% protein? how many pounds of each should be mixed to get a 350 pound mixture that is 12% protein?

Question

soybean meal is 16% and corn meal is 9% protein? how many pounds of each should be mixed to get a 350 pound mixture that is 12% protein?

Answer 1

Let s=pounds of soybean meal

     c=pounds of corn meal

We have 2 unknowns, so we need 2 equations to solve this:

Eq. 1)  s+c=350

Eq. 2)  (16%)s+(9%)c=(12%)350

           .16s+.09c=(.12)350

           .16s+.09c=42

Let's use the substitution method in Eq. 1 and solve for "s":

           s+c=350

           s=350-c

Use this value for "s" and solve for "c" in Eq. 2:

           .16(350-c)+.09c=42

           56-.16c+.09c=42

           56-.07c=42

           56-42=.07c

           14=.07c

           14/.07=c

           200=c

Use this value for "c" in Eq.1 and solve for "s":

           s=350-c

           s=350-200

           s=150

Therefore, s=150 and c=200. Check these answers in both equations:

Eq. 1) s+c=350

         150+200=350

         350=350   Check

Eq. 2) .16s+.09c=42

         (.16)(150)+(.09)(200)=42

         24+18=42

         42=42   Check

 Therefore, you need 150 pounds of soybean meal and 200 pounds of corn meal to get a 350 pound mixture of 12% protein.