Soybean meal is 18% protein; cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360-lb mixture that is 11% protein?

Question

I need to calculate how many pounds of cornmeal should be in the mixture and how many pounds of the soybean meal should be in the mixture.

Answer 1

You have two unknowns here which will in turn become your variables.

 

If the pounds of soybean meal equals s and the pounds of corn meal equals c, then we obtain the following equation:

 

s + c = 360

 

Now we know the percent of protein in each of the variables which translates in the following equation.

(.18)s+(.09)c=(.11)360

 

Now... let's do this step by step. 

 

s=360-c so Let's find c first by re-writing the equation.

(.18)(+(.09)c=(.11)360

 (.18)(360-c)+(.09)c=39.6

 

and now simplify to

 64.8-.18c+.09c=39.6

simplify even more to get:

 -.09c=-25.5

 

and solving for c gives us: 283 pounds of corn meal. 

 

Now since s=360-c then s= 77 pounds

 

That means you need 283 pounds of corn meal and only 77 pounds or soybean to obtain 360 pounds of mixture with 11% protein.