soybean meal

Question

soybean meal is 14% protein;cornmeal is 7%. how many pounds of each should be mixed together in order to get 280-lb mixture that is 12% protein

Answer 1

Assign variables:

S = pounds of Soybean meal

C = pounds of Corn meal

 

We need 2 equations to solve for 2 unknowns.

 

First, we are told the total weight, so:

 

S + C = 280  <<equation # 1>>

 

Next, we can write and equation for the amount of protein:

 

S (0.14) + C (0.07) = 280 (0.12)  = 33.6   <<equation #2>>

 

From equation #1:

S = 280 - C    <<equation #3>>

Substitute for S in equation #2:

 

(280 - C) (0.14) + C (0.07) = 33.6

Expand and rearrange:

 

280 (0.14) - 0.14C + 0.07C =33.6

 

- 0.14C + 0.07C =33.6 - 280 (0.14)

 

-0.07C = 33.6 - 39.2 =  -5.6

 

C = 80

 

Then, from equation #1:

 

S = 200

 

CHECK THE ANSWER USING THE 1ST 2 EQUATIONS