Please help?

Question

a corn meal feeds is 10% protein and a feed supplement is 40% protein. how much of each must of each must be combined to get 2400 pounds of feed that is 19% protein

Answer 1

Let T = amount of 10% protein feed

Let F = amount of 40% protein feed 

 

2400 pounds total  ==>  T + F = 2400

 

The total amount of protein desired in the mix is 19% of 2400 = 0.19*2400 = 456 pounds 

 

The total amount of protein in a mix of T pounds of 10% protein and F pounds of 40% protein is 0.10*T + 0.40*F, so 

 

0.10*T + 0.40*F = 456

 

Solve the first equation for T to get T = 2400 - F

 

Substitute this value for T into the second equation and solve for F

 

0.10*(2400 - F) + 0.40*F = 456

240 - 0.10*F + 0.40*F = 456

0.30*F = 216

F = 216 / 0.30 = 720

 

So T = 2400 - 720 = 1680.  

 

So use 1680 pounds of 10% protein feed and 720 pounds of 40% protein feed.  

 

Check:  1680 + 720 = 2400 pounds total 

            0.10*1680 + 0.40*720 = 168 + 288 = 456 pounds of protein = 19% of 2400