A milling company want to mix alfalfa, which contains 20% protein and wheat mids, which contains 15% protein to make cattle feed. The milling company wants to make 1000 pounds of cattle feed that contains 17% protein. How many pounds of alfalfa and how many pounds of wheat mids must be used?
Let& a be the part of alfalfa in one pound of cattle feed, then& (1-a) is the part of wheat mids in one pound of cattle feed. Then the percent of protein in this mix is & a*0.2 + (1-a)*0.15, We have to find such a that & a*0.2 + (1-a)*0.15 = 0.17 & 0.2 a + 0.15 - 0.15 a = 0.17 & 0.05 a = 0.02 & a = 2/5 = 0.4.
Thus it is necessary to take 40 % of& alfalfa and 60% of& of wheat mids.