Answer to Question #2349 in Algebra for Kyle

Question

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?

Answer 1

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.