A milling company wants to mix alfalfa, which contain 20% protein, and wheat mids,† which contain 15% protein, to make cattle feed.
(a) If you make a mixture of 40 pounds of alfalfa and 60 pounds of wheat mids, how many pounds of protein are in the mixture? (Hint: In the 40 pounds of alfalfa there are
40 × 0.2 = 8 pounds of protein.)
Suppose 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?
alfalfa _____
wheat mids ______
+33665 (a) 40 pounds of alfalfa gives 40*0.2 = 8 pounds of protein. 60 pounds of wheat gives 60*0.15 = 9 pounds of protein so, in total, there are 8 + 9 = 17 pounds of proptein in the mixture.
(b). Let A = pounds of alfalfa and W = pounds of wheat.
A + W = 1000 ...(1) Total weight of mixture
0.2A + 0.15W = 0.17*1000 Total weight of protein
0.2A +0.15W = 170 ...(2)
Multply (2) by 5
A + 0.75W = 850 or A = 850 - 0.75W
Put this into (1)
850 - 0.75W + W = 1000 or 0.25W = 150 or W = 600
Put this back into (1) A + 600 = 1000 so A = 400
400 pounds of alfalfa and 600 pounds of wheat mids.
