Problema Solution
A cattleman wants to mix 2,100 pounds of cattle feed that is to be 14% protein. Barley (11.7% protein) will make up 20% of the mixture. The remaining 80% will be made up of oats (11.8% protein) and soybean meal (44.5% protein). How many pounds of each should he use? (Round your answers to the nearest pound.)
Answer provided by our tutors
we assume that the phrase "Barley (11.7% protein) will make up 20% of the mixture" is a reference to how much barley "by weight" the mixture is composed of, so that the weight of barley will be:
2100 * 0.20 = 420
let 'x' represent the pounds of oats used in the mixture, then '2100-420-x' represents the pounds of soybean meal used in the mixture
2100*0.14 = 0.117(420) + 0.118x + 0.445(2100-420-x)
solving for 'x' we have x=1537.43
2100-420-1537.43 = 142.57
rounding to the nearest pound, 420 pounds of Barley should be mixed with 1537 pounds of Oats and 143 pounds of Soybean Meal