DMF Feeds has two different types of cattle feed containing crude protein in the amount of 45% and 20% respectively. How many of each type must a feed lot manager mix together to obtain 10000lbs of a mixture that is 25% protein?
if x lbs of 40%, then
.40x + .20(10000-x) = .25(10000)
To solve this problem, we can use a system of equations.
Let's assume that x represents the amount of feed with 45% crude protein, and y represents the amount of feed with 20% crude protein.
The first equation we can write based on the amount of protein is:
0.45x + 0.20y = 0.25(10000)
This equation states that the sum of the protein from the two types of feed, when mixed together, should be 25% of the total weight of the mixture.
The second equation is based on the weight of the mixture:
x + y = 10000
This equation states that the sum of the weights of the two types of feed should equal the total weight of the mixture, which is given as 10000 lbs.
Now, we can solve these equations simultaneously to find the values of x and y.
To do this, we can use any method of solving simultaneous equations. Here, we will use the substitution method.
First, solve the second equation, x + y = 10000, for x:
x = 10000 - y
Substitute this value of x into the first equation:
0.45(10000 - y) + 0.20y = 0.25(10000)
Simplify and solve for y:
4500 - 0.45y + 0.20y = 2500
-0.25y = -2000
y = (-2000) / (-0.25)
y = 8000
Now substitute this value of y back into the second equation to find x:
x + 8000 = 10000
x = 10000 - 8000
x = 2000
Therefore, to obtain a mixture of 10000 lbs that is 25% protein, the feed lot manager must mix 2000 lbs of feed with 45% crude protein and 8000 lbs of feed with 20% crude protein.