Question 145889: 1. An animal feed is made from three ingredients: corn, soybeans, and cottonseed. One unit of each ingredient provides units of protein, fat, and fiber, as shown below:
Each unit of corn provides .25 units of protein, .4 units of fat, and .3 units of fiber.
Each unit of soybeans provides .4 units of protein, .2 units of fat, and .2 units of fiber.
Each unit of cottonseed provides .2 units of protein, .3 units of fat, and .1 units of fiber.
How many units of each ingredient should be used to make a feed that contains 22 units of protein, 28 units of fat, and 18 units of fiber?
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! An animal feed is made from three ingredients: corn, soybeans, and cottonseed. One unit of each ingredient provides units of protein, fat, and fiber, as shown below:
Each unit of corn provides .25 units of protein, .4 units of fat, and .3 units of fiber.
Each unit of soybeans provides .4 units of protein, .2 units of fat, and .2 units of fiber.
Each unit of cottonseed provides .2 units of protein, .3 units of fat, and .1 units of fiber.
How many units of each ingredient should be used to make a feed that contains 22 units of protein, 28 units of fat, and 18 units of fiber?
:
Let x, y, z = amt of corn, soybeans, cottonseed respectively
:
Three equations:
pro: .25x + .40y + .20z = 22
fat: .40x + .20y + .30z = 28
fib: .30x + .20y + .10z = 18
:
Multiply the 1st equation by -1 and add the 3 equations.
-.25x - .40y - .20z = -22
+.40x + .20y + .30z = 28
+.30x + .20y + .10z = 18
-------------------------
+.45x + 0y + .20z = 24
:
Multiply the 3rd equation by -1 and add to the 2nd equation
+.40x + .20y + .30z = 28
-.30x - .20y - .10z = -18
--------------------------
+.10x + 0y + .20z = +10
:
Two equation where we are dealing only with x and z
.45x + .20z = 24
.10x + .20z = 10
------------------subtracting eliminates z, find x:
.35x = 14
x = 
x = 40 units of corn
:
Use equation: .10x + .20z = 10; substitute 40 for x:
.10(40) + .20z = 10
4 + .2z = 10
.2z = 10 - 4
z = 
z = 30 units of cottonseed
:
I'll let you find y
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! An animal feed is made from three ingredients: corn, soybeans, and cottonseed. One unit of each ingredient provides units of protein, fat, and fiber, as shown below:
Each unit of corn provides .25 units of protein, .4 units of fat, and .3 units of fiber.
Each unit of soybeans provides .4 units of protein, .2 units of fat, and .2 units of fiber.
Each unit of cottonseed provides .2 units of protein, .3 units of fat, and .1 units of fiber.
How many units of each ingredient should be used to make a feed that contains 22 units of protein, 28 units of fat, and 18 units of fiber?
--------------------------
Let amt. of corn be "r"; amt. of soybeans be "s", amt of cottoseed be "c".
----------------------
EQUATIONS:
Protein: 0.25r + 0.4s + 0.2c = 22
Fat....: 0.4r + 0.2s + 0.3c = 28
Fiber..: 0.3c + 0.2s + 0.1c = 18
------------
Solve the system of equations to get:
r = 40
s = 15
c = 30
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Cheers,
Stan H.
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