Set up a system of equations that describes the data above. Solve the system.

Question

A farm has 200 acres available to plant corn, wheat and soybeans. An acre of corn requires 6 hours of labor, wheat 3, and soybeans 4. There are 1000 hours of labor available.

 

Set up a system of equations that describes the data above. Solve the system.

 

If the farm decides to plant 120 acres of corn, how much will be planted in soybeans and wheat? 

 

If the farm plants no wheat, how much will be planted in corn and soybeans?

Answer 1

let assum

no. of acres  corn farm =x  

no. of acres wheat  farm=y

no. of acres soybeans farm=z

 

x+y+z=200 -------------------equation 1

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x acres of corn  require 6 x labor hour

y acres of wheat require 3x labor hour

z acres of soybeans require 4z labor hour

 

 

6x+3y+4z = 1000  -------------------equation 2

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These 2 equations describes the data above

 

x+y+z=200

6x+3y+4z = 1000

 

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1.If the farm decides to plant 120 acres of corn, how much will be planted in soybeans and wheat?
  x=120

 

then our first equation became

x+y+z=200

120+y+z=200

y+z=80  -------------------equation 3

 

our second equation became

 

6x+3y+4z = 1000

6(120)+3y+4z=1000

720 +3y +4z =1000

3y+4z =280  -------------------equation 4

 

solving equation 3 and 4 

z=40 and y=40

 

wheat farm= 40acres

 

soybeans farm =40 acres

 

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2. If the farm plants no wheat, how much will be planted in corn and soybeans?

 y=0

 

 

then our first equation became
x+y+z=200
x+0+z=200
x+z=200 -------------------equation 5

our second equation became
6x+3y+4z = 1000
6x+3(0)+4z=1000
6x +4z =1000
6x+4z =1000 -------------------equation 6

solving equation 5 and 6

 

x=100 and z=100

 

 

corn arm= 100acres

soybeans farm =100 acres