a farmer has sheep and hen .the sheep and hen together have 100heads and 356 legs .how many sheep and hens does the farmer have?​

22 hens and 78 sheep

Step-by-step explanation:

Let the number of hens = x

Number of sheep = y

Total heads = 100

x +  y = 100      (I)

 x = 100 - y

Number of legs of 'x' hen = 2*x = 2x

Number of legs of 'y' sheep = 4*y = 4y

total legs = 356

2x + 4y =  356 (II)

Substitute x = 100 -y in equation (II)

2(100 - y) + 4y = 356

2*100 - 2*y + 4y = 356

200 - 2y + 4y    = 356 {Combine like terms}

        200  + 2y = 356          {Subtract 200 from both sides}

                   2y = 356 - 200

                  2y = 156       {Divide both sides by 2}

                    y = 156/2

                  y = 78

Plugin  y = 78 in equation (I)

x + 78 = 100

       x = 100 - 78

       x = 22

22 hens and 78 sheep

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step-by-step explanation: