Question

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?​

Answer 1

22 hens and 78 sheep

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