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A Farmer Keeps Hens and Rabbits on His Farm. One Day, He Counted a Total of 70 Heads and 196 Legs. How Many More Hens than Rabbits does He have?

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Explanation

Animals that farmer keeps

  • Hen
  • Rabbit

As it is quite obvious that each animal has 1 head but legs are not same. Each hen has 2 legs and each rabbit has 4 legs.

We are provided with the total number of heads i.e. 70. It means h + r = 70 and total number of legs are 196 i.e. 2h + 4r = 196.

Now we have 2 equations and by solving them simultaneously we can find out the required answer.

To Find

How many more hens than rabbits does the farmer have = ?

Solution

Let

h shows the hens and r shows the rabbits

So, total number of heads

h + r = 70 ___________ (i)

As, each hen has 2 legs so h hen will have 2h legs and each rabbit has 4 legs so r rabbit will have 4r legs.

So total number of legs

2h + 4r = 196 (Dividing the both sides of the equation with 2)

h + 2r = 98 __________ (ii)

Subtracting (i) from (ii)

(h + 2r) – (h + r ) = 98 – 70

h + 2r – h – r = 28

r = 28

Put r = 28 in equation (i)

h + 28 = 70

h = 70 – 28

h = 42

Now,

h – r = 42 – 28 = 14 hens

Conclusion

A farmer keeps hens and rabbits on his farm. One day, he counted a total of 70 heads and 196 legs. There would be 14 hens more than rabbits that he have.

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