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On a cold winter’s night that was so deep, the poor shepherds lay huddled amongst their sheep. If there were 100 heads and 300 legs in the field, how many sheep did the shepherds have?
The First Noel The first Noel the angles did say Was to certain poor shepherds in fields as they lay In fields where they lay keeping their sheep On a cold winter’s night that was so deep.
Details and assumptions A sheep has 4 legs, a shepherd has 2 legs.
The answer is 50.
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1 solution
Since it is said that there are 100 heads and each shepherd or sheep can have only 1 head, so let us take the no. of sheeps as x and the no. of shepherds as ( 1 0 0 − x ) .
Now, since each sheep has 4 legs, so total no. of sheep legs = 4 x and since each shepherd has 2 legs, so total no. of shepherd legs = 2 ( 1 0 0 − x ) .
Now, according to the question, there are a total of 300 legs in the field, so we can say that,
(No. of sheep legs) + (No. of shepherd legs) = 3 0 0 ⟹ 4 x + 2 ( 1 0 0 − x ) = 3 0 0 ⟹ 4 x + 2 0 0 − 2 x = 3 0 0 ⟹ 2 x = 1 0 0 ⟹ x = 5 0
So, finally we get no. of sheeps = x = 5 0