Question

There are some rabbits and some birds in a small cave and the number of heads is $35$ and the number of feet is $98$. Find the number of birds and rabbits.

Answer 1

Number of heads $=35$

Number of feet $=38$

We know that birds have two feet and rabbits have four.

Let the number of birds be $x$ and rabbits be $y$.

From the given information, we have,

$2x+4y=\mathrm{98........}\left(i\right)andx+y=35=>x=35-y........\left(ii\right)$

Substituting (ii) in (i), we get,

$2x+4y=98=>2(35-y)+4y=98=>70-2y+4y=98=>2y=28=>y=14\therefore x=35-y=35-14=21$

Therefore, number of birds$=x=21$ and rabbits$=y=14$.