we are given
there are hens and rabbits
Let's assume
number of hens =x
number of rabbits =y
Since, number of heads for hen is 1
and number of head for rabbit is 1
and we are given
total number of heads =43
so, we get equation as
[tex]x+y=43[/tex]
now, we can solve for y
[tex]y=43-x[/tex]
There are two legs of hens
and there are four legs of rabbit
and total number of legs =124
so, we will get equation as
[tex]2x+4y=124[/tex]
now, we can plug back y
[tex]2x+4(43-x)=124[/tex]
now, we can solve for x
[tex]-2x+172=124[/tex]
[tex]-2x+172-172=124-172[/tex]
[tex]-2x=-48[/tex]
[tex]x=24[/tex]
now, we can find y
[tex]y=43-24[/tex]
[tex]y=19[/tex]
So,
Number of hens =24
Number of rabbits =19.........Answer
