I need an equation form for this...If i have 72 legs and 22 heads in a barn..How many rabbits and hens I have?

Answer 1

Rabbit heads = (x)
Rabbit legs = 4 times heads = 4x

Hen heads = y
Hen legs = 2 times heads = 2y


x + y = 22

4x + 2y = 72

Multiply first equation by -2.

-2x -2y = -44
4x + 2y = 72

Add them together.

2x = 28
x = 14

So, there are 14 rabbits and 8 hens

14 + 8 = 22

14 x 4 = 56
8 x 2 = 16

56 + 16 = 72.

Regards,

Mysstere

Answer 2

Clearly there are different approaches. It seems more direct to say
heads = R + H = 22 (each animal has one head)
legs = 4R + 2H = 72 (rabbits have 4 legs, hens have 2)
after simplify the second equation by dividing by 2, we
have two equations in two unknowns
R + H = 22
2R + H = 36
rearrange the first equation:
H = 22 - R
substitute it into second:
2R + 22 - R = 36
R = 14
put this back in the first equation
H = 22 -14 = 8

8 hens and 14 rabbits

Answer 3

well count the legs and heads on rabbits and hens first:

~ a hen has 1 head and 2 legs
~ a rabbit has 1 head and 4 legs

Now you have two unknowns: X=number of hens, Y=number of rabbits

Now you also know you have 72 legs and 22 heads -- these are comprised of some combination of hens and rabbits

I think we now have enough info to write some equations:

~ 22 = # of hen heads + # of rabbit heads = X + Y
~ 72 = # of hen legs + # of rabbit legs = 2X + 4Y

So now you have two equations that you can solve for X and Y for:

22 = x + y
72 = 2x + 4y

SOLUTION:

72 = 2x + 4y
-44 = -2x -2y {multiply 22 = x + y by -22)

now add the above two to get:

28 = 2y

so y = 14 (# of rabbits)

and x = 22-y = 8 (# of hens)

Answer 4

4*R + 2*H = 72 each rabbit has 4 legs, each hen has 2 legs
R + H = 22 rabbits have one head, hens have one head.
Think of R + H =22 as 1*R + 1*H = 22

OK so now you can solve the bottom equation for R:
R=22-H
and then plug this value for R into the top equation:
4*(22-H) + 2*H = 72
solve for H, then plug the value for H back into one of the original equations to solve for the R.

Answer 5

R=abbits; H=hens
R+H=22
4R+2H=78

H=22-R
4R+2(22-R)=78
4R-2R+44=78
2R=34
R=17
H=22-R=22-17=5
check
4*17+5*2=68+10=78 legs
17+5=22 heads
17 rabbirs & 5 hens

Answer 6

If you have 22 heads then you have 22 animals with a combined total of 72 legs.

Hens have two legs each.

Rabbits have four legs each.

Now, you do the thinking and complete your homework.

Answer 7

Yup, i agree, the last answer beat me to it!

4r + 2h = 72

r+h = 22

h = 22 - r

so

4r + 44 - 2r = 72

so

2r = 28

r = 14, h = 9

14 rabbits and 8 hens