Help with maths problem?

Question

On a farm, a farmer counts 81 heads and 252 legs.

How many chickens are there? How many sheep are there?

Please show working.

Answer 1

c =chickens
s = sheep
(c + s = 81
(2c + 4s = 252

c = 81 - s
2(81 - s) + 4s = 252
162 - 2s + 4s = 252
2s = 252 - 162
2s = 90
s = 90 : 2
s = 45

c = 81 - 45
c = 36
Answers: There are 45 sheeps and 36 chickens.
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Answer 2

To begin with, we must assume that all the relevant information has been given and that there are no hidden tricks. Thus we assume there are only chickens & sheep on the farm all the animals have been counted, the farmer has counted correctly and that no animal is missing any of its legs. With this in mind, we can solve the problem in the following manner.

If the animals were all chickens, there would have been 81x2=162 legs to go along with the 81 heads. There are in fact 252 legs, giving an excess of 252-162=90 legs.

Next step: Each sheep replacing a chicken in the 'head count' would add 2 legs to the total since a sheep (with 4 legs) has 2 more legs than a chicken (which has only 2). Since the excess (see above) is 90 legs, we divide this by 2 'extra' legs per sheep - and 90/2=45.

Consequently, we find there must be 45 sheep. Since the total number of animals (heads) = 81, there must also be 81-45=36 chickens.

Let's check this out:

45 sheep @ 4 legs each = 45x4 = 180 legs
36 chickens @ 2 legs per chicken = 36x2 = 72 legs
Total of legs = 180+72 = 252
Each animal has 1 head, so the total = 45+36 = 81 heads.

The answer thus passes the test. There are 36 chickens & 45 sheep.

Answer 3

45 sheep
36 chickens == 81 heads
45x4=180
36x2= 72
+252 ==252 legs

Answer 4

Copy this
1chicken=2 legs.
1sheep=4 legs.
252-52=200
52divided by 2 =26
200divided by 4=50
So there are 50 sheep and 26 chickens.
There...

Answer 5

let S=no of sheep
C=no of chickens
assume:
i)each sheep and each chicken
has a head
ii)each sheep has four legs
iii)each chicken has two legs

C+S=81{81 heads given}
>>2C+2S=162....(1)
2C+4S=252........(2)
{given no of legs=252}
subtract (1) from(2)
2S=90
>>S=45
substitute for S in (1)
2C+90=162
>>C=36

therefore, there are 36 chickens
and 45 sheep

i hope that this helps

Answer 6

Say x number of chicken are there and y number of sheep

x+y=81 (heads) ----> eqn 1

2x+4y=252 (legs)

x+2y = 126 -----> eqn 2

x = 126 - 2y

Substitute in eqn 1

126 -2y+y=81 -> 126-y=81 -> y = 126-81= 45 sheep


x+81=45 -> x = 36 chickens

Answer 7

Did the farmer count his own legs? What if one of the chickens was standing on one leg? Was there a sheep dog?

Answer 8

36chikens & 45 sheep

2c+4s=252 ; c+s=81 ; therefore s=81-c
2c+4(18-c)=252
...
c=36
thus
s=81-36=45

Answer 9

81 x 2 = 162
252 - 162 = 90
90/2 = 45
45 x 4 = 180
36 x 2 = 72
36 chickens and 45 sheep

Answer 10

Let c be the number of chickens.
Let s be the number of sheep.

What's the number of critters in total? How does this relate to c and s?

What's the number of chicken legs?
What's the number of sheep legs?

What's the total? How does this relate to the number of chicken legs and sheep legs?

If you've answered all these, you should have two simple equations which are easy to solve.