Farmer had 20 pigs and chickens in the farmyard and 54 legs. How many of each animal were there?

Question

I need to find another way to solve this problem besides trial and error.

Answer 1

1) p + c = 20  or  c = 20 - p

2) 2c + 4p = 54

substitute eq(1) into eq(2):

2(20 - p) + 4p = 54

40 - 2p + 4p = 54

2p = 14

p = 14/2 = 7

using eq(1):

c = 20 - 7 = 13

check using eq(2):

2(13) + 4(7) = 54

26 + 28 = 54

There are 13 chickens and 7 pigs.

Answer 2

Draw 20 animal bodies 9 (circles)  get 54 beans (legs) and start putting "legs" on the "animals". This will allow you to rearrange the legs very quickly to find the solution!

Answer 3

20 animals x 2 legs each = 40 legs minimum (all chickens have two legs, all pigs get their first two legs)

54-40 = 14 legs left over

Each pig needs another pair of legs

14/2=7

Therefore, there are 7 pigs, and (20-7=13) 13 chickens.

Now check, 7 x 4 = 28 and 13 x 2 = 26

28 + 26 = 54

 

OR, draw a picture.  Draw 20 animals.  Give each animal two legs first.  Then add two more legs at a time, counting as you go, until you have 54 legs.

 

Or, act it out.  Get 20 people to stand on two legs, then assign some of those people to get on all fours, until you have 54 "legs".

Answer 4

Let's assume there are only chickens in the farmyard.

Then the total number of legs would be;

2 * 20 = 40 ---(1)

But the total number of legs is 54.

Thus 54 - 40 = 14 legs are missing.

It's because (1) didn't include the number of pigs, each of which has 2 more legs than a chicken. Therefore;

14 missing legs / (pig's 4 legs - chicken's 2 legs) = 14 / 2 = 7

So by dividing the number of missing legs by the difference between the number of pig's leg and that of a chicken brings the number of pigs.

Thus the number of chickens are 20 - 7 =13

Answer; 7 pigs and 13 chickens

(7 * 4 ) + (13 * 2) = 54

Answer 5

(20) (2)

40

54-40= 14

14/ 2

7 pigs

20-7=13 chickhen

Answer 6

i hate math this s question is soooo stupid

Answer 7

Assume that pigs are standing on their hind legs, 2 hind legs for each pig.

A chicken has 2 legs a head, so the leg count would be 40 (=20x20) in total.

But actual leg count is 54, so the surplus,14 (=54-40), must be the count 
of pig's forelegs.

Thus, the head number of pigs: 14/2=7,

so the head number of chickens: 20-7=13

CK: 7x4+13x2=28+26=54   CKD.

The answer: There are 7 pigs and 13 chickens.