Farm Question

Question: A farm raised the same number of chickens and pigs. In total the animals have 30 legs. How many chickens and pigs were in the farm?

Asumption: one chicken has two legs and one pig has four legs.

Solution (1) based on number of legs:

X = number of legs of pigs
Y = number of legs of chickens

(a) X + Y = 30
(b) X/4 = Y/2 is equivalent to X/2 = Y, or X = 2Y

Put Equation (b) into Equation (a), we get a new equation

(c) 2Y + Y = 30, or 3Y = 30, or Y = 10.

Put Equation (c) into Equation (b), we get another equation

(d) X = 2*10 = 20

So there are 20 legs of pigs and 10 legs of chickens. That means there are 5 pigs and 5 chickens.

Solution (2) based on number of chickens and pigs:

M = number of pigs
N = number of chickens

(a) M = N
(b) X = 4M
(c) Y = 2N

Knowing that X + Y = 30, we get a new equation

(d) 4M + 2N = 30

Put Equation (a) into Equation (d), and we get another equation

(e) 4N + 2N = 30, or 6N = 30, or N = 5.

Put Equation (e) into Equation (a), and we know M and N = 5.


Solution of question: 5 chickens and 5 pigs.