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.

Zero is an Equalizer

"Zero is the only number that can be divided evenly by any number", George said while we were on our way to a local Chinese restaurant yesterday. I thought he said that while he was thinking about some math problems. He was not thinking about any thing beyond that.

Then J said that was right. She further said "now I understand that why people cannot be equal unless they are all poor." Because if there is not much to be divided among people, then everyone gets very little, then everyone is very equal. Zero is the number very close to very little.

I told George I was very proud of him for said nice sentence. I told him that "your statement is mathematically beautiful and philosophically profound".

When everyone is very poor, then the society is very equal for everyone. If there are the rich and the poor in the society, there is hardly any equality among people.