The chicken-rabbit cage problem is a classic mathematical problem, usually described as: there are some chickens and rabbits in a cage, we can see their heads and feet, but we don't know how many chickens and how many rabbits.
We're going to find out how many chickens and how many rabbits are in this cage.
Let's say the number of chickens is x and the number of rabbits is y.
Depending on the problem, we can build the following equation:
The sum of the number of heads of chickens and rabbits is x + y.
The sum of the legs of the chicken and rabbit is 2x + 4y (since the chicken has 2 legs and the rabbit has 4 legs).
Using a mathematical equation, we can express it as:
x + y = sum of the number of heads.
2x + 4y = sum of the number of legs.
Now we're going to solve this system of equations and find out the values of x and y.
The mantra for solving the problem of chickens and rabbits in the same cage is:
The number of heads is the same to see the number of feet, and the number of feet is the rabbit;
The number of feet is the chicken, and the number of feet is divided by two and then subtracted, which is the difference between chickens and rabbits.
The meaning of this mantra is:
First of all, if the chicken and rabbit have the same number of heads, then we can look at the number of their feet.
Because rabbits have more feet than chickens, the animal with more feet is a rabbit.
We can then divide the number of feet by 2 and subtract the number of heads to get the difference between the number of chickens and rabbits.
Finally, by the difference between the number of heads and the number, we can find the specific number of chickens and rabbits.
For example, if the sum of the heads is 35 and the sum of the legs is 94, then:
Number of rabbits = (sum of legs - sum of 2 heads) 2 = (94 - 2 35) 2 = 12
Number of chickens = sum of heads - number of rabbits = 35 - 12 = 23
So, there are 23 chickens and 12 rabbits in the cage.