Chickens and rabbits caged together is one of the famous typical anecdotes in ancient China, which was recorded in Sun Tzu's Art of War. The problem of chickens and rabbits in the same cage is a common problem in primary school Olympic mathematics. In its solution, the assumption method is usually simpler and easier to understand.
The problem of chickens and rabbits in the same cage is a math problem in the fifth grade of primary school. This is not only a mathematical problem, but also a mathematical idea.
analysis
The topic is that chickens and rabbits live in the same cage, with head 36 and feet 120. Find the number of chickens and rabbits.
Suppose all chickens, suppose all rabbits.
After getting the question, we can assume that the chickens and rabbits in the cage are both chickens or rabbits. If all the chickens are assumed, then the 36 heads in the cage are all heads of chickens, then there are 36 chickens, and we all know that chickens have two legs, so the total number of legs of chickens should be twice, that is, 36×2=72.
How many feet are there? How many feet are missing?
Compare it with other conditions and see where the gap is. Comparing with another known condition in the topic, if there are 120 legs, you will find that there are 120-72=48 legs missing, because each chicken has two legs less than a rabbit, which means that the legs are all rabbits'.
Divided by the foot difference, it is the number of chickens and rabbits.
Assuming that the leg difference is divided by 2, it is the number of chickens and rabbits. In the above hypothesis, we get the result that there are 48 legs that are different from those under the known conditions, so dividing by 2 is 24, which means the number of rabbits is 24.
In the future mathematics study, hypothetical conditions are often used, just like the topic of chicken and rabbit in the same cage. By assuming, many conditions can be deformed. The method mentioned in this formula is simple and easy to understand. In fact, it can be assumed that there are chickens or rabbits in the cage.