How to solve the problem of chickens and rabbits living in the same cage
The problem of chicken and rabbit in the same cage is a classic mathematical application problem in ancient China and a common logical reasoning problem in modern mathematics education. This type of problem usually involves solving the number of chickens and rabbits based on the known total number of heads and total number of feet. This article will introduce in detail how to solve the problem of chickens and rabbits living in the same cage, and provide structured data to help understand.
1. Problem description
Suppose there are chickens and rabbits in a cage. It is known that:
| Project | numerical value |
|---|---|
| Total number of heads | 35 |
| Total number of feet | 94 |
Question: How many chickens and rabbits are there in the cage?
2. Problem-solving methods
There are usually several methods to solve the problem of chickens and rabbits living in the same cage:
1. Algebraic method (equation method)
Assume the number of chickens is x and the number of rabbits is y. According to the meaning of the question, the following equations can be listed:
| Equation | expression |
|---|---|
| Number of heads equation | x + y = 35 |
| foot count equation | 2x + 4y = 94 |
By solving the system of equations, we get: x = 23 (chicken), y = 12 (rabbit).
2. Hypothesis method
Assuming the cage is full of chickens, the total number of feet is 35 × 2 = 70, which is 24 feet less than the actual number. Each rabbit has 2 more legs than a chicken, so the number of rabbits is 24 ÷ 2 = 12 and the number of chickens is 35 - 12 = 23.
| steps | Calculation process |
|---|---|
| Assume they are all chickens | 35 × 2 = 70 |
| Difference in number of feet | 94 - 70 = 24 |
| number of rabbits | 24÷2=12 |
| number of chickens | 35 - 12 = 23 |
3. Lift your feet (interesting solution)
Assuming that the chicken and rabbit lift half of their feet at the same time (the chicken lifts 1 and the rabbit lifts 2), the number of remaining legs is 94 ÷ 2 = 47. At this time, each animal has 1 foot left, and the total number of heads is 35. Therefore, the number of rabbits is 47 - 35 = 12, and the number of chickens is 35 - 12 = 23.
| steps | Calculation process |
|---|---|
| The number of remaining feet after lifting the foot | 94÷2=47 |
| number of rabbits | 47 - 35 = 12 |
| number of chickens | 35 - 12 = 23 |
3. Summary
The problem of chickens and rabbits living in the same cage can be solved in a variety of ways, each with its own characteristics:
| method | Applicable scenarios | Advantages |
|---|---|---|
| algebraic method | Strong versatility | Clear logic, suitable for equation learning |
| Hypothesis method | Quick calculation | No need for complicated equations, suitable for oral calculation |
| Lifting your feet | Fun teaching | Vivid images for easy understanding |
After mastering these methods, similar mathematical problems (such as the number of vehicle wheels, the number of animals, etc.) can be easily solved. I hope that through the explanations in this article, readers can easily solve the problem of chickens and rabbits in the same cage!
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