The chicken-rabbit cage problem is a classic mathematical problem, and its solution can be achieved in a variety of ways. In order to facilitate memorization and solve problems quickly, people have summed up many mantras. This article will bring together some good problem-solving formulas for you, and make corresponding explanations and case demonstrations to help you better grasp the problem-solving skills of the chicken-rabbit same cage test.
Chicken head plus rabbit head, the total number of heads to make up; Chicken feet minus rabbit feet, the total number of feet to find; To match the head and feet, convert the number of feet to seek.Chicken head plus rabbit head, the total number of heads to make up; This mantra refers to adding the total number of heads, because each chicken has 1 head and each rabbit has 1 head, so adding the number of heads of chickens and rabbits gives the total number of heads.
Chicken feet minus rabbit feet, the total number of feet to find;
This mantra refers to subtracting the number of rabbit's feet from the total number of feet. Because a chicken has 2 legs and a rabbit has 4 legs, the number of chickens can be found by subtracting the number of rabbit's feet from the total number of feet.
To match the head and feet, convert the number of feet to seek.
This mantra refers to the fact that if the total number of heads and the total number of feet is known, but the specific number of chickens and rabbits cannot be directly derived from the above formula, the number of feet of the rabbit can be converted to the number of heads, or it can be converted to the number of feet, so as to obtain another solution method.
Use this mantra to quickly solve the problem of chickens and rabbits in the same cage. For example, if there are a total of 10 heads and 26 feet, then it can be deduced from the above mantra: 10 heads contain a certain number of chicken and rabbit heads, and 26 feet contain a certain number of chicken feet and rabbit feet. According to the mantra calculation, there are 73 chickens and 3 rabbits.
Speaking of which, many students and parents may be confused, what is going on with this conversion foot? How do you know that there are 73 chickens and 3 rabbits?
Since the chicken has 2 legs and the rabbit has 4 legs, then 10 heads, assuming that they all have 2 legs, there are 20 legs in total, and the total number of legs is 26 minus 20, and the difference is the extra feet of the rabbit, that is, 6 legs.
Because the extra feet are the 2 more feet of the rabbit, if 6 is divided by 2, then there are 3 rabbits. In this way, the total number of heads minus the total number of rabbits 3 is the total number of chickens, and the result is 7. So the chickens were calculated, and there were 7 in total.
The number of heads is fixed, the number of feet is clear, and it is assumed that they are all chickens. The number of extra feet rabbit is supplemented, and each rabbit has two more legs.
The meaning of this mantra is to first assume that all animals are chickens (because chickens have the least number of legs, 2), and then calculate the number of rabbits based on the difference between the actual number of feet and the hypothetical number of feet. Each rabbit has two more legs than a chicken, so the difference divided by 2 is the number of rabbits.
In fact, this mantra is the same as the principle of the previous mantra "if the head and feet match the number of feet", so I will not do case analysis and explanation here.
If you still have any good formulas, please leave a message to share with you.
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