What is the formula for the chicken rabbit cage problem using the hypothetical method? No equations

1.Suppose it's all chickens or all rabbits2With a quadratic equation.

3.If there are 35 heads and 100 feet, it can be seen that if all the rabbits are rabbits, the rabbits have 4 legs, multiply 35 by the rabbit's 4 feet, there are 140 feet, use 140 to subtract the actual 100 feet, 40 more feet, divide 40 by 2, calculate the number of rabbits to supply chickens, there are 15 rabbits, and 20 chickens.

Chicken and Rabbit Problem Formula].

1) Know the total number of heads and the total number of feet, find the number of chickens and rabbits

Total number of feet - number of feet per chicken Total number of heads) (number of feet per rabbit - number of feet per chicken) = number of rabbits;

Total number of heads - number of rabbits = number of chickens.

or (number of feet per rabbit total number of heads - total number of feet) (number of feet per rabbit - number of feet per chicken) = number of chickens;

Total number of heads - number of chickens = number of rabbits.

Hypothetical method. 1. Suppose it is all 5 yuan 5x100 = 500 yuan.

800-500=300 yuan.

300 (The formula for 10-5 is:.)

Number of rabbits = (actual number of feet - number of feet per chicken Total number of chickens and rabbits).

The number of feet per one.

The little red lips have two yuan and five yuan, a total of two small red lips, two yuan and five yuan, a total of 25 pieces, a total of 80 yuan. How many pieces of each of these two renminbi are in Xiaohong's deposit.

The chicken-rabbit co-cage hypothetical method requires four steps to solve the problem, and the steps are as follows:

1. Suppose it's all chickens (or rabbits).

2. Find the total foot difference.

3. The total foot difference of a single foot = the number of rabbits (or the number of chickens) 4. The total number of animals minus the number of animals calculated first is not worse than the number of other animals.

Attention: When using the hypothetical method to answer the problem of "chickens and rabbits in the same cage", if the assumption is that all chickens are used, the rabbit is calculated first; If you assume that it is all rabbits, then the first thing that is calculated is the chicken.

Example: Chickens and rabbits are in a cage, and there are 15 chicken heads and rabbit heads, and a total of 48 chicken feet and rabbit feet.

Step 1: Suppose the cage is full of chickens, or all rabbits. So let's assume that the cages are all rabbits, 15*4=60 (only).

Step 2: Find the total foot difference. 60-48=12 Step 3: Number of chickens. 12 divided by 2 = 6 (chain skin) Step 4: The number of rabbits. 15-6=9 (only).

The formula of the chicken and rabbit in the same cage assuming that the law attacked Wuzhou is chicken (head 4-foot) 2 rabbit (foot - head 2) 2, chicken and rabbit with the same shot of the cage, is one of the famous typical interesting questions in ancient China, recorded in the "Sun Tzu Sutra", which can attract people's interest in arithmetic.

Sun Tzu's Sutra is an important mathematical work in ancient China, and it was written about the first time.

4. In the fifth century BC, that is, about 1,500 years ago, the author's life and year of writing are unknown. The biography of the "Sun Tzu Sutra" consists of three volumes.

Summary. For example, there are several chickens and rabbits in the same cage, counting from above, there are 35 heads, and counting from the bottom, there are 94 legs. Q: How many chickens and rabbits are in each cage?

Let the total number of chickens be x heads, and the total number of rabbits be (35-x) heads, according to the equivalence relationship of the number of feet, the equation 2x+4(35-x)=94 can be listed, if the system of equations can be set to have x rabbits and y chickens, two equations of x+y=35 and 4x+2y=94 can be obtained, and the system of equations can be solved simultaneously.

The chickens and rabbits in the same cage assumption method and the equation method assume that all rabbits are rabbits, (the total number of heads of each rabbit of the number of feet - the total number of feet) (the number of feet of each rabbit - the number of feet of each chicken) = the number of chickens assumes that all are chickens, (the total number of feet of the stool - the total number of heads of each rabbit the number of feet of each rabbit) (the number of feet per rabbit - the number of feet of each chicken) = the number of rabbits.

Column equation method, Gaozhou can be listed as a one-dimensional liquid sail one-time equation, and can also be listed as a two-element one-dimensional equation. The chickens and rabbits in the same cage problem contain two equal relations of hail: (1) the total number of chicken feet + the total number of rabbit feet = the total number of feet, (2) the total number of chickens + the total number of rabbits = the total number of heads.

For example, Sun Min has several chickens and rabbits in the same cage, counting from above, there are 35 heads, and counting from below, there are 94 legs. Q: How many chickens and rabbits are in the cage? Let the total number of chickens be x, the total number of rabbits is (35-x) heads, according to the equal relationship of the number of feet, the equation 2x+4(35-x)=94 can be listed, if the system of equations can be set to have x rabbits and y, two equations of x+y=35 and 4x+2y=94 can be obtained, and the system of equations can be solved by intermodal transportation.

It can be solved with equations and assumptions.

Generally, chickens and rabbits have the total number of legs and the total number of birds in the same cage, and the unary equation generally sets the number of one of the oak banquet Liangxi animals as x, and the number of the other animal as (total number of animals - x). In this way, multiplying the number of legs set by one animal, and multiplying the number of legs by the number of legs of another animal, equals the total number of legs. For example:

A total of 100 legs, 40 animals, among which there are chickens and rabbits.

Set x chickens, (40-x) rabbits.

2x+4（40-x）=100

2x+160-4x=100

2x+160=100+4x

2x+60=4x

60=2xx=30

40-x=40-30=10

So a total of 30 chickens, 10 rabbits.

Note that when 2x+160-4x, move the item and move 160 or 4x to the right.

Hypothesis method: Ideas: Assuming that all of them are rabbits, in this example, there are a total of 4*40=160 legs, but there are 60 more legs than the actual one, because some chickens are counted as rabbit legs.

Whereas, rabbits have 2 more legs per than chickens. There are a total of 60 more legs, each with 2 more legs, so there are a total of 60 2 = 30 chickens, 40-30 = 10 chickens. The equation is:

Chicken: (40*4-100) (4-2)=60 2=30 (only).

Rabbits: 40-30 = 10 (only).

Note: The number of legs of the "chicken" and "rabbit" can be changed, for example, to become a tricycle and a car, but the number can be calculated by replacing the number with the number of the equation above.

You should be a primary school or junior high school student, just teach you the unary equation and the hypothetical method, read the translated version of "Sun Tzu's Sutra", and you will understand it all.

The methods of solving the problem of chickens and rabbits in the same cage include hypothesis method, formula method, equation method, etc.

1. There are several methods such as hypothetical method, formula method, equation method and so on.

2. Hypothetical method: assume that all chickens or all rabbits are assumed.

3. Unary equation method: Suppose there are x chickens or rabbits, and the other is the total number of -x.

4. Binary Equations: Let there be x chickens and y rabbits. x+y = total number of legs, 2x+4y = total number of feet.

5. Leg lifting method: Suppose the rabbit lifts two feet.

6. Formula method Formula 1: (The number of rabbit feet, the total number of feet, the total number of feet) (the number of rabbit feet, the number of chickens) = the number of chickens, the number of chickens, the number of chickens = the number of rabbits, the total number of rabbits, the number of rabbits = the number of chickens.

Introduction to the Hypothetical Method:

The hypothesis method is an important method of thought in science, which is widely used in mathematics and physics research, and is a kind of creative thinking activity.

When the existence form of a variable factor is limited to several possibilities (such as whether a proposition is true or not, such as the magnitude of a and b: there are three cases greater than less than or equal to), it is assumed that the factor is in a certain situation (such as the proposition is true, such as a>b), and the reasoning is based on this condition, which is called the hypothetical method. It is an important method of thought in science and is widely used in mathematical physics research.

Mathematics: The method of counterargument is to use this idea to first assume the opposite direction, and then deduce the contradiction of the proposition in this direction, so that the original direction is true.

The hypothetical method (contradictory method).

The hypothesis method is one of the common solutions to solve the problem of "chickens and rabbits in the same cage", and like the naming method, this method is to make appropriate assumptions according to the conditions given in the conditions, and then get the correct answer through reasoning. The core of the solution of this method is to find the contradiction between the quantitative relations given by the hypothesis.

Here, the meaning of the hypothetical method can be explained more intuitively through examples. For example, there are some chickens and rabbits in the same cage, which are known to have 46 heads when viewed from above, and 104 legs when viewed from below. Now excuse me, how many rotten cores are there in this cage, how many chickens are missing, and how many rabbits are there?

So the thought process for this question is like this:

Find the quantitative relationship in the question: "46 heads" and "104 legs", and here you can get the information that, according to common sense, there are 46 animals in it.

Make a reasonable assumption: if the cage is full of chickens, then the number of legs should be "46 2=92 (only)", but the title is known that there are 104 feet in it, so the first contradiction arises.

Analyze the contradiction: 104-92 = 12, i.e. 12 feet are missing. Let the child think about the reason and understand that it is because the rabbit has 4 legs and the chicken has only 2.

Assuming that all the cages are full of chickens, the rabbit legs are reduced by 2, then it can be analyzed that every 2 of the 12 legs missing by the ant is a rabbit. Although this process is simple, it inadvertently develops the habit of serious thinking in children.

Find a solution: From the above thinking and analysis, it can be obtained: 12 feet less, that is, there are:

12 2 = 6", that is, 6 rabbits, then knowing one unknown, you can find another unknown, so that the number of chickens can be known, that is, 46-6 = 40, then there are 40 chickens.

Finishing formula: In summary, you can list the relevant equations, that is, the number of rabbits is: (104-46 2) (4-2)=6 (only); The number of chickens is: 46-6=40 (only).

Summary of the law: If all the cages are chickens, then the number of rabbits is: (total number of feet - total number of heads number of chicken's feet) (number of rabbit's feet - number of chicken's feet).