Chickens and rabbits in the same cage problem list method, chickens and rabbits in the same cage sol

If there are x rabbits, then there are 35-x chickens. 4x+2(35-x)=94 4x+70-2x=94 2x=24 x=24 2x=12 35-12=23 Answer: There are 12 rabbits and 23 chicks.

It is to substitute one by one according to the meaning of the topic.

For example, there are a few chickens and rabbits in a cage. There are 8 heads from the top and 26 legs from the bottom.

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Here's how to solve the problem:

1.Let the number of chickens be x and the number of rabbits be y, then there are two equations:

x + y = m (total number of heads).

2x + 4y = n (total number of feet).

2.Solve the values of x and y by solving the system of equations or by substitution.

3.Determine the number of chickens and rabbits based on the values of x and y.

It is important to note that in order to ensure that the problem is solved, the following conditions need to be met:

1.The number of chickens and rabbits is a non-negative integer.

2.The total number of heads m must be greater than or equal to the total number of legs n.

If m and n do not meet the above conditions, then the problem is unsolvable.

For example, if there are 10 heads and 28 rotten feet in a cage, how do you find the number of chickens and rabbits?

1.The root scatter is listed as a system of equations according to the above equations:

x + y = 10

2x + 4y = 28

2.Solve the values of x and y by solving the system of equations or substitution method, and obtain:

x = 6，y = 4

3.The number of chickens and rabbits is determined based on the values of x and y, i.e., there are 6 chickens and 4 rabbits in the cage.

Therefore, the solution to the chickens and rabbits in the same cage problem needs to determine the number of chickens and rabbits by listing the system of equations and solving the system of equations, and it is necessary to pay attention to the conditional Penner limit.

Chicken and rabbit co-cage enumeration method (list method):

The method is very simple, but the process is very complex, more changing the number of chickens and rabbits, respectively, the number of chickens and rabbit legs is filled in **, until the answer is found, this method is only suitable for students in the classroom to explore and guide each other without a spine, not commonly used.

Leg Lift Method: 1Suppose both the chicken and the rabbit raise their two feet, leaving 94 35 2 = 24, and there are only rabbit legs on the ground, and each rabbit has two feet on the ground, so 24 2 = 12 rabbits, there are 35 12 = 23 chickens.

2.If the chicken is allowed to lift one foot, and the rabbit lifts two feet and withers, there are 94 2 = 47, and the rabbit in the cage has 1 more feet than the chicken, then the difference between the total number of feet and the head is 47-35 = 12, which is the number of rabbits, 35-12 = 23 chickens.

2) Jumping Tan Leap List Method: When enumerating, according to the value of the number of feet, Tong refers to jumping to let the wheel bridge enumerate, simplifying the number of enumerations. Mr. Wu Yang|Unique.

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3) Neutralization list method: first try to have the same or close number of chickens and rabbits, and then adjust according to the number of feet.

Whatever the future is born with.

Although the above three list methods can be used to find the results, they are too cumbersome and we generally do not use them when solving problems.

Use the what-if method" to solve.

That is, if all chickens or rabbits are all, and then the number of chickens or rabbits is calculated according to the difference in the number of feet. Find the number of another animal (chicken or rabbit) after touching the cherry blossoms.

The basic quantitative relationship can be divided into two aspects:

Assuming that all chickens are there, then there are: the number of rabbits = (total number of feet - 2 total number of heads) 2;Number of chickens = total number of heads - number of rabbits.

Assuming that all rabbits are there, then there are: the number of chickens = (4 total number of heads - total number of feet) 2;Number of rabbits = total number of heads - number of chickens.

Chicken and rabbit cage formula:

Equation 1: Number of rabbit's feet Total number of feet Total number of feet) (Number of rabbit's feet Number of chicken's feet) = Number of chickens.

Total number of chickens = number of rabbits.

Equation 2: Total number of feet Number of chicken's feet Total number of feet) (Number of rabbit's feet Number of chicken's feet) = Number of rabbits.

Total number of rabbits = number of chickens.

Formula 3: Total number of feet 2 - total number of heads = number of rabbits.

Total number of rabbits = number of chickens.

Formula 4: The number of chickens = (4 total number of chickens and rabbits - total number of feet of chickens and rabbits) 2 The number of rabbits = chickens and rabbits.

Total number - the number of chickens.

Formula 5: Total number of rabbits = (total number of feet of chickens and rabbits - 2 total number of chickens and rabbits) 2 number of chickens = chickens and rabbits.

Total number of rabbits - the total number of rabbits.

Equation 6: Number of heads x 4 - actual number of feet) 2 = chicken.

Equation 7: 4 +2 (total x) = total number of laughing bushes (x = rabbits, total x = number of chickens, used in the equation).

As far as I know, the chickens and rabbits in the same cage problem is a classic mathematical puzzle, which usually asks the following questions: There are several chickens and rabbits in a cage, and it is known that there are n heads and m legs in total, how many chickens and rabbits are in the cage? This problem can be solved with an algebraic equation.

Assuming the number of chickens is x and the number of rabbits is y, there are two equations: x + y = n (1) 2x + 4y = m (2) where equation (1) represents the total number of heads and equation (2) represents the total number of feet. Multiply equation (1) by 2 to get 2x + 2y = 2n.

Then substituting this equation into equation (2), subtracting x, we get: 2y = m - 2n Therefore, we can find the value of y, and then use equation (1) to find the value of x, and we can get the number of chickens and rabbits. The specific steps are as follows:

Based on known conditions, a system of equations is listed. Transform the system of equations to eliminate one of the unknowns. Find the relationship between the known quantity and the variable to be solved.

The value of the variable to be solved is calculated based on known conditions. Bring the value of the variable to be solved back into the equation to solve another unknown. In this way, you can easily solve the problem of chickens and rabbits in the same cage.

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Hello, this question is answered by me for you, the solution to the problem of chickens and rabbits in the same cage: 1. Assuming that the cage is full of chickens, there are a total of 35 2 = 70 feet, but there are actually 94 feet, a total of 94-70 = 24 feet, because each rabbit is regarded as a chicken, less than two feet, so the number of rabbits can be 24-2 = 12, then the chicken has 35-12 = 23. 2. Assuming that the cage is full of rabbits, there are a total of 35 4 = 140 feet, which is 140-94 = 46 feet more than the actual number of feet, and each rabbit has two more feet, so there are 46 + 2 = 23 chickens, and 35-23 = 12 free chickens.

Solution to the problem of chickens and rabbits in the same cage.

Hello dear <>, this question is answered by me, the solution to the problem of chickens and rabbits in the same cage: 1. Assuming that the cage is full of chickens, there are a total of 35 2 = 70 feet, but there are actually 94 feet, and the total number of laughing wild is 94-70 = 24 feet, because each rabbit is regarded as a chicken, counting two feet less, so the number of rabbits can be 24-2 = 12, then there are 35-12 = 23 chickens. 2. Assuming that the cage is full of rabbits, there are a total of 35 4 = 140 feet, which is 140-94 = 46 feet more than the actual number of feet, and each rabbit has two more feet, so there are 46 + 2 = 23 chickens, and 35-23 = 12 chickens.

<>The chickens and rabbits in the same cage problem is a classic mathematical problem, also known as the "chicken-rabbit co-column problem" or "chicken-rabbit co-cage number problem". The essence of this question is to find the number of chickens and rabbits when the total number of ears and legs is known.

The solution to the chickens and rabbits in the same cage problem is as follows:

Method. 1. Hypothetical method.

The most common way to solve the problem of "chickens and rabbits in the same cage" is the hypothetical method, and children will also like to use this simple and fast method in the learning process.

Common assumptions are: Suppose the cage is full of rabbits or chickens, for example: there are 30 heads and 68 legs in the cage, how many rabbits are there? How many chickens?

The solution is to assume that the cage is full of rabbits, so that you can get the number of chickens (4 30-68) (4-2) = 26 (birds), then the rabbits are 30-26 = 4 (birds).

Method. Second, the leg cutting method.

As the name suggests, the leg cutting method is to remove the extra legs, that is, to turn the rabbit's legs into two, then the number of remaining legs in the cage should be: 30 2 = 60, and the original should have 68 feet, then here should be reduced 68-60 = 8 (only) feet, when the rabbit removes 2 legs, the number of legs in the cage will be reduced by 2, then there are 8 2 = 4 (only) rabbits, the number of rabbits can be obtained, and the number of chickens can be obtained.

Method. 3. Leg lift method.

Like the leg chopping method, the method of the leg lifting method is the same as the name. The steps in this method are to have the chicken lift one leg and the rabbit lift both legs, so that the number of legs in the cage will become half of the original number, i.e. 68 2 = 34.

Then let the raised legs of the chicken and rabbit land to the ground, so that the rabbit's feet will be 1 more than the rabbit's number, and the chicken's feet are the chicken's number. Therefore, it can be deduced that the number of rabbits is the number of legs minus the number of heads, that is, 34-30 = 4 (only), and the number of chickens is 30-4 = 26.