How to calculate the problem of chickens and rabbits in the same cage, to assume the method

Let the number of heads be all rabbits or chickens [chickens have 2 legs, rabbits have 4 legs], that is, [the number of heads multiplied by the number of legs] to get the number of legs of the whole chicken or the whole rabbit, and then subtract the number of legs given by the original question and the number of legs assumed after [usually set the chicken to use the original subtraction, set the rabbit to subtract the original] use the difference of the previous part to divide the number of rabbit legs minus the difference between the number of chicken legs = the opposite of the animal set [that is, set the rabbit to get the chicken, set the chicken to get the rabbit] and finally use the total number of heads to subtract the number of heads just found to get the number of heads of another animal. Hope!

Equation 1: (Number of Rabbit's Feet, Total Count, Total Feet) (Rabbit's Feet, Chicken's Feet) The number of chickens. Total number of chickens = number of rabbits.

Equation 2: ( Total number of feet Number of chicken's feet Total number of birds) (Number of rabbit's feet Number of chicken's feet) The 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.

Equation 4: Number of chickens = (4 total number of chickens and rabbits - total number of chickens and rabbits) 2 Number of rabbits = total number of chickens and rabbits - number of chickens.

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

Equation 6: (number of heads x 4 - actual number of legs) 2 = chicken.

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

In the fifth grade, 46 students went rowing, and a total of 10 boats were occupied, with 6 people in each large boat and 4 people in each small boat, all of which were full. Q: How many are there for the big boat and the small boat?

Solution: Set up x large boats and 10-x small boats.

6x+（10-x）×4=46

6x+40-4x=46

2x=46-40

2x=6x=3

Small boats = 10-3 = 7 pcs.

Method 2, assuming that all are big boats, then take 6 10 = 60 (people), more than 60-46 = 14 (people), the reason is that some boats are originally small boats, each more than 6-4 = 2 (people), these small boats are counted as big boats have 14 2 = 7 (only), and the big boat is naturally 10-7 = 3 (only).

Method 2: Assuming it's all boats, ......Let the smart ones take care of the rest.

This kind of problem belongs to the "chickens and rabbits in the same cage problem".

When there are several chickens and rabbits in the same cage, counting from above, there are 35 heads; Counting from below, there are 94 feet:

Arithmetic: Suppose all chickens: 2 35 = 70 (only).

Less than the total number of feet: 94 70 = 24 (only).

Rabbits: 24 (4-2)=12 (pcs).

Chickens: 35 12 = 23 (only).

Hypothetical method (popular): Assuming that both the chicken and the rabbit listen to the command, then, let all the animals raise one foot, the foot standing in the cage: 94-35 = 59 (only) and then lift one foot, at this time the chicken has both feet up and falls, leaving only the rabbit standing on two feet, standing foot:

59-35=24 (only).

Rabbit: 24 2 = 12 (only).

Chickens: 35 12 = 23 (only).

Unary Linear Equation Method:

Solution: If there are x rabbits, then there are (35-x) chickens.

4x+2(35-x)=94

4x+70-2x=94

2x=24x=24÷2=12

A: There are 12 rabbits and 23 chicks.

Binary Linear Equation Method:

Solution: There are x chickens and y rabbits.

x+y=35

2x+4y=94

x+y=35）×2=2x+2y=70

2x+2y=70)-(2x+4y=94)=（2y=24）

y=12 Substitute y=12 (x+y=35).

x+12=35

x=35-12

x=23 A: There are 12 rabbits and 23 chicks.

The basic formula of the chicken-rabbit co-cage hypothesis method.

Assume that the number of rabbits: the number of chickens: (the number of rabbits 4 minus the total number of chickens and rabbits) (4-2) the number of rabbits: the total number of chickens minus the number of chickens.

Suppose the number of chickens: rabbits: (total number of chickens minus 2) (4-2) number of chickens: total number of chickens minus number of rabbits. bar.

1.Chickens and rabbits in the same cage, a total of 27 heads, 72 feet, ask how many chickens and rabbits are in the cage?

If there are x chickens in the cage, there will be 27-x rabbits in the cage.

2x+4(27-x)=72

2x=36x=18

There are 18 chickens in the cage and 9 rabbits.

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).

1.It can be said that the hypothetical method:

For example, if you assume that all rabbits are there, it will be less than the actual number of legs.

2.It can also be said that the substitution method:

For example, replace a chicken with a rabbit and add two legs ......

There are 50 chickens and rabbits in the same cage, 102 legs, how many chickens and rabbits are there?

Assuming all chickens, 50 chickens share legs:

2 50 = 100 entries.

Then less than the total number of legs:

102-100 = 2 articles.

A rabbit has two more legs than a chicken, so the extra two legs are a rabbit.

Therefore: a rabbit.

Chickens 50-1 = 49.

I'm too familiar with this kind of problem, and there are x solutions to introduce to you.

Method 1: The first step is to assume that there are x chickens and y rabbits;

The second step, column: x+y=total number of chickens and rabbits, 2x+4y=total number of chickens and rabbits;

The third step is to solve the system of equations and find the values of x and y respectively.

Method 2: The first step assumes that the total number of chickens and rabbits is all rabbits.

In the second step, the total number of chickens and rabbits is multiplied by 4, which is the number of hypothetical total legs, and the difference is obtained by subtracting the actual number of legs from the total number of legs of the hypothetical chickens and rabbits, and the difference is divided by 2 to get the number of chickens (why?). Since chickens only have 2 legs, it is assumed that chickens also have four legs, so hypothetically the extra legs are actually split to give each chicken 2 legs. ）

The third step is to use the total number of chickens and rabbits - the number of chickens = the number of rabbits.

That's it, it's not easy to organize, remember to like it before you go

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 spear from the hypothesis, that is, to find the contradiction between the quantitative relations given by the conditions from the hypothesis.

Here, the meaning of the hypothetical method can be explained more intuitively through the use of 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 chickens and rabbits are in this cage?

Parents should learn to cultivate the habit of thinking before tutoring their children to solve problems. In the process of thinking, it not only improves the child's correct rate of doing the questions, but also exercises the child's logical thinking ability.

So the thought process for this question is like this:

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

2. 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 appears.

3. Analyze the contradiction: 104-92=12, that is, 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.

When the cage is full of chickens, the rabbit feet are reduced by 2, so it can be analyzed that every 2 of the 12 feet missing is a rabbit.

Although this process is simple, it inadvertently develops the habit of serious thinking for the child.

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.

Let the number of chickens be x, and the number of rabbits be y

x+y=total.

2x+4y=total number of legs.

Two equations, two unknowns, x, y can be solved, respectively.

Using the binary one-dimensional equation, directly set how many chickens, how many rabbits, two unknowns, and the two equations are completed directly.