What to do if the child can t understand the problem of chickens and rabbits in the same cage

Bao Bell: If the rabbit lifts its front feet...

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. Finally, find the number of animals (chickens or rabbits).

The basic number touches the cherry blossom amount relation, and the ridiculous bush is 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;The number of chickens = the total number of sedan attacks - the 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: Number of chickens = (4 total number of chickens and rabbits - total number of feet of chickens and rabbits) 2 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 feet (x = rabbits, total x = number of chickens, used in the equation).

The solutions to the problem of chickens and rabbits in the same cage include equation method, drawing method, golden rooster independence method, and whistle blowing method.

1. Equation method

Let the number of chickens be x, then there are (14-x) rabbits, 2x+4(14-x)=38, and x=9 is solved, so there are 9 chickens and 14-9=5 rabbits.

2. Drawing method

Drawing makes math visual, and drawing regularly helps to develop creativity! Assuming that all 14 of Tuanhui are chickens, draw the chickens first. 14 2 = 28 chickens, the difference is 38-28 = 10 chickens, and each chicken makes up 2 legs to become rabbits, and it is necessary to make 5 chickens each with 2 legs, so there are 5 rabbits, 14-5 = 9 chickens.

3. Golden Rooster Independence Law

Let each chicken stand on one foot and each rabbit on two hind feet, then the total number of feet on the ground is only half of the original, that is, 19 feet. The number of legs of a chicken is the same as the number of heads, and the number of feet of a rabbit is twice the number of heads of a rabbit, so subtracting the number of heads from 19 to 14 leaves the number of heads of a rabbit 19 14 = 5, and the number of chickens having 14 5 = 9.

4. Whistle blowing method

Assuming that both chickens and rabbits are well trained and whistle blows, and all animals (35) raise one foot, the number of feet on the ground remains: 94-35=59 (only); When the whistle is blown again, each animal raises another foot, and the number of feet touching the ground is still 59-35=24 (only), and all the chicken's feet are not touching the ground, and all 24 feet are rabbit's feet.

Therefore, we can know that the number of rabbits is: 24 2 = 12 (only), then the number of chickens is: 35-12 = 23 (only) Na or Jean.

There are several chickens and rabbits in the cage. Counting from above, there are 35 heads. Counting from below, there are 94 feet. How many chickens and rabbits are there?

Answer: <

Solution: Command the chicken and the rabbit to sit down, then there is 35 2 = 70 feet missing, and the remaining feet 94-70 = 24 are all rabbit feet, so it is concluded that there are 24 2 = 12 rabbits.

So there are 35-12 = 23 chickens.

So 23 chickens and 12 rabbits.

Well, if you want the answer, you might as well turn to the bottom, the forelimb disfigurement part is the content of the solution, and part of the idea, the front part may be very diaphragmatic.

A typical chicken-rabbit cage problem can be done in an "alternative" way: first suppose that all of them are spiders, and the spiders are usually eight-legged (secretly removing the exception of six-legged spiders), then there are a total of 25*8=200 legs, 200-170=30 (strips) and 30 more, 8-6=2 (strips).

Because all spiders will have thirty extra legs, replace a certain number of spiders with grasshoppers, and the total number of spiders will change to: total number - number of spiders replaced by grasshoppers * 8 + number of spiders replaced by grasshoppers * 6, which is equivalent to total number - spiders replaced by grasshoppers *2 The following is an example: 24 spiders and 1 grasshopper are replaced by 24 spiders and 1 grasshopper, which is 24 * 8 = 192 (strips) 192 + 6 = 198 legs, or 200-2 can be counted in this way.

Therefore, if there is an extra 30, the number of spiders to be replaced by grasshoppers is 30 2=15, that is, 15 grasshoppers, and 25-15=10 spiders You can also secretly check it, 15*6=90 (pieces) 10*8=80 (pieces) The sum of the two is still 170, and there is no miscalculation.

8 25=200 (pieces) 200-170=30 (pieces) 8-6=2 (pieces) 30 2=15 (pieces) This is the number of grasshoppers This is the number of spiders 25-15=10 (pieces).

I feel that the previous explanation is difficult to understand, and there is nonsense xd

Chicken = x Rabbit = y

There are a total of 48 chickens and rabbits.

2x+4y=48

x+2y=24 (1)

If you swap the number of chickens with the number of rabbits, there are 42 big feet.

2y+4x=42

4x+2y=42 (2)

3x=18x=6

from (1)

x+2y=24

6+2y=24

y=9 chickens=x=6.

Rabbit = y = 9 pcs.

If the two front feet of the rabbit are tied with a rope and regarded as one foot, and the two hind feet are also tied with a rope and regarded as one foot, then the rabbit becomes a chicken with two legs, that is, the rabbit is first regarded as a chicken with two legs. The total number of feet of chickens and rabbits is 35 2 = 70 (only), which is 94-70 = 24 (only) less than the 94 mentioned in the question.

Now, if you untie the rope on a rabbit's foot, the total number of feet will increase by 2, i.e. 70 + 2 = 72 (only), and if you release the rope on a rabbit's foot, the total number of legs will increase by 2, 2, 2 ......, continue to go until it increases by 24, so the number of rabbits: 24 2 = 12 (only), so that the chickens have 35-12 = 23 (only).

Let's summarize the solution idea of this problem: first assume that they are all chickens, so according to the total number of chickens and rabbits, you can calculate how many feet there are under the assumption, compare the number of feet obtained in this way with the number of feet given in the question, and see how much the difference is, every 2 feet indicates that there is 1 rabbit, and divide the number of legs by 2, you can calculate how many rabbits there are. To sum up, the basic relationship for solving the chicken-rabbit same cage problem is:

Number of rabbits = (actual number of feet - number of chickens per chicken total number of chickens) (number of feet per rabbit - number of chickens and rabbits). Similarly, it can be assumed that it is all rabbits.

We can also use the method of column equations: let the number of rabbits be x and the number of chickens be y

So: x+y=35 then 4x+2y=94 When the equation is solved, I laugh at it: there are 12 rabbits and 23 chickens.