How to solve the problem of chickens and rabbits in the same cage

z to find a difference. Each chicken rabbit is 2 feet off.

1 chicken, 1 rabbit, 2 heads and 6 legs.

1 chicken, 2 rabbits, 3 heads and 10 feet.

Such topics. Let's start with the assumption that all chickens are calculated, and the difference between the feet is 2 feet for each chicken and rabbit.

For example: 1 chicken, 2 rabbits, 3 heads and 10 feet.

Suppose there are all 3 chickens, 3 heads and 6 legs, now 10 feet, 10-6 feet more, each chicken and rabbit is 2 feet apart, and the extra rabbits, (10-6) 2=2, that is, there are 2 rabbits, 3-2=1 chicken.

Or. Suppose all rabbits, 3 heads and 12 feet, now 10 feet, less 12-10 feet, each chicken rabbit is 2 feet short, less is chicken, (12-10) 2=1, that is, there is 1 chicken, 3-1=2 rabbits.

The simplest way to solve the problem is to use equations.

When you reach junior high school, you will find it very simple.

Hypothetical Method:

1. Suppose all chickens: 2 35 = 70 (only) 2. Chicken feet are less than the total number of feet: 94 - 70 = 24 (only) 3. The number of rabbits with more feet than chickens:

4 - 2 = 2 (only) 4, the number of rabbits: 24 2 = 12 (only) 5, the number of chickens: 35 - 12 = 23 (only) 6, assuming all rabbits:

4 35 = 140 (only) 7, more rabbit feet than the total: 140 - 94 = 46 (only) 8, more rabbit feet than chickens: 4 - 2 = 2 (only) 9, number of chickens:

46 2 = 23 (only) 10, the number of rabbits: 35 - 23 = 12 (only).

(Total number of feet.)

Total number of heads Number of chickens' feet) (Number of rabbit feet - Number of chickens' feet) = Number of rabbits (94 35 2) 2 = 12 (number of rabbits) Total number of heads (35) Number of rabbits (12) = Number of chickens (23).

Explanation: Let the rabbit and chicken lift both feet at the same time, so that the total number of feet in the cage is reduced by 2, since the chicken only has 2 feet, so there are only two feet left in the cage of the rabbit, and then 2 is the number of rabbits.

The formula for chickens and rabbits in the same cage:

Solution 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.

Solution 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.

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

Total number of rabbits = number of chickens.

1. There are x rabbits and y chickens.

According to known conditions, it is available:

x+y=45

4x+60=2y

solution, x=5, y=40

So, there are 40 chickens and 5 rabbits.

2. If you buy x tickets of type A, then you will have tickets of type B (x+9).

According to known conditions, it is available:

4x+3（x+9）=97

Solution: x=10, x=9=19

So, I bought 10 tickets for type A and 19 tickets for type B.

The total fare is an integer, so the number of people on the tram must be a multiple of 5, and the equation limits the term, and then enumerated.

Set up to be a tram x person, a minibus y person, and a subway z person.

x+y+z=50

7x-5z=225

3) Because z>=0, then 7x>=225, x>=32, and because x<=50 is properly obtained by (3) x=50, z=25

x+z>50 is impossible.

x=45,z=18

x+z>50 is impossible.

x=40,z=11

x+z>50 is impossible.

x=35,z=4

So y=50-35-4=11

I wrote it when I thought of it.,It's probably more convenient to use xy.,I didn't think of a good way to do it all at once.,Let's do it first.。

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

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

Chickens and rabbits in the same cage solution.

I'll answer with a reward.

byfrippy

Let's talk about following to become the 860th fan.

Hypothetical method: 1. Suppose all chickens: 2 35 = 70 (only) 2. Chicken feet are less than the total number of feet: 94 - 70 = 24 (only) 3. The number of feet of rabbits is more than that of chickens:

4 - 2 = 2 (only) 4, the number of rabbits: 24 2 = 12 (only) 5, the number of chickens: 35 - 12 = 23 (only) 6, assuming all rabbits:

4 35 = 140 (only) 7, more rabbit feet than the total: 140 - 94 = 46 (only) 8, more rabbit feet than chickens: 4 - 2 = 2 (only) 9, number of chickens:

46 2 = 23 (only) 10, number of rabbits: 35 - 23 = 12 (only) Extended information:

There's a simplest algorithm for this.

Total number of feet - total number of heads Number of chicken's feet) (Number of rabbit's feet - Number of chicken's feet) = Number of rabbits.

94 35 2) 2 = 12 (number of rabbits) Total number of heads (35) Number of rabbits (12) = number of chickens (23).

Explanation: Let the rabbit and chicken lift both feet at the same time, so that the total number of feet in the cage is reduced by 2, since the chicken only has 2 feet, so there are only two feet left in the cage of the rabbit, and then 2 is the number of rabbits.

1.The head teacher, Mr. Zhang, led 50 students in the fifth grade (7) class to plant trees, Mr. Zhang planted 5 trees, each boy planted 3 trees, and each girl planted 2 trees, a total of 120 trees were planted.

Solution: There are x number of boys.

Girls have (50-x people).

3x=120-5-2（50-x）

3x = 115-2 times 50 + 2x

3x=115-100+2x

3x=15+2x

x=1550-15=35 (person).

A: There are 15 boys and 35 girls.

2.One large oil bottle contains 4 kg, two small oil bottles contain 1 kg, and there are a total of 60 bottles of 100 kg of oil. Q: How many large and small oil bottles are there?

1 2 = kg) 4 60 = 240 (kg) 240-100 = 140 (kg) 140 (pcs) 60-40 = 20 (pcs).

A: 20 large bottles and 40 small bottles.

3.Xiaomao participated in the math competition, did a total of 20 questions, scored 67 points, knew to do one correctly scored 5 points, did not do 0 points, and deducted 1 point for a wrong question, and knew that he did the same number of questions as he did not do. How many questions did Xiaomao get right?

In this question, you can set Xiaomao to do the correct x, then do (20-x) 2 incorrectly, do not do (20-x) 2, and then multiply 5 by 5 to multiply 1 to do wrong, which is equal to 67.

Equation: 5x-(20-x) 2 1=67

x = 14 small hairs do 14 right.

4.There are 18 spiders, dragonflies, and cicadas, with a total of 118 legs and 20 pairs of wings (spiders have 8 legs; Dragonfly 6 legs, 2 pairs of wings; Cicadas have 6 legs and 1 pair of wings), how many of each of the three animals?

Solution: The equation assumes x for spiders, y for dragonflies, and z for cicadas

Then x+y+z=18

8x+6y+6z=118

2y+z=20

This is calculated. x=5y=7

z=6so.

Spiders are 5 pcs.

Dragonflies are 7 pcs.

There are 6 cicadas.

Hypothesis Assuming that all of them are chickens, then the number of heads 2 = the number of chickens' feet, but this is not the number of chickens' feet, and the number of chickens' feet is 2 fewer than that of rabbits.

So (total number of feet, number of chickens' feet) 2 = number of rabbits, total number of heads—number of rabbits = number of chickens.

The total number of legs divided by 2 minus the total number of heads equals the number of rabbits.

The classic chickens and rabbits in the same cage problem can be quickly solved in two ways.

I just liked to say it well.

There are 100 chickens and rabbits, 80 chicken feet, and how many chickens and rabbits.

Very well, it's as simple as that, because of jealousy and disgrace, that power first bolted out the total number of chickens.

It's better to set rabbits for x, don't set chickens, chickens are not easy to do!!

If there are x tortoises and y cranes, the turtles have 4x legs, and the cranes have 2y legs, then x+y=40

4x+2y=112

Generally speaking, the solution to this kind of problem is to set the unknowns, and then the system of equations can get the result.

4 Rabbit + 2 Chicken = Total Legs.

Rabbit + Chicken = Total number of heads.

Turtles and cranes have 40 and only 112 legs.

Each turtle has 4 retreats, and x has a total of 4x turtles.

Each crane has 2 legs, and the turtle has x, so the crane has (40-x) and the crane has 2 (40-x).

Crane leg + turtle leg = 112

4x+2（40-x）=112

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 this method is to find the spear by Pihu, 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 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?

The thought process for this question is as follows:

1. Find the quantitative relationship in the question: that is, "46 heads" and "104 feet" are teased, and the information can be obtained 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.

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 is a rabbit. Although this process is simple, it inadvertently develops the habit of serious thinking in children.

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

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.

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

6. Summary of the law: If it is assumed that all the chickens in the cage are chickens, then the number of rabbits is: (the total number of feet - the total number of heads and the number of chicken's feet) (the number of rabbit feet - the number of chicken's feet).

Chicken and rabbit in the same cage leg lifting method one:

Let's say each chicken lifts one foot and each rabbit lifts two feet.

By 94 2 = 47, i.e. there are 47 feet under the cage, so a chicken corresponds to 1 leg, a rabbit corresponds to 2 legs, and the cage has 35 heads on it.

From 47-35 = 12, that is, if 35 heads correspond to 35 feet, there will be 12 more feet, which means that there are 12 rabbits in the cage.

By 35 12 = 23, i.e. there are 23 chickens in the cage.

Chicken and rabbit in the same cage to raise the leg method two:

Suppose each chicken and rabbit lift 2 feet.

By 35 2 = 70, 94 70 = 24, i.e. there are 24 feet under the cage, and these feet are rabbits. So 24 2 = 12, i.e. there are 12 rabbits in the cage.

By 35 12 = 23, i.e. there are 23 chickens in the cage.

Chickens and rabbits raise their legs in the same cage method three:

Let the rabbit lift 2 feet first, that is, from 35 2 = 70, 94 70 = 24, and there are 24 feet under the cage, and these feet are all rabbits.

By 24 2 = 12, i.e. there are 12 rabbits in the cage.

By 35 12 = 23, i.e. there are 23 chickens in the cage.

The practice of chickens and rabbits in the same cage:1) Hypothetical method.

2) Equation method.

The details are as follows:

There are several chickens and rabbits in the same cage, counting from above, with 35 heads, and counting from below, with 94 legs. Find the number of chickens and rabbits.

1) Hypothetical method.

Suppose it's all chickens: 2 35 = 70 (only).

Chicken feet are less than the total number of feet: 94 70 = 24 (pcs).

The number of feet that rabbits have more than chickens: 4-2=2 (only).

Number of rabbits: 24 2=12 (only).

Number of chickens: 35 12 = 23 (chickens).

2) Equation method.

In the unary equation, if there are x rabbits, then there are (35-x) chickens. 4x+2（35-x）=94。

Binary equation, let the rabbit scatter there are x and the chicken has y. x+y=35，4x+2y=94。