Today there are chickens and rabbits in a cage, there are thirty five heads on the top, and there ar

Hypothetical method. Let's say it's all rabbits.

Number of chickens: (4 times 35-94) divided by (4-2).

140-94) divided by 2

46 divided by 223.

Number of rabbits: 35-23=12.

Let's say it's all chickens.

Number of rabbits: (94-35 times 2) divided by (4-2).

94-70) divided by 2

24 divided by 212.

Number of chickens: 35-12=23.

2.Foot lifting.

94 divided by 2 = 47.

Rabbits: 47-35 = 12 pcs.

Chickens: 35-12 = 23 chickens.

There are 23 chickens and 12 rabbits.

Note: Let the chicken lift one foot, the rabbit lift two feet, the total number of feet is half of the original, then the number of chicken's feet and the number of heads are the same, the rabbit has two legs, the number of feet is one more than the number of heads, so, as long as there is a rabbit in the cage, the total number of feet is one more than the total number of heads.

Equation method. Solution: If there are x chickens, then rabbits have (35-x), which is derived from the title:

2x+4(35-x)=94

Solution: x=23

So: 35-23 = 12 (only).

A: There are 23 chickens and 12 rabbits.

Let's say it's all rabbits.

Number of chickens: (4 times 35-94) divided by (4-2).

140-94) divided by 2

46 divided by 223.

Number of rabbits: 35-23=12.

Let's say it's all chickens.

Number of rabbits: (94-35 times 2) divided by (4-2).

94-70) divided by 2

24 divided by 212.

Number of chickens: 35-12=23.

2.Foot lifting.

94 divided by 2 = 47.

Rabbits: 47-35 = 12 pcs.

Chickens: 35-12 = 23 chickens.

There are 23 chickens and 12 rabbits.

Note: Let the chicken lift one foot, the rabbit lift two feet, the total number of feet is half of the original, then the number of chicken's feet and the number of heads are the same, the rabbit has two legs, the number of feet is one more than the number of heads, so, as long as there is a rabbit in the cage, the total number of feet is one more than the total number of heads.

Chicken Clearing Town or=x

Rabbit = Y has thirty-five brigade orders.

x+y=35 (1)

There are ninety-four feet underneath.

2x+4y=94 (2)

2y=24y=12

from (1)

x+12=35

x = 23 chickens = x = 23.

Rabbit = y = 12 pcs.

1.Hypothetical method.

Let's say it's all rabbits.

Number of chickens: (4 times 35-94) divided by (4-2).

140-94) divided by 2

46 divided by 223. Number of rabbits: 35-23=12.

Let's say it's all chickens.

Number of rabbits: (94-35 times 2) divided by (4-2).

94-70) divided by 2

24 divided by 212. Number of chickens: 35-12=23.

2.Foot lifting.

94 divided by 2 = 47.

Rabbits: 47-35 = 12 pcs.

Chickens: 35-12 = 23 chickens.

There are 23 chickens and 12 rabbits.

Note: Let the chicken lift one foot, the rabbit lift two feet, the total number of feet is half of the original, then the number of chicken's feet and the number of heads are the same, the rabbit has two legs, the number of feet is one more than the number of heads, so, as long as there is a rabbit in the cage, the total number of feet is one more than the total number of heads.

Set x chickens, 38-x rabbits.

2x+4(38-x)=106

2x+162-4x=106

2x=56x=28

28 chickens and 10 rabbits.

This question is one of the famous interesting questions in ancient China. About 1,500 years ago, this interesting question was recorded in the "Sun Tzu's Sutra". Here's how it is narrated in the book:

Today, there are chickens and rabbits in the same cage, there are thirty-five heads on the top, and ninety-four feet on the bottom. The meaning of these four sentences is: there are several chickens and rabbits in the same cage, counting from above, there are 35 heads; Counting from below, there are 94 feet.

How many chickens and rabbits are in the cage?

The idea is this: if you cut off half of the feet of each chicken and each rabbit, then each chicken will become a "one-horned chicken" and each rabbit will become a "two-legged rabbit". Thus, (1) the total number of chickens and rabbits has changed from 94 to 47; (2) If there is a rabbit in the cage, the total number of feet is 1 more than the total number of heads.

Therefore, the difference between the total number of feet 47 and the total number of heads 35 is the number of rabbits, i.e., 47 35 12 (only). Obviously, the number of chickens is 35 12 23 (only).

This idea is novel and peculiar, and its "foot cutting method" has also amazed ancient and modern Chinese and foreign mathematicians. This method of thinking is called naturalization. Reduction is to solve the problem by not taking a direct analysis of the problem, but deforming the conditions or problems in the problem and transforming them until they are finally reduced to a solved problem.

The solution on the Sun Tzu Sutra is very ingenious, it is calculated according to the formula: the number of rabbits and the number of heads, the specific calculation is as follows: the number of rabbits (only), the number of chickens and the number of heads 35 12 23, and the book also gives the origin of the formula:

After dividing the number of feet by 2, each chicken only has one foot left, and each rabbit has two legs left, subtracting the number of heads, which is equivalent to subtracting one more per chicken and rabbit, and the chicken feet are reduced, and each rabbit has only one foot, and the number of feet left is exactly equal to the number of rabbit heads.

There are thirty-five on them, which is 35 animals. Then cut off all of them with one foot 94-35, and the rest is a three-legged rabbit and a one-legged chicken, a total of 59. 59-35, all that is left is a two-legged rabbit and a legless chicken.

A total of 24 feet. Because a rabbit has 2 legs, divide 24 by 2 to get 12 rabbits. 35-12 = 23 chickens.

There are x and y chickens and rabbits.

Equations according to the question:

x+y＝35 2x+4y＝94

Solve the equation to get x 23 y 12

A: There are 23 chickens and 12 rabbits.

There are x chickens and rabbits with locust buckets.

From the question to get Suiwei, guess Mingpei x+y=35, 2x+4y=94 solution, x=23, y=12

23 chickens and 12 rabbits.