How to list 30 in the same cage list of chickens and rabbits in the same cage in grade 5

Hypothetical method: Suppose all chickens: 2 35 = 70 (only) less than the total number of feet:

94 70=24 (only) Rabbit: 24 (4-2)=12 (only) Chicken: 35 12=23 (only) Hypothetical method (popular) Suppose both chickens and rabbits listen to the command So, let all the animals lift one foot, the foot standing in the cage:

94-35=59 (pcs) Then lift one more foot, at this time the chicken lifts both feet and falls, leaving only the rabbit standing on two feet, standing foot: 59-35=24 (only) Rabbit: 24 2=12 (only) Chicken:

35-12=23 (only) Unary Linear Equation Solution: If there are x rabbits, then chickens have (35-x). 4x+2(35-x)=94 4x+70-2x=94 2x=24 x=24 2 x=12 35-12=23 A:

There are 12 rabbits and 23 chicks. Binary Linear Equation Solution: Let there be 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 into (x+y=35) x+12=35 x=35-12 x=23. A: There are 12 rabbits and 23 chicks.

List method: the number of chickens.

The number of rabbits has a total number of legs.

As follows:

1. Hypothetical method: (total number of feet total number of heads 2) 2 = number of rabbits, total number of heads number of rabbits = number of chickens.

2. Judgment method: (total number of heads 4 - total number of feet) 2 = number of chickens, total number of heads number of chickens = number of rabbits.

3. Foot lifting method: total number of feet 2 - total number of heads = number of rabbits, total number of heads - number of rabbits = number of chickens.

4. Learning method: (total number of feet - number of feet per chicken Total number of heads) (number of feet of each rabbit - number of feet of each chicken) = number of rabbits. (Number of feet per rabbit Total number of heads - Total number of feet) (Number of feet per rabbit - Number of feet per chicken) = Number of chickens.

Ideas for solving application problems:

1) There are some application problems in the variable problem, the conditions are more complex, and the expression of the known conditions in the question can be appropriately changed when solving, so as to make the quantitative relationship more obvious, so as to find a way to solve the problem.

2) The inverse method can think backwards for some application problems with specific structures, starting from the final result, and taking the opposite operation, so as to explore the solution ideas.

The chickens and rabbits in the same cage problem were learned in the 5th grade. Chickens and rabbits in the same cage is one of the famous interesting topics in ancient China, and the ant shed is contained in the "Sun Tzu Sutra". The problem of chickens and rabbits in the same cage is a common question type in the Mathematics Olympiad in primary schools.

Many elementary school and Sakura arithmetic problems can be transformed into this type of problem, or solved using the "what-if method", which is the typical solution to solve it.

Chickens and rabbits in the same cage is one of the famous interesting topics 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 pheasants and rabbits in the same cage, there are thirty-five heads on the top, and there are ninety-four feet under it. The meaning of these four sentences is: There are a number of chickens and rabbits in the same cage, and counting from above, there are 35 heads; Counting from below, there are 94 feet.

Ask how many chickens and rabbits are in each cage.

1. There are several chickens and rabbits in the cage, with a total of 35 heads and 94 legs, how many chickens and rabbits are there?

2. There are 40 turtles and cranes, 112 legs, how many turtles and cranes are there?

3. There are 38 people in the class, a total of 8 boats are rented, each boat is full, 6 people in the big boat and 4 people in the small boat. How many small and small boats are there?

4. There are a total of 10 bicycle tricycles, a total of 26 wheels, how many bicycle tricycles are there?

5. The unit price of the table is 60 yuan more expensive than the unit price of the chair. , bought 6 chairs and 10 tables today, and paid a total of 1224 yuan. How much is the unit price of a table and a chair?

6. In a parking lot, there are 48 cars and motorcycles, of which each car has 4 wheels, each motorcycle has 3 wheels, and these cars have a total of 172 wheels.

7. Xiao Gang bought back a total of 100 stamps of 8 cents and 4 stamps, and paid a total of yuan. How much do you pay?

8. Chickens with infiltration rabbits in the same cage, 15 more chickens than rabbits, a total of 132 chickens and rabbits, ask how many chickens and rabbits?

9. Chickens and rabbits are in the same cage, 10 more chickens than rabbits, 10 more chicken feet than rabbit feet, how many chickens and rabbits are there?

10. In the knowledge competition, there are 10 true/false questions, and the scoring stipulates that 2 points will be awarded for each correct answer, and one point will be deducted for one wrong answer. Although Xiao Ming answered all the questions, he only scored 14 points in the end.

11. There is a group of ostriches and giraffes in the zoo, they have a total of 30 eyes and 44 legs, how many ostriches and giraffes are there? Bun ridge.

12. There are 20 questions in the English competition, 7 points are awarded for doing one question correctly, 4 points are deducted for doing one question wrong, and 0 points are awarded for not answering. Xiaogang scored 100 points, how many questions did he not answer? How many questions did you get wrong?

Solution: There are x chickens.

2x+（14-x）×4=40

56-2x=40

2x=16x=8, then there are 14-8=4 rabbits.

There is a similar question that goes like this:

There are several chickens and rabbits in the cage. There are 8 heads from above, and 26 feet from below. How many chickens and rabbits are there?

Think of it this way:

1) If the cage is full of chickens, then there are 8 times 2 = 16 feet, so there are 26-16 = 10 feet more.

2) A rabbit has 2 more legs than a chicken, that is, there are 10 divided by 2 = 5 rabbits (3) so there are 3 chickens and 5 rabbits in the cage.

Think of it this way:

Solution: If there are x rabbits, then there are (8-x) chickens.

4x+2（8-x）=26

2x+16=26

x=58-5=3 (only).

A: There are 5 rabbits and 3 chickens.

Absolutely original, please rest assured, look at the owner of the building plus a few points, thank the owner.

Chickens and rabbits in the same cage The key is the problem of the legs. Rabbits have two more legs than chickens, so start here.