Chickens and rabbits in the same cage type of questions 50 questions 40

The turtle crane has a total of 100 heads and 350 legs. How many turtles and cranes are there?

2.The school has a total of 26 chess and checkers, which can accommodate 120 students at the same time. 2 players play a deck of chess and 6 players play a deck of checkers. How many decks are there in chess and checkers?

3.Some 2 cents and 5 cents coins have a total value of yuan, where the number of 2 cents is 4 times the number of 5 cents coins, ask how many 5 cents coins?

4.A person receives a salary of 240 yuan, and there are three kinds of yuan, 2 yuan, 5 yuan, and 10 yuan, a total of 50 sheets, of which 2 yuan is as many as 5 yuan. So how many are 2 yuan, 5 yuan, and 10 yuan?

5.A project was completed in 12 days by A alone, and B was completed in 18 days alone, and now A has done it for a number of days, and then B has completed the rest alone, so that there are 16 days before and after. How many days did A do it first?

6.The 281-kilometre motorcycle race is divided into stages, each of which consists of an uphill (3 km), a flat (4 km), a downhill (2 km) and a flat (4 km). Some are made up of an uphill (3 km), a downhill (2 km) and a flat (4 km). It is known that after the motorcycle completed the course, it ran a total of 25 uphill steps.

How many of these two phases are included in the process?

7.There are a total of 15 stamps of 4 cents, 8 cents and 1 jiao for 1 yuan, and how many stamps can you buy at most 1 jiao?

8. There is a truck transporting 2,000 glass bottles, the freight is calculated according to the number of bottles in good condition when they arrive, each with 2 corners, if damaged, the damaged bottles will not be given freight, and each will be compensated for 1 yuan. As a result, I got the freight yuan, and asked how many glass bottles were damaged in this transportation?

9. There are two nature tests, the first time there are 24 questions, 5 points are awarded for 1 correct answer, and 1 point is deducted for 1 question if you answer incorrectly (including not answering); The second 15 questions, 8 points for 1 correct answer, 2 points will be deducted for answering 1 question incorrectly or not answering, Xiao Ming answered a total of 30 questions correctly in the two tests, but the score of the first test was 10 points more than the score of the second test, how many points did Xiao Ming score in each of the two tests?

The total number of legs is the "sum of the two numbers", if the condition is replaced by "the difference between the two numbers", how should it be solved?

10. There are 100 chickens and rabbits, and the number of chickens' feet is 28 less than the number of rabbitsQ: How many chickens and rabbits are there?

11. In ancient poems, the five-character quatrain is a four-sentence poem, and each sentence is five words; The seven-character quatrain is a four-line poem, each of which is seven words. There is an anthology of poems, in which there are 13 more five-character quatrains than seven-character quatrains, but the total number of words is 20 words less. Ask how many poems there are for each of the two poems.

1. There are a total of 80 heads and 208 legs in the same cage, how many chickens and rabbits are there?

Analysis: Assuming that these 80 heads are all chickens, then the feet should be 2 80 160 (only), which is 208 160 48 (only) less than the actual one

Feet, this is because 1 rabbit has 4 legs, think of it as a chicken with 2 legs, each rabbit is less than 2 feet, a total of 48 feet are undercounted, 48 have a few 2s in it, that is, a few rabbits.

Solution: (208 2 80) (4 2).

24 (only) - rabbits.

80 24 56 (only).

A: There are 56 chickens and 24 rabbits.

It can also be assumed that all 80 are rabbits, and the answer is as follows:

Solution: (4 80 208) (4 2).

56 (pcs) - Chickens.

80 56 24 (only).

2. Xiao Ming participated in a mathematics competition, there were 10 test questions, 10 points for each correct question, 5 points for the wrong question, Xiao Ming scored a total of 70 points, how many questions did he do correctly?

Analysis: Suppose he does 10 questions correctly, then he should get 10 10 100 (points), but he actually only gets 70 points, 30 points less, this is because every time he does a wrong question, not only can he not get 10 points, but he will deduct 5 points, so if he gets a wrong question, he will lose 10 5 15 (points), and if you look at how many 15 points are in 30 points, you will get a few questions wrong.

Solution: (10 10 70) (10 5).

2 (Dao) - Wrong.

10 2 8 (Dao).

A: He got 8 questions right.

3. There are 100 banknotes with a face value of 5 yuan and 10 yuan, with a total value of 800 yuan. How many $5 and $10 bills are there?

Analysis: Assuming that all 100 banknotes are 5 yuan, then the total value is 5 100 500 (yuan), and the difference between the actual difference of 800 500 300 yuan is 300 yuan, because the chicken and rabbit in the same cage of 10 yuan 1 piece is counted as 2 pieces of 5 yuan, and each piece is less than 10 5 5 (yuan), and how many 5 yuan are in the difference of 300 yuan, which is how many 10 yuan banknotes.

Solution: (800 5 100) (10 5).

60 (sheets) - 10 yuan face value.

100 60 40 (sheets).

A: There are 60 bills of $10 and 40 bills of $5.

Chickens and rabbits in the same cage questions and answers:

Chickens and rabbits have a total of 80 heads and 208 feet in the same cage, how many chickens and rabbits are there?

Analysis: Assuming that these 80 are all chickens, then, the feet should be 2 80 160 (only), which is 208 160 48 (only) feet less than the actual one, this is because 1 rabbit has 4 legs, it is regarded as a chicken with 2 legs, each rabbit is less than 2 feet, a total of 48 feet are missing, and there are several 2s in 48, which is a few rabbits.

Solution: (208 2 80) (4 2) 48 2 24 (only) - rabbit, 80 24 56 (only) - chicken.

A: There are 56 chickens and 24 rabbits.

Chickens and rabbits in the same cage is one of the famous mathematical problems 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 several chickens and rabbits in the same cage, counting from above, there are 35 heads, and counting from below, there are 94 legs. Q: How many chickens and rabbits are in each cage?

The essence of this problem is a binary equation. If taught properly, primary school students can gain a preliminary understanding of concepts such as unknowns and equations, and develop their ability to abstract numbers from application problems. Generally, in the fourth to sixth grades of primary school, it is taught with the content of unary equations.

There is also a variation in the same book: there is a beast today, with six songs and four legs; Fowl, four heads and two legs, seventy-six on the top and forty-six feet on the bottom. Q:

What are the geometries of birds and beasts? Answer: Eight beasts and seven birds.

The questions include different numbers of heads and different numbers of feet.

Solution to the problem 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 (rabbits) Rabbits have more feet than chickens: 4-2 = 2 (chickens).

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。

In a binary equation, let there be x rabbits and y chickens. x+y=35，4x+2y=94。