Find the difficult chicken and rabbit in the same cage example, chicken and rabbit in the same cage

1.A school arranges dormitories for students. If there are 5 people in each dormitory, 4 people will not be able to accommodate; If there are 6 people in each room, there will be only 4 people in one room, and there will be no occupancy in the two dormitories. Find the number of students in the grade and the number of dormitories.

Solution: The number of students in the grade is x, and the dormitory is y).

2.Prepare two kinds of paints with two kinds of raw materials A and B, and it is known that the ratio of A paint containing A and B raw materials is 5:4, 50 yuan per kilogram, and the ratio of B paint containing A and B raw materials is 3:

2. Yuan per kilogram, find how many yuan per kilogram of raw materials A and B are respectively.

Solution: Set X yuan per kilogram of A raw materials and Y yuan per kilogram of B raw materials).

3.A and B are 24 kilometers apart, and buses and direct express buses leave at 8:45 in opposite directions from A and B, both of which are at 8:45

52 Arrive at halfway point A. Once, the direct express train was 8 minutes late, and the two cars met at 8:58 on the way to B, and the speed of the two trains was calculated.

Solution: Direct express buses are set up at x kilometers per hour, and buses are set up at kilometers per hour).

4.To use two antiseptic potions containing 30% and 75% of the medicine, and prepare 18 kilograms of preservative solutions containing 50% of the medicine, how many kilograms of each of the two potions should be taken?

Solution: Set the potion containing 30% of the medicine x kg, and the potion containing 75% of the medicine y kg).

5.An express train is 70 kilometers long, slow train is 80 kilometers long, if two cars are going in the same direction at the same time, the fast train from catching up with the slow train to completely leaving the slow train is 20 seconds, if the two cars are going in the opposite direction, then the two cars meet and leave the time of 4 seconds, find how many kilometers each car travels per hour.

Solution: Let the fast train travel x kilometers per hour, and the slow train travel y kilometers per hour).

6.Li Yang saved 2,000 yuan and 1,000 yuan respectively in two ways, and took them all out after a year, and he could get interest yuan after deducting interest income tax. Knowing what is the annual interest rate of these two types of savings, what percentage is the annual interest rate of each of these two types of savings?

Note: Interest income tax paid by citizens = interest amount * 20%.

Solution: Let the annual interest rate of 2000 yuan be x, and the annual interest rate of 1000 yuan is y).

7.In order to celebrate Children's Day, primary and secondary schools in a certain city organized a unified theatrical performance. A and B schools have a total of 92 people (of which the number of school A is more than the number of school B, and the number of school A is less than 90 people) is ready to buy costumes to participate in the performance, the following is the first table of performance costumes given by a garment factory:

Number of sets of clothing purchased: 1 to 45 sets; 46 sets to 90 sets; 90 sets and above.

** for each set of clothing: 60 yuan 50 yuan 40 yuan.

If the two schools buy clothing separately, a total of 5,000 yuan should be paid.

1) If School A and School B join forces to buy clothing, how much can they save compared to buying clothing separately?

2) How many students from each school A and B are ready to participate in the performance?

3) If there are 10 students from School A who are selected to participate in the calligraphy and painting competition and cannot participate in the performance, please design a cost-effective costume purchase plan for the two schools.

8.100 pennies for 100 chickens. Big chickens are 8 yuan each, small chickens are bought for three dollars, and three dollars are used to buy a medium chicken, how many chickens are large, medium and small?

There were 38 people in the class, and a total of 8 boats were rented, each large boat for 6 people, and each small boat for 4 people, and each boat was full. Q: How many large boats and small boats are there?

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Chickens and rabbits in the same cage small burial solution: 1Think of chickens and rabbits as rabbits.

Count how many legs there are and divide by "2" to get the number of rabbits. 2.Think of chickens and rabbits as chickens, count out how many legs are missing, and divide by "2" to get the number of rabbits.

3.Let's say half rabbit, half chicken. Calculate how many legs there are, subtract the number of legs in the original question from the number of legs "calculated", and then divide by "2" to dress up the calendar, which is the number of extra rabbits, and then add half of the total number of rabbits after the lack of ants.

Hello, dear, happy to answer your questions. Chickens and rabbits in the same cage is a classic mathematical problem, and the solution is as follows: Assuming that the number of chickens and rabbits is x and py respectively, then according to the meaning of the problem, there are two equations:

1.x + y = total number (total number of chickens and rabbits); 2.2x + 4y = total number of legs (chickens have two legs, rabbits have four).

In this case, we can solve the values of x and y by concatenating these two equations, and we can get the respective numbers of chickens and rabbits. After the equation is simplified, we can get: 3

x = total number of legs - 2 * total number) 2;4.y = total quantity - x. If the value of x or y is not an integer, this is not possible.

It should be noted that sometimes there may be multiple solutions to the results of the dusty rock, so you need to pay special attention to the conditions in the question, such as the possible restrictions on gender, weight, age, etc.

Chickens and rabbits in the same cage to solve the problem are the list method that everyone loves, the happiest drawing method, the coolest golden rooster independence method, etc.

1. The list method that everyone loves.

For example, after listing 0 chickens and 14 rabbits, and finding that the number of legs is 56, which is quite different from the 38 in the question, then the number of chickens that can be skipped is 2, and the number of chickens is 3, which will be faster.

2. The happiest way to draw.

Drawing can make math visual, and drawing regularly also helps to develop creativity.

3. The coolest golden rooster independence method.

Let each chicken stand on one foot and each rabbit on two hind feet, then the number of feet on the ground is only half of the original. 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 it's good to forget.

Historical background of chickens and rabbits in the same cage

Chickens and rabbits in the same cage is one of the famous mathematical problems in ancient China, and about 1500 years ago, this interesting problem was recorded in the "Sun Tzu Sutra". The book is described like this, there are pheasants 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 that there are several chickens and rabbits in the same cage, counting from the top, there are 35 heads, counting from the bottom, there are 94 legs, and ask how many chickens and rabbits are in each cage? The essence of this problem is a binary equation, and if taught properly, it can give primary school students a preliminary understanding of concepts such as unknowns and equations, and exercise their ability to abstract numbers from applied problems. Generally, in the fourth to sixth grades of primary school, it is taught with the content of unary equations.

The above content reference: Encyclopedia - chickens and rabbits in the same cage.

8 courses.

Let's say it's all right.

10 10 100 (points).

100 70 30 (points) 30 points more than the actual score.

False: 30 (10 5) 2 (question).

For clear shirts: 10 2 8 (question liquid or).

A typical chicken-rabbit co-cage problem, the solution strategy of the hypothetical method.

Multiplication is in trouble:

Find out how many are the numbers;

Find out how many multiples of a number are;

Find the area and volume of the object;

Find out what fractions or hundredths of a number are.

Division: divide a number into several parts and find one of them;

Find how many other numbers there are in one number;

Knowing what fractions or hundredths of a number are, find this number;

Find how many times one number is another.

1. Chickens and rabbits live in a cage, and there are 35 known chicken heads and rabbit heads, and 94 chicken feet and rabbit feet. How many chickens and rabbits are there?

2. A total of 120 students in grades 4 and 6 watered the trees. One of the sixth-graders carried two buckets of water, and two fourth-graders carried one bucket of water, and they watered a total of 180 buckets at one time. How many people in each of the 4th and 6th grades participated in watering?

1) There are x chickens and y rabbits.

x+y=35

2x+4y=94

The joint solution yields x=23 and y=12

A: There are 23 chickens and 12 rabbits.

2) If there are x people in the fourth grade, then there are 120-x people in the sixth grade.

x/2+（120-x）*2=180

x+480-4x=360

x=40 (person).

A: There were 40 people in the fourth grade who participated in watering and 80 people who participated in the sixth grade.

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:

Let there be x number of boys and (50-x) number of girls. 3x=120-5-2(50-x) 3x=115-2*50+2x 3x=115-100+2x 3x=15+2x x=15 50-15=35 (person) Answer: 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, 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. Ask Xiaomao to get a few questions right.