2. How many heads of chickens and rabbits are there in a cage with 35 heads*** and 94 feet***?
3. There are 32 cars and motorcycles parked in a parking lot. The cars have 4 wheels, the motorcycles have 3 wheels, and the cars have 108 wheels. Find how many cars and motorcycles are there each?
4. Xiaohua bought 34 2-yuan and 5-yuan commemorative stamps, using 98 yuan. How many 2 yuan and 5 yuan commemorative stamps did Xiaohua buy?
5. 46 people in the class went boating, *** by 12 boats, in which the big boat sits 5 people each, and the small boat sits 3 people each, how many big boats and small boats each?
6, Zhang Auntie raise chickens and rabbits *** 200, chickens and rabbits foot *** 560, how many chickens and rabbits each?
7. Cranes and turtles in the same pool, 12 more cranes than turtles, cranes and turtles foot ***72, how many cranes and turtles each?
8, Xiaogang buy back 8 cents stamps and 4 cents stamps *** 100, *** pay 6.8 yuan, ask, Xiaogang buy back these two kinds of stamps how many? And how many dollars did he pay for each?
9, Dongfeng Primary School, three students to participate in the math competition, a paper *** 10 questions, answer a question 10 points, answer a wrong not only do not score, but also deducted 3 points, these three students have answered all the questions, Xiaoming 74 points, Xiaohua 22 points, Xiaohong 87 points, the three of them *** answer how many questions?
10, in the knowledge contest, there are 10 judgment questions, scoring regulations: each answer to a question to get 2 points, a wrong answer to be deducted a point. Although Xiaoming answered all the questions, he only scored 14 points in the end, how many questions did he answer wrongly?
11. A transportation team delivers 500 cases of thermos flasks to a supermarket, with each case containing 6 thermos flasks. Known as every 10 thermos of freight for 5 yuan, damage to a then not only do not give the freight but also accompanied by the cost of 10 yuan, after the shipping settlement, the transport team **** got 1350 yuan of freight. Asked, *** damaged how many thermos?
12. A spider has 8 legs, a dragonfly has 6 legs and 2 pairs of wings, and a cicada has 6 legs and 1 pair of wings. Now there are 16 of these three species of small insects, **** has 110 legs and 14 pairs of wings. Ask, how many of each kind of little bird are there?
13. A crab has 10 legs, a praying mantis has 6 legs and 1 pair of wings, and a dragonfly has 6 legs and 2 pairs of wings. Now there are 37 of these three animals and *** has 250 legs and 52 pairs of wings. How many of each type of animal are there?
14. Xiaodong's mother received a bonus of 400 yuan from her unit, of which there are 80 RMB 2, 5 and 10 ****, and the number of RMB 5 and 10 is equal, how many of each of these three kinds of RMB?
15. Xiaohua has 38 coins*** of 1 cent, 2 cents and 5 cents, totaling 92 cents and 2 cents, and it is known that the number of coins of 1 cent and 2 cents is equal. How many coins of each of these three kinds of coins?
16. A math contest***20 questions, the scoring criteria is: each correct question 5 points, each wrong or do not do a question deducted 1 point. Xiaohua participated in the competition and scored 64 points. Q: How many questions did Xiaohua get right?
17. Chickens and rabbits*** have 100 feet. If you replace chickens with rabbits and rabbits with chickens, there are 86 feet***. Q: How many chickens and rabbits each?
18. A cargo ship weighing 260 tons, the volume of 1000 m 3, is now loaded with A, B two kinds of goods, known as the volume of A goods per ton is 8 m 19. B goods per ton of volume of 2 m 3, in order to make full use of the ship's capacity and volume, A, B two kinds of goods should be loaded respectively how many tons?
20. Bicycle cross-country race full 220 kilometers, the whole is divided into 20 sections, part of which is 14 kilometers long, the rest of the long 9 kilometers. How many sections are 9 kilometers long?
21. How many rabbits are there in a flock of chickens and rabbits where the total number of legs is 18 more than twice the total number of heads?
22. If the multiplier is increased by 15 and the multiplier remains the same, the product is increased by 180. If the multiplier remains the same and the multiplier is increased by 4, the product is increased by 120. What is the product of the two numbers multiplied together?
23. How many numbers are used to number the pages of a 695-page storybook, one ****? How many of the digits "5" are used?
24. How many pages of a 6889-page storybook does it take to number a ****?
25.
25. A and B two people shooting, if hit, A scored 4 points, B scored 5 points; if not, A lost 2 points, B lost 3 points, each person shot 10 rounds, *** hit 14 rounds, the settlement of scores, A more than B 10 points, asked A, B in how many rounds?
26. a math test *** 20 questions, do a question to get 5 points, do a question wrong deduct 1 point, do not do 0 points. Xiaohua scored 76 points. How many questions did he get right?
27. There is a truck transport 2000 glass bottles, freight according to the arrival of the number of intact bottles, each 20 cents, if broken, broken 1 bottle but also back to compensate for 1 yuan, the results of the freight costs 379.6 yuan, asked how many of the glass damaged in this handling?
28. chickens and rabbits **** there are 200, the chicken's feet than the rabbit's feet 56 less, ask how many chickens and rabbits each?
29. There are chickens and rabbits*** living in a cage, known chicken head and rabbit head*** 35, chicken feet and rabbit feet*** 94, ask how many chickens and rabbits each?
30. Spiders have 8 legs, butterflies have 6 legs and 2 pairs of wings, cicadas have 6 legs and a pair of wings, the existing three animals *** 21, *** 140 legs and 23 pairs of wings, ask the spider, butterflies, cicadas have how many?
31. There are 34 people playing on 12 table tennis tables***, ask: How many tables are being used for singles and doubles?
32. There are 100 chickens and rabbits***, and there are 80 more chicken feet than rabbit feet, ask how many chickens and rabbits each?
33. class teacher Mr. Zhang with fifth grade (2) class of 50 students planting trees, Mr. Zhang a person to plant 5, boys a person to plant 3, girls a person to plant 2, the total **** planted 120 trees, ask how many boys, how many girls?
34. A large bottle of oil containing 4 kilograms, a small bottle of oil 2 bottles containing 1 kilogram. There are 100 kilograms of oil in ****60 bottles. How many bottles of oil are there in each of the big and small bottles?
35. Hongying Primary School, third grade, there are three classes ***135 people, the second class than the first class of five people, the third class than the second class of seven people less than the three classes, how many people each?
36. Mr. Liu took 41 students to the Beihai Park boating, **** rented 10 boats. Each big boat sitting 6 people, each small boat sitting 4 people, ask the big boat, small boat rent a few?
37. There are chickens and rabbits*** 20, 44 feet, how many chickens and rabbits each?
38. Xiaohong's money jar has 65 RMB*** of 2 yuan and 5 yuan, totaling 205 yuan, how many of each?
39. The size of the existing oil drums 50, each large drum can be loaded with 4 kg of oil, each small drum can be loaded with 2 kg of oil, large drums than small drums **** more oil 20 kg, ask the size of the barrels of how many?
40. There are two barrels of oil *** weighing 86 kilograms, if the oil from the barrel A poured into the barrel B 4 kilograms, then the weight of the two barrels of oil is the same. How many kilograms of oil are in each of the two barrels?
41. Porcelain store commissioned the transport station to transport 800 vases, both sides agreed that the freight is 0.35 yuan each, if you break 1, not only the freight, but also to compensate for the 2.50 yuan, the results of the transport to the destination, the transport station *** to get the cost of freight 268.6 yuan, how many vases broken?
42. The school held a sports meeting, 35 people in the third grade to participate in the competition, the number of fourth grade to participate in the third grade is three times the number of people, the number of people in the fifth grade to participate in the total number of people than the third and fourth grades to participate in the number of people more than 10 people, the fifth grade to participate in the competition, how many people?
43. Blue ink and red ink, used to be 30 cents a bottle, Wang Ying Elementary School spent 12 yuan to buy a number of bottles each semester. Now the price of each bottle of blue ink increased by 5 cents, each bottle of red ink increased by 3 cents, although the number of bottles of the two kinds of ink bought and semesters equal, but more than each semester are paid 1.8 yuan. How many bottles of each of the two types of ink does the school buy each semester?
44. There are three kinds of animals in the compound, each goat wears three bells, each poodle wears a bell, and the white goose does not wear a bell. Xiaoming counted a ***9 heads, 28 legs, 11 bells, how many of each of the three animals?
45. small hair to participate in the math competition, *** do 20 questions, scored 64 points, known to do a right to 5 points, do not do 0 points, wrong a deduction of 2 points, but also know that he did not do the same number of wrong questions and did not do. Ask Xiaomao to do right how many questions?
46. Zhao Chuanlun exchanged a 50 yuan and a 5 yuan RMB for 50 RMB*** of two yuan and 50 cents. How many yuan of each of the two denominations did he exchange?
47. The kindergarten bought 20 small tables and 30 small stools *** with 1860 yuan, known that each small table is more expensive than the small stools 8 yuan, ask the price of small tables, small stools, how much each?
48. The zoo keeps carnivorous animals divided into large animals and small animals in two categories, the provisions of tigers, lions, a class of large animals every time to feed the meat of three pounds per head, foxes, bobcats, a class of small animals every three head to feed a catty. The zoo **** have these two types of animals 100 heads, each time you need to feed 100 pounds of meat, ask how many large and small animals?
49. Xiao Zhang's deposit box has 20 pieces of 20 cents, 50 cents and 1 yuan RMB, *** 12 yuan, calculate how many pieces of each of the three denominations of RMB?
50. chickens, rabbits *** cage, chickens than rabbits 26 more, foot *** 274, ask how many chickens, rabbits each?
Chickens and rabbits in the same cage application problem body detailed (four stages)
Chickens and rabbits in the same cage problem (1) basic level
1. Chickens and rabbits in the same cage, chickens and rabbits ***35 heads, 94 legs, ask how many chickens and rabbits each?
2. Chickens and rabbits in the same cage, 20 heads***, 62 legs***, find how many chickens and rabbits each?
3. In a parking lot, there are 32 cars and 32 motorcycles. The cars have 4 wheels, the motorcycles have 3 wheels, and the cars have 108 wheels. Find how many cars and motorcycles are there each?
4. Xiaohua bought 34 2-yuan and 5-yuan commemorative stamps and spent 98 yuan on them. How many 2 yuan and 5 yuan commemorative stamps did Xiaohua buy?
5. 46 people in the class went boating, *** by 12 boats, in which the big boat each sits 5 people, the small boat each sits 3 people, how many big boats and small boats each?
6. Auntie Zhang raised 200 chickens and rabbits ***, the number of chickens and rabbits *** 560, how many chickens and rabbits each?
7. Xiaogang bought back 80-cent stamps and 40-cent stamps *** 100, *** pay 68 yuan, ask, Xiaogang buy back these two kinds of stamps how many? How many dollars did he pay for each?
8. In a parking lot, cars, motorcycles **** parked 48, where each car has 4 wheels, each motorcycle has 3 wheels, these cars **** have 172 wheels, how many cars, motorcycles in the parking lot each?
9. The physical education teacher bought sportswear tops and pants *** 21 pieces, *** with 439 yuan, of which the tops are 24 yuan each, pants 19 yuan each, ask the teacher to buy tops and pants each how many pieces?
10. mother squirrels picking pine nuts, sunny days every day to pick 20, rainy days can be picked up 12 per day, it was picked up 112, an average of 14 per day, which days in a few days is a rainy day?
11. The white rabbit's mother picks 24 mushrooms a day on a sunny day and 16 mushrooms a day on a rainy day. She picks 168 mushrooms in a row, an average of 21 mushrooms per day. How many mushrooms did she pick on a sunny day?
12. Wang bought 20 movie tickets for A and B. The average ticket price of the two kinds of movie tickets is 26 yuan each, while the actual ticket price of A is 30 yuan each and the actual ticket price of B is 20 yuan each, how many tickets were bought for each of the two kinds of movie tickets?
Chickens and rabbits in the same cage problem (2) to improve the level
1. Chickens and rabbits in the same cage, chickens than rabbits 15 more than the chicken, chicken and rabbit **** there are 132 feet, ask how many chickens and rabbits each?
2. Chickens and rabbits in the same cage, chickens and rabbits *** 40 heads, chicken feet than rabbit feet *** 32, ask how many chickens and rabbits each?
3. Chickens and rabbits in the same cage, the chicken is 10 more than the rabbit, but the chicken feet are 60 less than the rabbit, ask how many chickens and rabbits each?
4. There are 10 more chickens than rabbits in the same cage, but there are 10 more chicken feet than rabbit feet.
5. There are 13 more chickens than rabbits in Mrs. Zhang's house, and there are 16 fewer rabbit feet than chicken feet.
6. There are 12 more cranes than turtles in the same pool, and there are 72 cranes and turtles in the same pool, how many cranes and turtles are there in each pool?
7. The chicken and the rabbit*** have 110 heads, but the chicken's feet are 20 less than the rabbit's. How many heads do the chicken and the rabbit have?
8. A chicken and a rabbit*** have 110 feet, but the chicken has 20 fewer heads than the rabbit.
9. East Lake Elementary School held a math contest for the sixth grade,*** 20 questions. Doing a question right to get 5 points, did not do a question or do a question wrong to deduct 3 points. Liu Gang scored 60 points, how many questions did he get right?
Chicken and Rabbit Problems (3) Puzzle Level
1. A spider has 8 legs, a dragonfly has 6 legs and 2 pairs of wings, and a cicada has 6 legs and 1 pair of wings. Now there are 16 small insects of these three species, **** has 110 legs and 14 pairs of wings. Ask, how many of each type of insect?
2. The crab has 10 legs, the praying mantis has 6 legs and 1 pair of wings, and the dragonfly has 6 legs and 2 pairs of wings. Now there are 37 of these three animals and **** has 250 legs and 52 pairs of wings. How many of each animal are there?
3. There are 18 animals***spiders, dragonflies and cicadas***with 118 legs and 20 pairs of wings (spiders have 8 legs, dragonflies have 6 legs and 2 pairs of wings; cicadas have 6 legs and 1 pair of wings), how many of each of the three animals?
4. Xiaodong's mother received a bonus of 380 yuan from the unit, of which there are 2 yuan, 5 yuan, 10 yuan RMB **** 80, and 5 yuan and 10 yuan of the number of sheets are equal, try to find out, how many of each of these three kinds of RMB?
5. A, B, C three kinds of exercise books each price of 70 cents, 30 cents, 20 cents. Three kinds of exercise books a **** sold 47, paid 21 yuan 20 cents, bought the number of copies of the B exercise book is the number of copies of the C exercise book twice. How many copies of each of the three exercise books were bought?
6. A school purchased a large, medium, small 3 types of projectors **** 47 units, their unit prices were 700 yuan, 300 yuan, 200 yuan, **** expenditure of 21,200 yuan. Knowing that the number of medium-sized projectors is twice the number of small-sized projectors, how many large projectors were purchased?
7. There are one, five and ten yuan RMB***14 sheets,*** counting 66 yuan, of which the number of sheets of one yuan is 2 more than that of ten yuan. How many sheets of each of the three kinds of RMB?
8. buy some 4 cents and 8 cents stamps, *** spend 6 yuan 80 cents . Knowing that there are 40 more 8-cent stamps than 4-cent stamps, how many sheets of each of the two kinds of stamps were bought?
9. The food store sold 100 kilograms of three kinds of candies, A, B and C, in the morning *** and *** earned 2,570 yuan. A kind of candy: 20 yuan / kg, B kind of candy: 25 yuan / kg, C kind of candy: 30 yuan / kg, known to sell the B kind of candy and C kind of candy **** income of 1970 yuan, find C kind of candy sold how many kilograms?
10.bought 30 cents, 50 cents, 70 cents of stamps *** 400, *** used 192 yuan, of which 70 cents and 50 cents of stamps in equal number. How many of each type of stamp are there?
11. The school organized a New Year's Eve party, bought prizes pencils, ballpoint pens and pens *** 232, *** spend 100 yuan. Where the number of pencils is 4 times the number of ballpoint pens. It is known that pencils cost 20 cents each, ballpoint pens cost 90 cents each, and fountain pens cost 2 dollars and 10 cents each. Q: How many pens are there of each of the three kinds?
12. The school organized a New Year's Eve party, bought prizes pencils, ballpoint pens and fountain pens *** 232, *** spend 300 yuan. Where the number of pencils is 4 times the number of ballpoint pens. It is known that pencils cost 60 cents each, ballpoint pens cost 2 dollars and 70 cents each, and fountain pens cost 6 dollars and 30 cents each. Q: How many of each of the three kinds of pens?
Chicken and Rabbit Problems (4) Super Difficult Level
1. Xiaohua has 38 coins **** 1, 2, and 5 cents, totaling 92 cents, and it is known that the number of 1-cent and 2-cent coins is equal. How many coins of each of these three kinds are there?
2.100 steamed buns 100 monks to eat, the big monks eat 3 each, the small monks 3 people eat a, then the big monks have how many? How many small monks?
3.100 buns 100 monks to eat, the big monks eat 4 per person, the small monks 4 people to eat a, then the big monks have how many? How many small monks?
4. Big oil bottle a bottle of 4 kg, small oil bottle two bottles of 1 kg. Now 100 kg of oil is in 60 bottles. How many bottles of oil are there in each of the large and small bottles?
5. A long, long time ago, legend has it that there were nine birds with nine heads and one tail and nine birds with nine tails and one head. Once these two birds perched in the woods, a hunter passed by and counted, these two birds head **** 268, tail 332, then there are nine head and nine tail birds each how many?
6. A school math contest *** has 20 fill-in-the-blank questions. The scoring standard is: 5 points for each correct question, 3 points for each wrong question, and 0 points for each question not done. 69 points were scored by Xiao Ying, so how many questions did Xiao Ying not do?
7. A school math competition, *** there are 20 fill-in-the-blank questions. The scoring standard is: 5 points for each correct question, 3 points for each wrong question, and 0 points for each question not done, Xiao Ying's score is 72 points, so how many questions did Xiao Ying not do?
8. A math competition ****20 questions, do a right question to get 5 points, do a wrong question deducted 2 points, do not do deducted 1 point. Xiaohua scored 74 points, asked him to do a few questions? How many questions did he get right and how many questions did he get wrong? How many questions were not answered?
9. A project A alone to do 12 days to complete, B alone to do 18 days to complete, now by A first to do a number of days, and then B alone to complete the remaining tasks, so before and after **** used 16 days, A first to do how many days?
10. It takes A 6 hours to type a manuscript. B alone typing takes 10 hours to complete, now A alone typing a number of hours, due to something by B then finish typing, **** used 7 hours. How many hours did A spend typing?
11. Chicken and rabbit *** have 100 feet, if the chicken is replaced by a rabbit, rabbit is replaced by a chicken, then *** have 92 feet, how many chickens and rabbits each?
12. Chickens and rabbits *** have 220 feet, if the original all chickens are replaced by rabbits, all rabbits are replaced by chickens, then the feet are only 212, find the original chickens and rabbits have how many heads?
This can be solved in the following way.
Chickens and rabbits in the same cage (hypothetical method)
(1) Chicken as a rabbit: If all the chickens are seen as rabbits, each chicken will have to grow 2 feet, so that all the animals have become 4 feet. So there will be more "head x 4 - the actual number of feet" feet. These extra feet are all grown by the chicken. Therefore, the number of chickens = the number of extra feet ÷ 2.
(2) Rabbits as chickens: If all the rabbits are considered as chickens, and each rabbit lifts up 2 feet, then all the animals become 2 feet. So there will be less "actual number of feet - number of heads x 2" feet. These missing feet are all the feet that the rabbit lifted. Therefore, the number of rabbits = the number of missing feet ÷ 2.
It can also be said that: the assumption method to solve the "chickens and rabbits in the same cage" problem, generally based on the conditions or conclusions of the question to make some kind of assumptions, and then according to the assumptions of the projection, if the results of the projections and the question contradict each other, and then according to the number of differences in the replacement, to find out the correct answer. The answer to the question.
The chicken and the rabbit in the same cage (equation solution)
When solving the problem of "the chicken and the rabbit in the same cage", you can set up one of the unknown quantities χ, the other unknown can be used to contain the unknown χ expressed in the formula, according to the quantitative relationship between the question set out in the equation, and then solve the problem. The basic quantitative relationship equation is: the number of feet of the chicken + the number of feet of the rabbit = the total number of feet of the chicken and the rabbit.
It can also be said that the "method of equations" is a kind of algebraic solution, based on the number of feet and the number of quantitative relationships between the equation and solve.
This gives you an idea of how to solve the chicken and rabbit problem.
This is how you know how to solve the chicken and rabbit problem.