2, a basket of apples, with a basket of * * * weighing 35 kg, first give half to the kindergarten children, then give half to the first grade children, and the rest of the apples weigh 1 1 kg. How much does this basket of apples weigh?
There is some oil in the oil drum. If the oil is doubled, the oil drum will weigh 38 kilograms. If the oil quadruples, the oil and barrels here weigh 46 kilograms. How many kilograms of oil are there in the oil drum?
There are as many oranges in five wooden boxes. If 60 oranges are taken out of each wooden box, the sum of the remaining oranges in five wooden boxes is equal to the sum of the oranges in the original two wooden boxes. How many oranges are there in each wooden box?
There are five boxes of biscuits in a food store. If 20kg is taken out of each box, the remaining biscuits in five boxes are exactly equal to the weight of the original three boxes. How many kilograms of biscuits are there in each box?
6. There are two bags of sugar, 68 in one bag and 20 in the other. How many times can I take six pills from an extra bag and put them in a less bag to make two bags of sugar equal?
7. The sum of numbers A and B is 1 12. The quotient of the number a divided by the number b is 6. What are the numbers A and B respectively?
8. The circumference of a rectangular blackboard is 96 decimeters, and its length is three times its width. What is the length and width of this rectangular blackboard?
9. Uncle Li raised 960 chickens, ducks and geese, three times as many as geese and four times as many as ducks. How many chickens, ducks and geese have you raised?
10, the sum of a, b and c is 360, a is three times that of b, c is twice that of b, what is a, b and c?
1 1. There are 560 pencils, pens and ballpoint pens in the shop. There are three times as many ballpoint pens as pens, and as many pencils as ballpoint pens. How many pencils, pens and ballpoint pens are there?
12, the sum of a, b and c is 400. A is three times that of B, and C is four times that of A. What are A, B and C?
13, three steel plates * * * weigh 62 1kg, the weight of the first one is three times that of the second one, and the weight of the second one is twice that of the third one. How many kilograms does each of the three steel plates weigh?
14, team a, team b and team c * * * shop 1200m. The rice repaired by team a is twice that of team b, and the rice repaired by team b is three times that of team c. How many meters have each of the three teams repaired?
15, Xiao Ming from Obana took part in the math contest, and they got 168. Xiaohua's score is 42 points less than Xiaoming's twice. How many points do you each get?
16, the school bought 720 books and distributed them to senior, middle and junior grades. The senior grade took eight more books than the junior grade, and the middle grade took four more books than the junior grade. How many books are there in senior, middle and junior grades?
17, three tree planting teams planted 1900 trees. Team A planted twice as many trees as team B. Team B planted 300 fewer trees than team C. How many trees did the three teams plant?
18, the sum of three numbers is 1540, the number of A is 7 times that of C, and the number of B is 40 more than A. What are these three numbers?
There are 95 basketballs, soccer balls and volleyball balls in Chengdong Primary School * * *, 19, of which 5 are less than volleyball balls, and the number of volleyball balls is twice that of basketball balls. How many basketball, football and volleyball are there?
20. A refrigerator factory wants to produce 1560 refrigerators. It has been in production for 8 days, and 120 refrigerators are produced every day. The rest will produce 150 units per day. How many days will it take to complete this task?
2 1. A factory plans to produce 36,500 sets of bearings, with an average of 2 100 sets per day for the first five days. Later, the operation mode was improved, with an average of 2600 sets per day. How many days does it take to complete the production task of these bearings?
22. A machine tool factory plans to produce 40 machine tools every day and complete the task in 30 days. Now we must finish the task 10 days in advance. How many units will we produce every day?
23. Master Zhang started making 90 toys at the same time. Master Zhang makes 10 toys every day. When completing the task, Li Shifu must do 65,438+0 days to complete the task. How many does Li Shifu make every day?
24. Xiao Ming of Oubana began to write 192 Chinese characters at the same time, and Xiaohua wrote 24 Chinese characters every day. To complete the task, Xiao Ming has to write for 4 days. How many words does Xiaoming write every day?
25. Fenghua Farm Tools Factory planned to produce 2,400 farm tools in 20 days, but actually produced 30 more farm tools every day, so as to finish the task several days ahead of schedule.
26, there are two bags of flour, the first bag of flour is 24 kg, and the second bag of flour 18 kg. How many kilograms are taken from the first bag and put into the second bag, so that the weight of flour in the two bags is equal?
27. There are two boxes of thumbtacks, 72 in box A and 48 in box B. How many times do you take four from box A and put them in box B to make the two boxes equal?
28. A workshop in the toy factory will produce 900 toys. If it is done by hand, it takes 20 hours to complete, and it only takes 4 hours to use the machine. The workers in the first workshop did it by hand for 5 hours, and then turned to the machine for production. How many hours will it take to finish this task?
29. The distance between A and B is 200 kilometers. It takes 5 hours by car and 40 hours on foot. Zhang Qiang started from a place, first by car for 4 hours, and then on foot. How many hours did it take him to go from one place to another?
30. The distance between A and B is 300 kilometers. It takes five hours to ride a motorcycle and 25 hours to ride a bike. Wang Liang starts from City A, first by bike for 5 hours, then by motorcycle. How many hours did it take him to get from City A to City B?
3 1. Xiaoming reads a book. He originally planned to read 35 pages a day and finish it in 32 days. As a matter of fact, I read five more pages than planned every day. How many days did it actually take to read it?
32. Road repair, originally planned to repair 0.4 km a day, can be completed in 70 days. The actual number of meters repaired every day is 1.25 times as planned. How many days will it actually take to complete?
33. The greening team plans to plant trees and complete the task in eight days. Actually, 240 trees were planted every day, and all the tree planting tasks were completed in 7 days. How many more trees are actually planted every day than planned?
34. A neighborhood committee sent families of martyrs to solatium, and sent them brown sugar and white sugar. 2 bags of brown sugar and 5 bags of white sugar were distributed to every household. When they delivered it to the last household, the brown sugar had just arrived, and there were 10 bags of white sugar left. It is known that the number of bags of white sugar is three times that of brown sugar, so how many bags of brown sugar and white sugar do you bring?
35. The garment factory has to process a batch of garments. The first workshop and the second workshop were processed at the same time for 60 days, which has just been completed. It is known that the clothing processed in the first workshop accounts for 45% of the total clothing, and the second workshop processes 132 pieces every day. How many pieces are processed in the first workshop every day?
The washing machine factory plans to produce a batch of washing machines. Results 37.5% of the plan was completed in 9 days. According to this calculation, how many days will it take to complete the plan?
37. There is a pile of coal that can be burned for 120 days. Due to the improvement of coal-burning technology, 0.25 tons of coal was saved every day, and as a result, this pile of coal burned 150 days. How many tons is this pile of coal?
38. Take seven yellow cattle and put them among the buffaloes, then the number of the three groups of cattle will be exactly the same. How many cows are there?
39. Workshop A and Workshop B process a batch of the same parts. If workshop A processes 35 pieces first, then workshop B processes 1 day first, and then workshop B starts processing again. After 5 days, the number of parts processed by the two workshops is equal. So how many parts does workshop B process in a day?
40. Grass100kg, with water content of 66%. After drying, the water content decreased to 65,438 05%. How many kilograms do these grasses weigh after drying?
4 1. Reduce one side of the square by 1/5, and increase the other side by 4 meters to get a rectangle. This rectangle has the same area as the original square. So how many square meters is the square area?
42. A workshop processes A and B parts. Part a accounts for 30% of the processing part, and then 24 parts b are processed, at which time part a accounts for 25%. So how many two kinds of parts have been processed now?
43. Party A, Party B and Party C produce * * * 1760 pieces. If Party A produces 2/9 less and Party B produces 80 more, then the number of parts produced by Party A, Party B and Party C is equal. How much did A, B and C each produce?
44. Xiaoming's age this year is 65438+ 0/6 of his father's age, and after 15, it is 4/9 of his father's age. How old are Xiaoming and his father this year?
45. There are 3 14 students in a school, of which 2/3 boys are 40 less than 4/5 girls. How many boys and girls are there in this school?
46. The number of students in Class A and Class B is equal, and some students in each class participate in the math group. The number of people in class A who participated in the math group was exactly1/3 of the number of people in class B who did not participate in the math group; The number of people who participated in the math group in Class B is exactly 0.4 of the number of people who did not participate in the math group in Class A+65438+A ... So, how many people who did not participate in the math group in Class A are from Class B?
47. There are several liters of alcohol solution with a certain concentration in the container, and the pure alcohol content is 25% after adding 1 liter of water; Add 1 liter of pure alcohol, and the content of pure alcohol in the container is 40%. So how many liters of alcohol solution were there in the original container? What is the concentration?
48. Party A, Party B and Party C can finish copying a manuscript within 1 hour. If Party A and Party B copy together, it will take 80 minutes to complete; If B and C are copied together, it will take 100 minutes to complete. If this manuscript is copied by B alone, how many hours will it take to finish?
49. A single project can be completed in 20 days; B alone can be completed in 30 days. Now working together, the middle one rested for 3 days, and the second one rested for several days. It took 16 days to complete. B how many days did you rest?
50. It takes 8 hours to fill a pool of water and only open the first pipe; It takes 12 hours to open only the second pipe; It takes 15 hours to open only the C tube. Starting today, only two pipelines A and B were opened, then two pipelines A and B were closed in the middle, and then pipeline C was opened. It takes 65,438+00 hours to fill a pool of water. So how many hours does it take to open the C pipe and inject water?
5 1. It takes an engineering team 12 days to undertake a project. If only two teams, A and B, are allowed to exchange work contents, the whole project will be delayed for three days. If the two teams A and B are allowed to exchange work contents, and the two teams C and D are also allowed to exchange work contents, then the whole project can still be completed as scheduled. If only C and D teams are allowed to exchange work contents, the whole project can be completed a few days in advance.
52. Team A and Team B cooperate on a project. After team A worked alone for 6 days, team B joined in and worked with team A, and it took another 4 days to complete 1/3 of the whole project. After another 10 day, the whole project was completed by 3/4. Because group A has another task, group B will continue to work until the whole project is completed. How many days did it take from the beginning to the end?
53. Party A and Party B leave from A and B at the same time and go to B and A respectively, with the speed ratio of 7: 6. After they met, they moved on, and then B's speed increased every hour compared with the initial speed.
1, general question.
(1) The highway maintenance team built a road with a length of 1400 meters, and started to repair 200 meters every day. It took two days to repair, and the remaining task was to repair 250 meters every day. How many days will it take?
(2) The road repair team built a road with a length of 1.400 meters, and started to repair 200 meters every day. It took two days to repair, and the remaining tasks were repaired 50 meters a day. How many days will it take?
(3) The construction team plans to dig a tunnel 36 meters a day and finish it in 30 days. In fact, it will dig 25% more every day, so how many days will it take to complete the task?
(4) The school environmental protection team plans to remove 960 kilograms of white garbage. Complete the planned 1/4 in the first four days and 1/3 in the second two days. How many kilograms do you need to pick up to complete the task?
(5) A production team has to process a batch of auto parts. It was originally planned to process 200 pieces a day and complete the task in 15 days. In fact, 50 pieces are processed every day. How many days did this finish the task ahead of schedule?
(6) Gucheng Toy Factory will produce a batch of electric toys. It was originally planned to produce 3000 electric toys every day, which can be completed in 24 days. In fact, it produces 4500 electric toys every day. How many days in advance actually?
(7) The school bought five desks and eight chairs and sent them to schools in disaster areas. * * * spent 762.5 yuan. It is understood that the price of each chair is 45 yuan. What's the price of each table?
2, the general problem.
(1) two classes in grade five collect scrap iron, with 64 people in one class and 600 kg in * * *; Class two, 50 people, * * * picked up 490 kilograms. How many kilograms of scrap iron does each person collect on average?
(2) A tractor cultivates 10 mu per hour in 3 hours in the morning and 22 mu per hour in 2 hours in the afternoon. How many acres are cultivated per hour on this day?
(3) An engineering team laid a section of water pipe, laying 150m every day for the first three days, and laying 200m every day the next day, which was just finished. How many meters does this engineering team average every day?
(4) War of Resistance against Japanese Aggression Memorial Hall receives tourists 1440 in the first three days, and receives 550 tourists every day in the last four days. How many tourists does it receive every day this week?
(5) Yucai Primary School 20 10 has 330 students in the lower grades and 400 students in the middle grades, and the number of students in the upper grades is 25% more than that in the middle grades. What is the average number of students in each grade in this school?
(6) A class of students planted trees to green the campus, including 23 boys and 229 trees; There are 22 girls, with an average of 8 trees per person. How many trees have been planted in this class?
(7) In Xiaohua's mid-term exam, I scored 92 points in Chinese, 98 points in mathematics and how many points in science, so that the average score of these three subjects can reach 95 points?
3, the problem of normalization.
(1) Eight workers in a machinery factory produced 768 machine parts in four hours. According to this calculation, how many parts can 48 workers produce in 8 hours?
(2) How many days does it take three workers in a workshop to complete 7500 parts in five days and seven workers to complete 3500 identical parts?
(3)8 looms weave1224m in 9 hours. According to this calculation, how many meters is 15 loom weaving 1 hour?
(4) Hongqi Cement Plant can produce 18 tons of cement in 2/3 hours after comprehensive technical innovation and equipment improvement. According to this calculation, how long will it take to produce 405 tons of cement?
(5) Weave1800m with 6 looms every day. How many meters can you weave every day with four identical looms?
4. Travel problems.
(1) The total length of the expressway between the two places is 420 kilometers. Two people, A and B, ride motorcycles from two places at the same time. A speed is 45 kilometers per hour, which is 3/4 of B speed. How many hours did they meet?
(2) Two cars leave relatively simultaneously from two places 276 kilometers apart. One car is 58 kilometers per hour, and the other car is slower than it 1 kilometer. The distance from the beginning to the meeting is 69 kilometers. How many hours did it take?
(3) On the map with the scale of 1:4000000, the distance between Party A and Party B is 20 cm. Two trains leave from A and B at the same time. The speed of A train is 45 kilometers per hour, and that of B train is 35 kilometers per hour. How many hours do the two trains meet?
(4) On the map with the scale of 1:5000000, the distance between the two places is 6cm. Two cars, A and B, leave from two places at the same time and meet in two hours. It is known that the speed ratio of A and B is 2:3. Q: How many kilometers per hour is B?
(5) The two trains A and B leave from two places1.050km apart at the same time. Car A travels at a speed of 80 kilometers per hour. After 2.8 hours, the distance between the two trains is 60% of the whole journey. How many kilometers does bus B travel per hour?
(6) The distance between the two stations is 432km, and two trains leave from both stations at the same time. Car A travels 52 kilometers per hour and car B travels 56 kilometers per hour. How many kilometers did car A travel when they met?
(7) The truck travels 45 kilometers per hour, and the speed of the car is 1.4 times that of the truck. At the same time, they set out from two places, which are 162 kilometers apart, face to face. If the departure time is 8 hours 15 minutes, when will they meet and when will they meet?
(8) The distance between A and B is 420 kilometers, and passenger and cargo vehicles start from both places at the same time. Four hours later, two cars met. As we all know, the speed ratio of passenger cars and trucks is 3:4. What is the speed of the two cars?
(9) On the expressway, it takes 65,438+00 hours for one car and 65,438+04 hours for another car. Now, two cars leave from both ends of the expressway. When the express train finished its journey, the local train just exceeded the midpoint by 255 kilometers. What is the total length of this highway?
(10) A car has just covered 5/6 of the whole journey from A to B in 3.5 hours. At this speed, how many hours will it take to complete the journey? (Answer in two different ways)
5. Overlapping problem.
Class 6 (1) students have participated in at least one computer and math interest group activity. There are 30 people in the computer interest group and 35 people in the math interest group, both of which have 20 people. How many people are there in this class?
6. plant trees.
(1) Install street lamps on both sides of the street with a total length of 2km (both sides should also be installed), and install one lamp every 50 m.. A * * *, how many street lamps should be installed?
7. The problem of chickens and rabbits.
(1) There are several chickens and rabbits in the cage, of which the first 28 are known and 86 have legs. How many chickens and rabbits are there?
(2) There are some chickens and rabbits in the cage. The first 35 are known, and the leg is 1 10. How many chickens and rabbits are there?
8, score, percentage.
(1) Li Shifu has produced a batch of parts. After he finished 70%, he produced 600 more, 30% more than originally planned. How many parts did Li Shifu actually produce?
(2) Squadron 5 (2) has four classes, class 1 and class 2 * * have 19 people, class 2, class 3 and class 4 * * have 35 people, and class 2 accounts for15 of the whole squadron. How many people are there in Class Two?
(3) Aunt Wang sold two sets of fashions in the morning, each set of 480 yuan. One set is 20% higher than the purchase price and the other set is 20% lower than the purchase price. Q: How much did Aunt Wang actually earn and lose when she sold these two sets of fashion?
(4) The fruit company put a batch of apples in storage, and after selling 30%, it delivered 160 boxes, which was110 more apples than the original storage. How many boxes of apples did it add?
(5) There is a barrel of oil. Take out 1/3 of the total amount for the first time and 40% of the total amount for the second time. At this point, there is 16kg oil left in the barrel. How many kilograms was there in this barrel of oil?
(6) The school bought a batch of children's books, of which 1/3 was distributed to the lower grades, and 120 was distributed to the lower grades; Then give 3/8 of these books to the senior students. How many books will senior students get?
(7) To build a highway, 2/7 of the total length, or 3.6 kilometers, was built in the first month, and 25% of the total length was built in the second month. (Add a question yourself and answer in parallel)
(8) The school assigns the task of planting trees to the fifth and sixth grades according to 1:3. In the fifth grade, 78 trees were actually planted, 20% more than the original assigned tasks. How many trees were planned to be planted in the sixth grade?
This shop delivered 320 kilograms of oranges, apples and pears. The ratio of oranges to apples is 5:6, and the weight of pears is 3/ 10 of apples. How many kilograms of apples did the store deliver?
(10) There are two goldfish bowls. If 25 goldfish are taken out of the first tank and put into the second tank, the goldfish in the second tank is just 6/7 of the first tank. It is known that there are 35 goldfish in the second tank. How many goldfish are there in the first fish tank?
9. Engineering problems.
(1) A job takes 3 hours for Party A, 4 hours for Party B, and how many hours for two people?
(2) A project can be completed by team A in 20 days and team B in 3 days110. How many days can two teams finish the project?
(3) To build a section of highway, Team A can complete 1/3 of the total length in 2 days, and Team B can complete 1/3 of the total length in 9 days. How many days does it take for the two teams to jointly repair112?
(4) For a project, Party A can complete it in 6 hours alone 1/3, and Party B can complete it in 9 hours alone 1/4. Now Party A and Party B are cooperating. How many projects has Party B completed by the time of completion?
(5) It takes 6 hours for Party A to do a job alone, and 4 hours for Party B to do a job alone. After Party A finishes13, how many hours will it take for two people to do it together?
(6) The manuscript will be typed by Party A alone for 8 days, and by Party B alone for 12 days. Party A will play alone for 3 days, and how many days will Party A and Party B play together?
(7) To build a road, Team A and Team B will cooperate for 8 days, and Team A will complete it alone 12 days. In fact, team B repaired it for several days, and then team A continued to repair it. It took 15 days to complete the repair. How many days did Team A and Team B repair each?
(8) It takes 8 days for Party A to process a batch of parts alone, and 10 days for Party B to process alone.
A. If two people work together, how many days will it take?
B if party a works alone for 5 days, there are still 150 parts left. How many parts are there in this batch?
10, pigeon coop principle.
(1) Six pigeons fly back to five dovecotes, and at least two pigeons will fly into the same dovecote. Why?
(2) Eight pigeons fly back to three dovecotes, and at least three pigeons will fly into the same dovecote. Why?
(3) There are 370 sixth-grade students in Xiangdong Primary School, including 49 students in Class 6 (2). A said: There must be two people in the sixth grade with the same Amanome. B said: At least five people in Class Six (2) were born in the same month. Are they right?
(4) Put the red, yellow, blue and white 10 balls into the bag. How many balls can you get at least two balls of the same color?
(5) Take out two trump cards from the playing cards, and randomly select five cards from the remaining 52 cards, at least two of which are of the same suit. Give it a try and explain why.
(6) Uncle Zhang participated in the darts competition and threw five darts with a score of 4 1. Uncle Zhang has at least one dart and no less than 9 rings. Why?
(7) Paint six faces of a cube with blue and yellow respectively, and at least three faces are painted with the same color anyway. Why?
(8) Mix 10 red, blue and yellow together. If you close your eyes, how many sticks can you take out at least once to ensure that there must be two sticks of the same color? Are you sure there are two pairs of sticks of the same color?
1 1, use equations to solve application problems.
(1) The students of Xiantao Primary School participated in tree planting activities, and the sixth grade planted 164 trees, twice as many as the fifth grade. How many trees were planted in the fifth and sixth grades?
(2) Students do exercises, with 20 people in each row, and can stand in 18 rows. If there are 24 people in each row, how many rows can you stand? (Use proportional solution)
(3) On the map with the scale of 1:200000, the distance between the two places is 25cm. If you draw it on the map with the scale of 1:500000, what is the distance between the two places?
(4) Young Pioneers planted pines and cypresses on the hillside, with 120 trees, and the number of pines was four times that of cypresses. How many trees have each person planted?
12, area and volume problems
(1) The ratio of the degrees of the three internal angles of a triangle is 1:2:3. What is the largest angle?
(2) On the map with the scale of 1/500, it is measured that the length of a playground is 25cm, which is 5cm more than the width. What is the actual area of this playground?
(3) Make a rectangular frame with a 48-decimeter-long iron wire, so that the ratio of length, width and height is 5:4:3. How many square decimetres of paper do you need to paste a layer of paper on the outside of this rectangular frame? How many cubic decimeters is its volume? (4) The square iron block with the length of 15cm is cast into a conical iron block with the bottom diameter of 10cm. What is the height of this tapered iron block? (Numbers are reserved as integers)
(5) The volume of the cylindrical reservoir is 62.8 cubic meters, and the known inner diameter of the reservoir is 4 meters. How deep is it? If cement is used on the inner wall and bottom surface, 20 kilograms of cement is used per square meter. How many kilograms of cement do you need? (Use rounding method to keep the final number as an integer)
(6) Put a rockery with a volume of 768 cubic decimeter in a rectangular glass fish tank with a length of 16 decimeter and a width of 12 decimeter, and the water in the fish tank just rises to the tank mouth. If this rockery is taken out, the water level is 16 decimeter. What is the volume of this glass fish tank?
(7) Cone-shaped sand pile, with a bottom radius of 4m and a height of 6m, with a sand weight of 2 tons per cubic meter. How many tons does this pile of sand weigh? (Numbers are reserved as integers)