1. A factory applied for two kinds of loans from ICBC, with an annual interest of 27,000 yuan. The annual interest rate of loan A is 12%, and that of loan B is 14%. What are the amounts of loans A and B respectively?
2. A vendor sold two clothes at the price of 135 yuan. According to the cost calculation, the first company earned 25% and the second company lost 25%. So how much did the supplier earn (or lose) in this business?
3. Company A borrows120,000 yuan from the bank, and the annual interest rate is 10% (excluding compound interest). Use this loan to buy a set of imported equipment to produce a commodity, and the production cost of each box of commodities is 100 yuan. The sales price is 150 yuan, and the comprehensive tax rate is 10% of the sales price.
4. Someone saved 100 yuan. At that time, the annual interest rate was 7.47% and the three-year interest rate was 8.28% (excluding compound interest). A deposit method: first deposit for one year, then deposit the principal and interest for another year after maturity, and then deposit the principal and interest for another year after maturity; The second deposit method: three years; Which deposit method has higher income? How much more?
5. There are 72 students from two classes who go to the construction site to take part in the voluntary labor of digging and moving earth. If each person digs 3 cubic meters or transports 5 cubic meters of soil every day on average, how should the number of people digging and transporting soil be distributed so that the excavated soil can be transported away in time?
6. There are 42 workers in a workshop, and each person can produce 2 bolts or 3 nuts per minute. How many workers should be assigned to produce bolts and nuts in order to make them just match (one bolt with two nuts)?
7. The number of workers in three workshops of a factory is 26, 39 and 65 respectively, and 40 contract workers are now recruited. How should it be distributed so that the proportion of workers in each workshop is the same as before?
8. 20 kg of salt water with salt content 15%. How many kilograms of salt does it take to increase the salt content to 20%?
9. There is 60 grams of 5% salt water. How many grams of water should be added to get the salt with the mass fraction of 10%?
10.40 kg of brine with salt content of 12.5%, how many kilograms of water can be evaporated to make brine with salt content of 20%?
1 1. How many grams does it take to get 1000% brine with 25% salt content?
12. Add 20g of salt into the brine with a salt content of 20% to obtain the brine with a salt content of 25%. How many grams of raw salt water?
13. How many kilograms of 98% pure sulfuric acid and water are needed to prepare 1000% pure sulfuric acid 1000 kg, compared with 85 kg of 60% pure sulfuric acid?
14. A worker originally planned to process a batch of parts in a limited time. If he processes 10 parts per hour, he can overfulfil 3 parts. If 1 1 parts are processed every hour, it can be finished at 1 hour in advance. How many parts are there in this batch? How long will it take to finish as planned?
15, Party A and Party B jointly produced a batch of parts, which took 20 days to complete the task. And Party B took five days off midway, knowing that Party A has made three more parts than Party B in one day, then the parts made by Party B are exactly half of those made by Party A. Find the total number of these parts.
16, it takes 12 days for Xiao Ming to make a batch of parts. Two days later, Xiaoming adopted advanced technology, and his work efficiency doubled. How long did it take Xiao Ming to finish this task?
It takes 17, Party A, Party B, Party C 10 days, 12 days and 15 days to complete the same job alone.
(1) If three people cooperate, * * * How many days will it take to complete this task?
(2) If Party B does it for 3 days first, and then Party A and Party C join in at the same time, how many days will it take to complete the work?
(3) A did it first, then B and C added * * *, and it took 7 days before and after. A How many days did you do it for the first time?
18. There are three water pipes A, B and C in a pool. A is the water inlet pipe, and B and C are the drainage pipes. A needs to fill a pool of water at 6 o'clock when driving alone, and B needs to drink it at 8 o'clock when driving alone. In an empty pool, first open water pipe A at 3 o'clock, and then open water pipes B and C at the same time. After 2: 24, all the water in the pool was drained. Request to open pipe C separately, complete.
19, A and B practice short distance running, A is 7 meters per second, and B is 6.5 meters per second.
(1) If A lets B run 5 meters first, how many seconds can A catch up with B?
② If A lets B run first 1 sec, how many seconds can A catch up with B?
A correspondent needs to deliver the letter to a certain place within the specified time. If he rides his bike every hour15km, he will arrive 24 minutes earlier. If your speed is12km, you will be 30 minutes late. When is the scheduled time? How far is his journey to a place?
2 1, Party A and Party B walk from A and B in expressway at 8: 00 a.m., and the distance between them is shortened to 10 km at 8:30 a.m., and increased to 44 km at 10: 20 a.m., so as to find the distance between A and B. 。
22. The two trains, A and B, are 200 meters and 280 meters long, respectively, and run in opposite directions on parallel tracks. It is known that it takes 18 seconds for two cars to meet in front and then separate, and the speed ratio of A to B is 5: 3. Find the speed of two cars.
23. It is known that the length of a railway bridge is 1000m, and a train passes through the bridge. It takes 1 minute for the train to cross the bridge completely from the beginning, and the whole train stays on the bridge completely for 40 seconds. Find the length and speed of the train.
24. Party A and Party B set out from two places, which are 18km apart, and walked towards each other. They met at 1. If Party A leaves before Party B, they will meet at 1 after Party B leaves. Seek the speed of both parties.
25. Someone rides a bicycle for one hour on the level road 12km, 8km on the uphill road and 1 hour on the downhill road 15km. It is understood that the horizontal road of a section of road is 28 kilometers long, and it took someone five hours and 4.39 minutes to come back by bike. How many kilometers is the uphill and downhill in this section?
26. For a two-digit number, the tenth digit is twice as large as the single digit. If the positions of ten digits and single digits are reversed, the number obtained is 36 less than the original number, and the original two digits are found.
26. A factory should complete the assembly task of 18 tractors within 5 days. Workshop A can assemble 2 tractors every day, and Workshop B can assemble 3 tractors every day. How to allocate the assembly tasks of two workshops so that the working days of both workshops are all day?
27. Hongqi Machinery Factory produces two kinds of machines, A and B. Each machine costs 40,000 yuan, and B costs 50,000 yuan.
(1) In order to make the sales amount reach 1.2 million yuan, how many machines should be arranged to be produced if two kinds of machines are to be produced?
(2) If the market demand for Type A machines does not exceed 20, and the demand for Type B machines does not exceed 15, how should the factory arrange the production plan to ensure the sales of 1.2 million yuan?
28. For a three-digit number, the sum of the hundredth digit and the last two digits is 58. If the number of the hundredth digit is shifted to the number of one digit, and the original number of the tenth digit and the number of one digit are successively raised to the number of the hundredth digit and the number of one digit, the new three digits are 306 larger than the original number. Find the original three digits.
29. Three digits, in which the decimal is less than 2, and the sum of hundred digits and single digits is 14. If the hundred digits and the single digits are exchanged, the new number is 396 larger than the original number, and the original three digits are found.
30. A warehouse has 20 A-class goods and 29 B-class goods to be delivered to department stores. Each truck can transport 5 Class A goods or 4 Class A goods and 3 Class B goods at a time. Each van can transport 10 pieces of Class B goods or 2 pieces of Class A goods and 5 pieces of Class B goods at a time. Long-distance charge for large trucks is 300 yuan, and long-distance charge for small trucks is 180 yuan.
(1) How many times does it take for a big truck to transport Class A goods and a small truck to transport Class B goods?
(2) How many times does it take for a big truck and a small truck to ship two kinds of goods at the same time?
(3) (1), (2) Which of the two transportation schemes saves the transportation cost, and what is the transportation cost with less?
3 1. A factory produces two different types of machines, A and B. According to the original production plan, the production cost of A machine is 30,000 yuan each, and the production cost of B machine is 20,000 yuan each. The total cost of completing all the plans is 690,000 yuan. Further accounting shows that if the output of A-machine increases by 5 and that of B-machine decreases by 5 in the original plan, the cost of A-machine will be reduced to each 2 yuan.
32. The original planned profit of an enterprise this year is 320,000 yuan more than the management expenses. The reward method is: the total bonus = the actual profit exceeds 40% of the planned amount+the management fee expenditure is lower than 60% of the planned amount. It is estimated that if the actual profit reaches 600,000 yuan, the management expenses will be reduced to 6.5438+0.2 million yuan, and the year-end bonus of employees will total 70,000 yuan. Now the total year-end bonus of employees will reach 90 thousand yuan, and the management fee expenditure will be controlled.
33, planting trees on both sides of the road, every 3 meters, leaving 3 trees; There is a tree every 2.5 meters, and 77 trees are gone, so we need a long way.
34. A toy company manufactures toy guards and toy cavalry on a machine with working hours of 10 every day. It takes 8 seconds and 8 grams of metal to be a toy guard, 6 seconds 16 grams of metal to be a toy cavalry, and the daily supply of metal materials is 64 kilograms. The profit of being a toy guard is 0.05 yuan, and the profit of being a toy cavalry is 0.06 yuan. How many toys were made? What is the daily profit of this production arrangement?
35. The distance between A and B is 10 km. A, B and C walk from A to B. The walking speed of A and B is 4 kilometers per hour, and the speed of C riding a motorcycle is 40 kilometers per hour. When starting, C rides a motorcycle with A first. After C gives A a ride, A gets off and walks, and C walks back to meet B.. As a result, three people arrived at B at the same time.
36. Party A, Party B and Party C leave from Party A to Party B at the same time. C walked first. A takes B somewhere on the way by bike. B got off and walked to B. A rode back to meet C and took C to B. As a result, three people arrived at B at the same time. It is known that walking is 4 kilometers per hour, cycling is 12 kilometers per hour, and the distance between A and B is 90 kilometers. B how many kilometers did you walk?
Solving application problems with column inequalities (groups)
1, Mars scored 72 points in the first math test and 86 points in the second. How many points should he take in the third test to make the average score of the three tests not lower than 80 points?
2. An engineering team plans to complete 780 earthwork projects in 10 days. In the first four days, it completed an average of 90 earthwork every day, and now it has to complete the task three days ahead of schedule. How much earthwork will be completed at least every day in the next few days?
3. In an exam, * * * gave 25 questions, and each question gave 4 answers, of which only one answer was correct. For each question, 4 points were correctly answered, and 2 points were deducted if it was not wrong. If a student scores at least 60 points, how many questions does he answer correctly at least?
4. Store A and Store B sell the same goods at the same price, and each offers different preferential schemes: after purchasing 100 yuan in Store A, the re-purchased goods will be purchased from 50 yuan at 90% of the original price, and the re-purchased goods will be charged at 95% of the original price. Q: How can customers choose a store to get a bigger discount?
5. Pump sewage with a pump that can pump 30 tons of water per minute. It is estimated that the cumulative sewage volume is between 1200 tons and 1500 tons. How long does it take to pump out the sewage?
6. The three teams plan to produce 500 products on 10 day (the daily output is the same), so it is impossible to complete the task at the original speed; If each team produces more 1 product every day than before, it can finish the task ahead of schedule. Q: How many products did each group initially produce every day?
7. In a mission, a combat company divided the soldiers into eight groups with the same number. If the number of soldiers assigned to each group is more than the predetermined number 1, the number of soldiers will exceed100; If the number of soldiers assigned to each group is 65,438+0 less than the predetermined number, the number of soldiers assigned to each group will be less than 90.
8. There is a two-digit number, and its ten digits are 2 larger than the single digits. This two-digit number is between 50 and 70. Can you find this two-digit number?
9. Xiaofang's monthly water fee is not less than 15 yuan, and the charging standard of the water supply company is as follows: if the monthly water consumption of each household does not exceed 5 cubic meters, it will be charged per cubic meter 1.8 yuan; Each household uses more than 5 cubic meters of water per month, and the excess is charged by 2 yuan per cubic meter. What is the minimum monthly water consumption in Xiao Fang?
10, the school allocated several dormitories to the girls' dormitory in Class 1, Grade 7. It is understood that there are less than 35 girls in this class. If there are five people living in each room, the remaining five people have no place to live; If there are 8 people in each room, one room is empty and the other room is not satisfied. How many dorms and girls are there?
165438+ Please design it.
12, give several children a few apples, if each person is divided into three, the remaining eight; If everyone gets five points, the last person won't get five points. * * * How many children are there? How many apples?
13. There are several students living in several dormitories. If there are four people living in each dormitory, there are still 19 people who have no dormitory. If there are 6 people in each room and one dormitory is not empty, please ask for the number of people staying and the number of dormitory rooms.
14. It is planned to transport 1240 tons of Class A goods and 880 tons of Class B goods to a certain place by freight train. It is known that there are 40 trucks of different specifications, A and B, and the use cost of A-class trucks is 6,000 yuan, and that of B-class trucks is 8,000 yuan.
(1) If each A-type car can armor 35 tons of Class A goods and 15 tons of Class B goods at most, and each B-type car can armor 25 tons of Class A goods and 35 tons of Class B goods at most, and arrange the number of sections of Class A and Class B cars according to this requirement, then * * * What kinds of car allocation schemes are there?
(2) Among the above schemes, which scheme is the most cost-effective? What's the lowest freight?
15. As we all know, A, B and C are three sides of a triangle. Try to calculate:
16. The postage standard for parcels sent from a certain place in Guangdong to Hong Kong is: 1kg (calculated as 1kg for those less than 1kg) 77. 10kg, with an increase of/kloc-every time it reaches or exceeds 1kg. The postage for sending a package by Mr. Li is 16 1.50 yuan. What is the quality range of Mr. Li's package (unit: kg)?
17. A factory organizes tourism activities. If you rent more than 54-seat buses, they are just full. If you rent 72 buses, you can rent two less, and 1 car has one and a half seats. It is understood that renting a 54-seat bus costs 285 yuan each, and renting a 72-seat bus costs 285 yuan each in 360 yuan. How does Z rent a car economically?
18. The price of each brush in the stationery department of a shopping mall in Shantou is 25 yuan, and the price of each calligraphy exercise book is 5 yuan. During the "June 1st" period, the shopping mall formulated the following two preferential measures for promotion.
If you buy a writing brush, you will get a free exercise book. B: 10% discount on the purchase amount;
A school wants to buy 10 brush and X(X≥ 10) calligraphy exercise books for calligraphy interest groups.
(1) Write down the relationship between the actual payment amounts Y A (Yuan), Y B (Yuan) and X (Ben) of the two preferential ways.
(2) When buying the same number of calligraphy exercise books, which preferential payment method is more economical?
19, 50 multiple-choice questions in a knowledge contest, scoring standard: 2 points for a correct answer; Answer a wrong question, 1 point, no answer, 0 point. If a student doesn't answer four questions, how many questions must the student answer correctly at least to make his score not lower than 82?
20. The National Tax Law of People's Republic of China (PRC) stipulates that if a citizen's monthly wage and salary income does not exceed 800 yuan, the part that exceeds 800 yuan is the monthly taxable income.
Monthly taxable income
tax rate
No more than 500 yuan.
5%
500 yuan above to 2000 yuan.
10%
More than 2000 yuan to 5000 yuan.
15%
……
……
(1) 80 yuan, someone should pay taxes in January. What's his salary and salary that month?
(2) If a company has 50 employees who pay 3080 yuan a month, and each employee's monthly salary is more than that of 800 yuan, but not more than 2000 yuan, how many employees' monthly salary may not exceed 1300 yuan?
2 1. The prices of bananas in the fruit wholesale market are as follows:
Buy bananas (kg)
No more than 20 kilograms
More than 20 kg but not more than 40 kg
More than 40 kilograms
Price per kilogram
6 yuan
5 yuan
4 yuan
Zhang Qiang quantifier * * * bought 50 Jin of bananas (the second time was more than the first time), and * * * paid 264 yuan. How many Jin of bananas did Zhang Qiang buy for the first time and the second time respectively?
22. A public factory has 226㎏ of raw materials A and 250㎏ of raw materials B. It is planned to produce 40 products A and B with these two raw materials. The materials used to produce products A and B are shown in the following table.
Need raw materials
Need raw material B.
A product
7㎏
4㎏
Class b products
3㎏
10㎏
Suppose X pieces of product A are produced, please answer the following questions:
(1) Find the value of x, and then explain which production schemes meet the question;
(2) If the raw material A is 50 yuan/,and the raw material B is 40 yuan /,( 1), which scheme is better?
23. Read the dialogue carefully:
Xiao Ming: "Auntie, this is 10 yuan. I want to buy a box of biscuits and a bag of milk. "
Aunt: "Little friend, you originally spent 10 yuan to buy a box of biscuits, but buying another bag of milk is not enough!" " Today is Children's Day. I'll give you a 10% discount on these cookies. Please keep these two things and your 80 cents change.
The price of a box of biscuits is an integer! )
According to the dialogue, find out the price of biscuits and milk.
On the 24th, in order to speed up the development of the western region, the Enshi section of Shanghai-Chengdu Expressway will be started soon. The construction of expressway passes through a village. Due to the needs of the project, a group of farmers need to be relocated. On the premise of "saving land resources, protecting the natural environment and ensuring the normal life of farmers", the state government has made a unified plan for the relocation of resettlement housing areas, and the planning requires that the green area in the area should not be less than 20% of the total area. If the relocated farmers occupy an area of1.50m2, the green area in this area still accounts for 35% of the total area. The state government adopted preferential policies to encourage other farmers with savings to build houses in the planning area, so 15 farmers joined. If the building area of each household is still 150 m2, the green area only accounts for 10% of the total planned area.
(1) How many households need to be relocated first? What is the total construction area planned by the government?
(2) In order to ensure that the green area is not less than 20% of the total planned area, how many households should be evacuated at least?
25. Students from Grade One and Grade Two in a school participate in social practice activities. It was originally planned to rent a number of 48-seat buses, but there were still 24 people without seats.
(1) Assuming that X buses with 48 seats were originally planned to be rented, try to express the total number of students in these two grades with an algebraic expression containing X. ..
(2) It is decided to rent 60 buses, 2 fewer than the original planned 48 buses. Among the 60 buses, 1 is not full, but there are more than 36 buses. Please check the total number of students in these two grades in this school.
26. A city grows an average of 700 tons of garbage every day, which is treated by two garbage treatment plants, A and B. It is known that factory A needs 550 yuan to treat 55 tons of garbage per hour, and factory B needs 495 yuan to treat 45 tons of garbage per hour.
(1) How many hours does it take for Factory A and Factory B to treat municipal waste simultaneously?
(2) If it is stipulated that the cost of garbage disposal in this city does not exceed 7370 yuan per day, how many hours does it take for A factory to dispose of garbage per day?
27. China Telecom has set up two communication services: GSM users pay 15 yuan and special service fee 5 yuan every month, and then pay 0.2 yuan every call 1 minute, and Shenzhou Bank pays 0.4 yuan every call 1 minute.
(1) Y 1 and Y2 are expressed by the algebraic expression of x, respectively.
(2) How many minutes do you talk a month, and which call service is more favorable?
(3) Mr. Chen spends about 300 minutes on his mobile phone every month. Which call service does he choose is more cost-effective?
Whew, I'm exhausted.