Netizens, help me find 200 application problems of binary linear equations, and then 200 application problems of binary linear inequalities.

1. There are two kinds of potions, one with 60% concentration and the other with 90% concentration. Now we need to prepare 300 grams of 70% concentration liquid medicine. How many grams do we need each?

2. There are some balls in Box A and Box B. If 10 balls are taken out of Box A and put into Box B, the number of balls in Box B is 6 times that of Box A. If 10 balls are taken out of Box B and put into Box A, the number of balls in Box B is more than 3 times that of Box A, then what are the original balls in Box A and Box B?

3. A two-digit number, which is 5 larger than the ten-digit number. If the positions of these two numbers are reversed, the sum of the new number and the original number is 143. Find this two-digit number.

Party A and Party B walk on the east-west highway. Party A is 300 meters west of Party B. If Party A and Party B walk eastward for 30 minutes at the same time, Party A will catch up with Party B; If A and B go in opposite directions at the same time and meet in two minutes, what is the speed of A and B?

5. An iron bridge is 1 000 meters long. A train crosses the bridge. It takes one minute from the front to the back of the bridge, and the whole train stays on the bridge for 40 seconds. Find the total length and speed of the train body.

6. A milk processing factory has 65,438+000 tons of fresh milk to be processed and sold in the market. The processing capacity of this factory is that if you make milk slices, you can process fresh milk 10 tons per day, and if you make yogurt, you can process fresh milk 30 tons per day. Due to personnel constraints, the two treatment methods cannot be carried out at the same time. Due to the temperature conditions, this batch of milk must be processed within 4 days. The factory will arrange to make milk tablets for several days. If selling milk slices can earn 2,000 yuan per ton of milk, and selling yogurt can earn 1 200 yuan, how much can factories earn by selling these processed fresh milk?

7. There are triple rooms and double rooms in the hotel housekeeping department. The charging data are as follows.

Ordinary (RMB/room/day) Deluxe (RMB/room/day)

Triple room 150 300

Double room 140 400

In order to attract tourists, group accommodation is offered a 50% discount. A 50-member tour group stayed in this hotel during the discount period, and stayed in some ordinary rooms with three people and two people. If each room is just full and the accommodation fee is 15 10 yuan for one day, how many ordinary rooms with three people and two people will the tour group stay in?

8. Party A and Party B drive at a constant speed on the circular road and meet every two minutes; Walking in the same direction, we meet every 6 minutes. It is known that A runs faster than B. How many laps do A and B run per minute?

9. A school in our district originally planned to donate 3,500 books to students in Chayou Banner, Inner Mongolia, but actually donated 4 125 books, including junior high school students and senior high school students. How many books have junior high school students and senior high school students donated?

10. The existing school building area of a school is 20 000m m. It is planned to demolish some old school buildings and rebuild new teaching buildings, so as to increase the school building area by 30%. If the area of the new teaching building is four times that of the old one, how many old teaching buildings will be demolished and what is the area of the new teaching building? (Unit: meter)

Crop varieties require labor and investment per hectare.

Rice 4 people 1 10,000 yuan

Cotton 8 people 1 ten thousand yuan

Vegetables for five people, 20,000 yuan

1 1. A farm has 300 employees and cultivates 5 1 hectare of land.

It is planned to grow rice, cotton and vegetables, and it is known to grow one crop per hectare.

The required labor force and investment funds are as follows:

It is understood that the farm plans to invest 670,000 yuan. How should I arrange it?

The planting area of these three crops can make all employees have jobs, and the investment is just enough?

12. A TV station plans to insert two kinds of advertisements with the length of 15 seconds and 30 seconds during the 2-minute advertising period in prime time. 15 second advertising charge 1 time, 30 second advertising charge 1 time. If each advertisement is required to be played at least once,

(2) Which broadcast mode does the TV station choose to gain more?

13. If a green vegetable is produced in a certain place and sold directly in the market, the profit per ton is 1 1,000 yuan; After rough machining, the profit per ton can reach 4 500 yuan; After finishing and selling, the profit per ton increased to 7 500 yuan. A local agricultural and industrial company bought 65,438+040 tons of this vegetable. The production capacity of the company's processing plant is: if vegetables are roughly processed, they can process 16 tons per day; If fine processing is carried out, 6 tons can be processed every day, but the two processing methods cannot be carried out at the same time. Due to the limitation of seasonal conditions, the company must process or complete all vegetables within 15 days. To this end, the company has formulated three processing schemes: scheme 1: rough processing all vegetables; Scheme 2: Refine the vegetables as much as possible, and take all the vegetables that have not been processed in time to the market for sale; Scheme 3: Sort out some vegetables and roughly process the remaining vegetables, which will be completed in 15 days. Which scheme do you think will benefit the most? Why?

14, asking price of two kinds of fruits: 999p, sweet fruit and bitter fruit 1000. Nine eleven pence for sweet fruit and seven fourpence for bitter fruit.

Ask a few sweet and sour fruits, and ask how much each should pay. (Note:, also known as Wen, ancient monetary unit)

15, express length168m, local length184m. If two cars are on the same road, it takes 4 seconds from meeting to leaving; If driving in the same direction, it takes 16 seconds from the express train to the local train. Find the speed of two cars.

16. A ship has a load of 260 tons and a volume of 1000 m3. At present, there are two kinds of goods transported, of which the volume of A goods is 8m3 per ton and that of B goods is 2m3 per ton. How many tons should cargo A and cargo B be loaded to make full use of the load and volume of this ship? (Assuming that there is no gap in delivery)

17. In order to make more effective use of water resources, a city has formulated a water standard: if the monthly water consumption of a family of three does not exceed Mm3, it shall be calculated as per cubic meter of water 1.30 yuan; If it exceeds Mm3, the excess will be charged at 2.90 yuan per cubic meter of water, and the rest will still be calculated at per cubic meter of water 1.30 yuan. There are three people in Xiaohong's family, 10 water consumption 12m3, and 22 yuan pays the water fee. What is the water standard m set by the city? How much m3 of water does Xiaohong's family exceed the standard?

18, the ticket price of a park is as follows. A school has two classes (1) and (2), with more than 50 students in class (1) and more than 50 students in class (2). If two classes join hands and buy tickets in groups, they can save a lot of money. How many students are there in each class?

The number of ticket buyers is 1-50, 51-kloc-0/00, and 100 or more.

Ticket price per person 13 yuan 1 1 Yuan 9 yuan.

1. Before the discount, 60 pieces and 30 pieces were spent 1080,50 pieces10 spent 840. After the discount, 960 yuan used 50 pieces, 50 pieces. How much is it less than no discount?

Party A and Party B each have several books. If Party A takes 10 books from Party B, then Party A has five times as many books as Party B. If B takes 10 books from A, then all the books of B are equal to the books left by A. How many books did A and B have?

Teacher Zhang went to the stationery store to buy pencils and erasers for 30 students of the Art Troupe. When she arrived at the store, she found that if she bought two pencils and 1 eraser for everyone in the group, according to the retail price, * * * would go out of 30 yuan; If you buy three pencils and two erasers for everyone in the group, you can pay 40.5 yuan according to the wholesale price. It is known that the wholesale price of each pencil is 0.05 yuan lower than the retail price, and the wholesale price of each eraser is 0. 1 yuan. What is the wholesale price of each pencil and eraser in this stationery store?

A new four-story teaching building has been built in a middle school. There are 8 classrooms on each floor, and there are 4 doors in and out of the building, of which two main doors are the same size and two side doors are the same size. During the safety inspection, four doors were tested: when a main entrance and two side doors were opened at the same time, 560 students could pass in 2 minutes; When a main entrance and a side door are opened at the same time, 800 students can pass in 4 minutes.

(1) How many students can pass through a main entrance and a side door every minute on average?

(2) During the inspection, it was found that the efficiency of going out would be reduced by 20% due to the crowded students in an emergency. According to the safety inspection regulations, in case of emergency, students in the whole building should be evacuated safely through these four doors within five minutes. Suppose there are at most 45 students in each classroom of this teaching building. Q: Do these four doors meet the safety regulations? Please explain the reason.

The car travels back and forth between A and B, which are 70km apart, because there is a hill with uniform slope in the trip. It takes 2 hours and 30 minutes for a car to travel from A to B and 2 hours and 48 minutes to return from B. It is known that cars travel 30km per hour on the flat ground, 20km per hour on the uphill road and 40km per hour on the downhill road. In the journey from A to B, it is necessary to level the road, climb the hill and descend the hill.

6. A middle school organized a group of students to go for a spring outing. It was originally planned to rent a number of 45-seat buses, but 15 people had no seats. If you rent the same number of 60 buses, there will be one more bus, and the rest of the buses are just full. It is understood that the rent for 45 buses is 220 yuan per bus, and the rent for 60 buses is 300 yuan per bus.

(1) What is the number of these students? How many 45-seat buses were originally planned to be rented?

(2) Rent the same car, so that every student can have a seat. How to rent it is more economical?

7. A hotel arranges accommodation for a tour group during the golden tour. If there are five people in each dormitory, four people cannot stay. If there are 6 people in each room, there are only 4 people in one room and two dormitories are empty. How many people are there in the group and how many dormitories are there?

8. There are two types of bonds, A and B, with annual interest rates of 65,438+00% and 65,438+02% respectively. The existing 400 yuan bonds will have 45 yuan's income after one year. How much are the two bonds?

9. Li Minghe and Wang Yun came from opposite directions. If they start at the same time, they will meet in 80 minutes. If Li Ming leaves Wang Yun after 60 minutes, then after 40 minutes, the two meet and ask Li Minghe Wang Yun to go alone.

How many hours does the whole journey take?

10, in a football match, it is stipulated that if you win a game, you will get 3 points, if you draw a game, you will get 1 point, and if you lose a game, you will get 0 point. A team scored 6 points in four football matches. How many games did the team win, draw and lose?

1 1. Two experimental fields in Dongfeng Farm produce 470 kilograms. Last year's peanuts. After switching to improved varieties, this year * * produced 523 kilograms of peanuts. It is known that the output of the first field increased by 16% and that of the second field increased by 10% compared with last year. These two plots were improved before planting. How many kilograms will each plot increase this year?

12, some oral liquid gift boxes are packaged in large boxes and small boxes. Now we know that there are 3 large boxes and 4 small boxes 108 bottles; Two big boxes and three small boxes contain 76 bottles. Now a man bought six big boxes and six small boxes and asked him how many bottles he bought.

13, the school calligraphy interest group is going to the stationery store to buy two kinds of writing brushes. The sales method of stationery stores is: when the number of brushes purchased at one time does not exceed 20, they are sold at the retail price; More than 20 brushes, each one is lower than the retail price by 0.4 yuan, and the rest are still sold at the retail price. When the one-time purchase brush does not exceed 15, it will be sold at the retail price. When it exceeds 15 pieces, each piece of the excess is lower than the retail price of 0.6 yuan, and the rest is still sold at the retail price.

(1) If there are 20 students in the whole group, if each person buys 1 brush and 2 brushes, * * * pays 145 yuan; If each person buys 2 brushes 1 brush, * * * pays 129 yuan. What is the retail price of two kinds of brushes in this stationery store?

(2) In order to promote sales, in addition to the original sales methods, stationery stores have also introduced new sales methods: no matter how many pieces are purchased, they will be sold at the original retail price (that is, the retail price of brushes found in (1)). Now I want to buy a paintbrush (), which way should I choose to buy it with less money? And explain why.

14. according to the requirements of the Ministry of information industry, a city adjusted the "internet access" fee as follows: the internet access fee is 0.22 yuan /3 minutes. Internet access fee shall not exceed one hour per month, calculated at 4 yuan/hour; The part exceeding one hour is calculated as 8 yuan/hour. Now Mr. Li, a netizen, spends 736 yuan on the Internet every month and 80 hours on the Internet. (1) Do you know what time a is stipulated in this city? Mr. Li spent more than an hour surfing the Internet? (2) There is another broadband network in this city, and the charging standard is: the telephone fee is 0.22 yuan /3 minutes, the internet access fee is 388 yuan/half a year, and the initial installation fee is paid to 240 yuan in one lump sum. If Mr. Li spends 80 hours online every month, is it appropriate to switch to broadband network?

15. The social practice team of a school visited 100 families and found that the concentration of general washing water is 0.2%-0.5%, that is, 100 kg of washing water contains 200-500 grams of washing powder. Because at this time, the surface activity is the greatest and the decontamination effect is the best. At present, a washing bucket can hold 15kg of washing water (including clothes). It is known that clothes weigh 4 kg, the concentration of washing water used is 0.4%, and two spoonfuls of washing powder are put (1 spoon is about 0.02 kg). How many kilograms should I add to washing powder and water?

16 There is a passage in "Arabian Nights": There are a group of pigeons, some in singing in the trees, and some are foraging on the ground. A pigeon in the tree said to the pigeons foraging on the ground, "If one of you flies, the pigeons under the tree will be a whole group." If one flies down from the tree, there will be as many pigeons on the tree as under it. " Do you know how many pigeons are on and under the tree?

17 As shown in the figure, eight identical rectangular floor tiles are spliced into a rectangle. What is the length and width of each rectangular floor tile?

Inequality should be one-dimensional, not binary.

1. A bunch of toys were distributed to several children. If each child is divided into three pieces, there will be four pieces left. If the front of each child is divided into four pieces, the last person will get at most three toys. How many children are there? .

2. A company of the People's Liberation Army is going to organize the soldiers into eight groups and perform one task at a time. If the number of soldiers in each group is more than the predetermined number 1, the number of soldiers exceeds 100. How many soldiers are planned to be assigned to each group?

3. A middle school arranges dormitories for boarding students in 8th grade. If there are 4 people in each room, then 20 people can't be arranged. If there are 8 people in each room, then one room is not empty and dissatisfied. Find the number of dormitory rooms and boarding students.

4. Put less than 40 chickens in several cages. If you put four chickens in each cage, there will be one chicken without a cage. If you put five chickens in each cage, there will be no chickens in one cage, and there will be less than three chickens in the last cage. How many cages are there? How many chickens are there?

5. Transport a batch of goods with a number of cars with a deadweight of 8 tons. If each car only carries 4 tons, there will be 20 tons of goods left; If each car is full of 8 tons, then the last car is not empty. Excuse me: How many cars are there?

6. A group of girls live in several dormitories, with 4 people in each dormitory, and the remaining 19 people have no room to live in; There are 6 people in each room, and one dormitory is not satisfied.

(1) If there are X dorms, then you can list the inequality groups about X:

(2) How many dormitories and students are there? How many solutions did you get? Does it fit the meaning of the question?

(Integral problem)

1, a math exam ***20 questions (full mark 100). Scoring method: 5 points for correct answer 1, 2 points for wrong answer 1, and no points for failure to answer. A student has 1 unanswered questions. So how many questions does he have to answer correctly to pass?

2. There are 25 questions in a contest, 4 points for each question, and 2 points for no answer or wrong answer. If the score of this contest is not less than 60 points, how many questions should you answer correctly at least?

3. A knowledge contest has 15 questions. The rules of the game are: 8 points for correct answer 1, 4 points for wrong answer 1, and 0 point for wrong answer. As a result, the Shen Jian team did not answer two questions, while the airship team answered all the questions. Both teams scored more than 90 points. How many questions did the two teams answer correctly?

4. In the competition, each shooter hits 10 times, and each hit gets 5 points, and each miss gets 1 point. The shooter who scores at least 35 points wins. How many times does he have to achieve his goal to become a winner?

(Comparative question)

1. The headmaster of a school will lead the "three good students" of the school to travel to the Three Gorges during the summer vacation. A travel agency said: if the principal buys a full ticket, the rest of the students can enjoy a half-price discount; Travel agency b said: all air tickets, including the principal, are 60% off. It is understood that the full fares of the two travel agencies are around 240 yuan. At least how many students should choose travel agency A?

During the summer vacation, two parents plan to take some classmates to travel. They contacted two travel agencies that quoted prices for each person in 500 yuan. After consultation, the preferential conditions of travel agency A are: two parents charge in full, and all students get a 30% discount; B The preferential terms of travel agency are: 20% discount for parents and students. Assuming that these two parents will lead many students to travel, which travel agency should they choose?

(Travel problems)

1, flood fighting and emergency rescue, transporting materials to dangerous sections, * * * original distance 120km, transportation needs1h. After 50km has been covered in the first half hour, how soon can it be delivered in time in the second half hour?

2. During blasting construction, the burning speed of the fuse is 0.8cm/s, and the escape speed of people is 5 m/s. How long does it take for the ignited soldiers to run to a safe area outside 100m during construction?

3. Wang Kai's home is 2. 1 km away from school, and now it takes 18 minutes to walk the whole distance. It is known that the walking speed in Wang Kai is 90m/min and the running speed is 2 10m/min. How long does it take for Wang Kai to run?

4. In flood fighting and emergency rescue, it takes 120km for materials to be transported to dangerous sections. It takes 65,438+0 hours to deliver the materials. There is 50km left in the first half hour. How soon can it be delivered in time in the second half hour?

(Fares)

1, taxi starting price 10 yuan (that is, when the driving distance is 5km, the domestic demand fare is 10 yuan). After reaching or exceeding 5km, the fare will be increased by 1.2 yuan for each additional 1km (the part less than 1km is counted as 1km). Someone is taking this taxi now.

2. The charging standard of a taxi is: the starting price is 7 yuan (that is, the 7 yuan fare is required for a distance less than 3km), and the 2.4 yuan will be charged for every increase of 1km over 3km (if it is less than 1km, it will be calculated as 1km). Someone took this taxi from A to B and handed it in to 19 yuan. What is the maximum distance for this person from place A to place B?

(engineering problems)

1. An engineering team stipulated that 300 earthwork should be completed in 6 days, and 60 earthwork should be completed on the first day. Now it has to be completed at least two days ahead of schedule, so how much earthwork should be completed at least every day on average?

2. Pump the pool water with the A-type pump that pumps 1. 1 ton of water per minute, and it can be pumped out in half an hour; If you switch to a B-type pump, it is estimated that it will take 20 to 22 minutes to finish pumping. How many tons of water does type B pump pump per minute more than type A pump?

3. A worker plans to process 408 parts in 15 days and 24 parts every day for the first three days. How many parts does he have to process every day in order to overfulfil the task within the specified time?

4. A workshop has the task of assembling 1200 washing machine. If it takes at most 8 days, how many washing machines should be assembled at least every day?

(Increase or decrease)

1 20cm long spring with one end fixed and the other end hung with an object. When the length of the spring after extension is not more than 30cm, the object with the mass of1will extend by 0.5cm every time. What is the maximum mass of an object suspended by a spring?

2. Take a photo with several classmates, each paying 0.70 yuan and 0.68 yuan for a negative. Print a photo of 0.5 yuan, each sharing one, and try to use up the money collected. How many students are there in this photo?

When someone lights a candle with a length of 25㎝, it is known that the candle is shortened by 5㎝ per hour. After several hours, the length of the candle is less than 10㎝?

(sales problem)

1. If a shopping mall buys m pieces of a certain commodity, and each piece is based on 30 yuan, it will increase the price by 65% of all the goods sold, and then reduce the price by 10%, then each piece will still make a profit 18 yuan, and 25% of all the goods will be sold.

(1) Try to find the purchase price and the first selling price of this commodity;

(2) In order to ensure that the total profit rate of this batch of goods is not less than 25%, what is the price of the remaining goods?

2. The fruit shop bought 1t China fruit at the purchase price of 7 yuan/kg. The price is set at 10 yuan/kg. Half sold, in order to sell out as soon as possible, ready to sell at a discount. If the total profit is not less than 2000 yuan, then the remaining fruits can be sold at a discount at the original price.

During the Mid-Autumn Festival, apples are very popular. A merchant bought a batch of apples at the price of per kilogram 1.5 yuan, and 6% of the apples lost money in the sales. Merchants should at least set the price per kilogram so as not to lose money.

2. A cinema is open to students in summer vacation, and each ticket is 2 yuan. In addition, you can sell 300 ordinary tickets to 5 yuan every time. If you want to keep the box office income at least 2000 yuan each time, how many discount tickets should you sell each time?

A middle school needs to burn a batch of computer CDs. If you burn in a computer company, you need 8 yuan for each CD (including blank CD fee); If the school engraves it by itself, the rent of the burner should be 120 yuan, and each CD should also be 4 yuan (including the blank CD fee). How can schools choose to burn these computer CDs to make the cost less?

5. An engineering team wants to recruit Class A and Class B workers 150, with monthly wages of 600 yuan and 1000 yuan respectively. At present, the number of B-type workers is required to be not less than twice that of A-type workers. When asked how many people A and B-type workers recruit, can the monthly salary be the least?

6. The school library is going to buy 80 magazines and novels priced at 8 yuan and 14 yuan respectively, and it is planned to spend them between 750 yuan and 850 yuan (including 750 yuan and 850 yuan). How many novels can 14 yuan buy at least?

Scheme selection and design

1. A factory produces a certain beverage with two raw materials, A and B. The vitamin C content of these two raw materials and the price of purchasing these two raw materials are known as follows:

raw material

Vitamin c and price a raw material b raw material

Vitamin C/ (unit/kg) 600 100

Price of raw materials/(yuan/kg) 8 4

At present, the preparation of this beverage 10 kg requires at least 4,200 units of vitamin C, and the cost of purchasing raw materials A and B should not exceed that of 72 yuan.

(1) Assuming that one kilogram of raw materials is needed, write the set of inequalities that should be satisfied.

(2) According to the above conditions, within what scope should I buy raw material A?

2. Red Star Company wants to recruit type A and type B workers 150, and the monthly salary is 600 yuan and 1000 yuan respectively. Now it is required that the number of Class B workers is not less than twice that of Class A workers, so how many Class A workers need to be recruited to make the minimum monthly wage? What is the monthly salary at this time?

3. To accept a production task, a factory needs to use 10 meter long iron bars as raw materials. Now we need to intercept 8 1 3-meter-long iron bars and 32 4-meter-long iron bars. Please help us design how to arrange the cutting scheme so as to use iron bars at least 10 meters long. How much do you need at least?

4. A school-run factory has produced a batch of new products, and there are two sales schemes. Scheme 1: You can make a profit of 30,000 yuan by selling this batch of products at the beginning of this semester, and then reinvest the invested funds and the 30,000 yuan earned by this batch of products, and make a profit of 4.8% by the end of this semester; Option 2: If you sell this batch of products at the end of this semester, you can make a profit of 35,940 yuan, but you need to pay 0.2% of the invested capital as the storage fee. Q:

(1) When the investment of this batch of products is RMB, the profits of Scheme I and Scheme II are the same?

(2) According to the required investment, discuss which scheme I and scheme II will benefit more.

5. One park ticket 10 yuan, each for one use. Considering the different needs of people, in order to attract more tourists, we should

In addition to retaining the original ticketing method, the garden also introduced the method of "purchasing annual tickets". There are three kinds of annual tickets: A, B and C. Each annual ticket is 120 yuan. You don't need to buy a ticket to enter. For Class B, tickets are required for each 60 yuan, and for Class C, tickets are required for each 2 yuan, 40 yuan. To enter the park by ticket, you need to buy a ticket of 3 yuan.

(1) If you only choose one way to buy tickets, and you plan to spend 80 yuan to buy tickets for the garden every year, then try to find out the way to buy tickets that will make you enter the garden the most times through calculation.

(2) If you want to enter the park within at least one year, it is more cost-effective to buy a class A annual ticket.

6. A city handles 700 tons of garbage every day on average. There are two treatment plants, A and B. It is known that plant A can handle 55 tons of garbage per hour, which costs 550 yuan, while plant B can handle 45 tons of garbage per hour, which costs 495 people. If it is stipulated that the cost of garbage disposal in this city should not exceed 7370 yuan per day, how many tons of garbage should a factory handle at least every day?

Not enough. Ask me for one.