Analyze and list the application problems of inequality according to practical problems.

A Collection of Application Problems of One-Yuan Linear Inequality

1. What is the maximum amount of mixed candy B, if the price is 8kg per kilogram of candy A in 2 yuan and several kilograms per kilogram of candy B in 18 yuan, so that the total price does not exceed 4 yuan and the candy is not less than 15kg? What is the minimum?

2. A middle school arranges dormitories for eighth-grade boarding students. If there are 4 students in each room, then 2 students can't arrange them. If there are 8 students in each room, then one room is not empty and dissatisfied. Find the number of dormitory rooms and the number of boarding students.

3. In order to reward the students who won the prize in the math contest, a school bought a number of extra-curricular reading books to give them. If each person gives three books, there are still eight left. If each person gives five books in front, and the last person gets less than three extra-curricular books, suppose the school buys m extra-curricular books and X students win prizes, please answer the following questions:

(1) use the algebraic expression with X to represent m;

(2) Find out the number of winners of the school and the number of books purchased for extracurricular reading.

4. (Jingmen City, 21) There are 1 vegetable farmers, each of whom can grow 3 mu of vegetables of type A or 2 mu of vegetables of type B. It is known that each mu of vegetables of type A can earn 5, yuan, and each mu of vegetables of type B can earn 8, yuan. If the total income is not less than 156, yuan, how should it be arranged?

5. (In 21, the starting price of taxis in Shaanxi Province was 1 yuan (that is, the driving distance was 5km to pay the fare in 1 yuan). After reaching or exceeding 5km, 1.2 yuan was increased for each additional kilometer (the part less than 1km was counted as 1km). Now, someone paid 17.2 yuan from A to B by this taxi. What is the approximate distance from A to B?

6. (Chongqing, 22) During the World Cup in Korea and Japan, a group of 56 Chongqing fans took a taxi from the hotel to the stadium to cheer for the China team. At present, there are two taxi fleets, A and B, and Team A has three fewer cars than Team B. If all teams are arranged to take Team A's cars, there are not enough cars, but there are six people in each car, and some cars are not full. If all the cars in Team B are arranged, each car will take four people, but there are not enough cars, each car will take five people, and some cars are not full, then Team A will have taxis ()

A.11 B.1 C.9 D.8

7. (Jingzhou, 21) On weekends, a company decided to organize 48 employees to take a boat in a nearby water park. The rent price list that this person saw is as follows:

The number of people (people) per ship type is limited. Rent (yuan)

Big ship 53

Small boat 32

Then, how to design a charter scheme to minimize the rent paid? (Overloading is forbidden)

8. (Anhui in 21) An engineering team wants to recruit 15 workers of two types of jobs, the monthly wages of which are 6 yuan and 1 yuan respectively. Now, it is required that the number of workers of type B is not less than 2 times that of type A. When asking how many workers of type A and type B are recruited, can the monthly wages be the least?

9. A certain plant is suitable for growing in the mountainous area with the temperature of 18℃ ~ 22℃. It is known that the temperature drops by .6℃ for every 1m elevation in the mountainous area, and now the average temperature at the foot of the mountain is measured to be 22℃. Ask which part of the mountain is suitable for this plant (let the average elevation at the foot of the mountain be m).

1. Make the price 8 kg of A candy per kg of 2 yuan and the price as follows. What is the minimum?

11. The mall buys m pieces of a certain commodity, and each piece is increased by 65% of all the goods sold in 3 yuan according to the purchase price, and then the price is reduced by 1%, so that each piece can still make a profit in 18 yuan, and 25% of all the goods are sold.

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

(2) in order to ensure that the total profit of this batch of goods is not less than 25%, how much should the selling price of the remaining goods be not less than?

12. (Anhui in 21) An engineering team wants to recruit 15 workers of two types of jobs, the monthly wages of which are 6 yuan and 1 yuan respectively. Now it is required that the number of workers of type B is not less than 2 times that of type A. When asking how many workers of type A and type B are recruited, can the monthly wages be the least?

13. A company went to a fruit base to buy some high-quality fruit to express condolences to medical workers. The fruit base adopted two sales schemes for customers who bought more than 3, kg (including 3, kg).

scheme a: each kilogram of 9 yuan is delivered to the door by the base; Scheme B: Each kilogram of 8 yuan will be transported back by the customer by car. It is known that the transportation cost of renting a car from the base to the company is 5 yuan.

(1) Write out the functional relationship between the payment amount Y (yuan) and the fruit quantity x(kg) of the two purchase schemes of the company, and write out the value range of the independent variable X ..

(2) when the purchase amount is in what range, which purchase scheme should be chosen to pay the least? And explain the reasons

14. (Jiamusi) A company deals in two kinds of goods, each of which has a purchase price of 12, yuan and a selling price of 145, yuan. Each of which has a purchase price of 8, yuan and a selling price of 1, yuan, and their purchase price and selling price remain unchanged. Now, we are going to purchase 2 pieces of two kinds of goods, and the funds used are not less than 1.9 million yuan.

(2) Which purchase plan can the company adopt to get the maximum profit? What is the maximum profit?

(3) Make use of the maximum profit obtained in (2) to purchase again, please directly write the purchase plan to obtain the maximum profit.

15. (Suzhou) Suzhou is located on the shore of Taihu Lake and has rich aquaculture resources. Uncle Li, an aquaculture farmer, is going to carry out mixed culture of hairy crabs and river shrimps. He learned the following information:

① The annual rent per mu of water surface is 5 yuan, and the water surface should be an integer mu.

② 4kg crab fry and 2kg shrimp fry can be mixed into each mu of water surface at the beginning of the year;

③ The price per kilogram of crab seedlings is 75 yuan, and its feeding cost is 525 yuan, which can earn 1 4 yuan in that year;

(4) The price per kilogram of shrimp fry is 15 yuan, and the feeding fee is 85 yuan, so you can get the income from 16 yuan in that year.

(1) If you rent an area of N mu of water, the annual rent will be _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

(2) The cost of aquaculture includes the annual rent on the surface of the water, the fry fee and the feeding fee, and the annual profit (profit = income-cost) of mixed culture of crabs and shrimps on the surface of the water per mu is sought;

(3) Uncle Li has 25, yuan, and he is going to borrow no more than 25, yuan from the bank for mixed culture of crabs and shrimps. It is known that the annual interest rate of bank loans is 8%. How many acres of water should Uncle Li rent and how much should he borrow from the bank, so that the annual profit can exceed 35, yuan?

16. (Harbin) The owner of Shuangrong Clothing Store goes to the factory to buy two types of clothing, A and B. If he buys 9 pieces of clothing of A type and 1 pieces of clothing of B type, he needs 1 81 yuan. If you buy 12 pieces of A-type clothing and 8 pieces of B-type clothing, you need 1 88 yuan. < P > (1) How much is each piece of A-type and B-type clothing?

(2) If you sell one A-type garment, you can get 18 yuan, and if you sell one B-type garment, you can get 3 yuan. According to the market demand, the clothing store owner decided that the number of A-type garments should be twice as much as that of B-type garments, and the maximum number of A-type garments can be 28, so that the total profit can be no less than 699 yuan after all the garments are sold. How many purchase schemes are there? How to purchase goods?

17. In order to expand its business, a company in (Henan) decided to purchase six machines to produce some kind of pistons. There are two machines A and B to choose from, and the price of each machine and the daily number of pistons produced by each machine are shown in the following table. After budget, the cost of purchasing the machines this time cannot exceed 34, yuan.

The price of Party A and Party B

is (1, yuan/set) 75 < p.

(2) If the daily production capacity of the six machines purchased by the company cannot be less than 38, which scheme should be chosen to save money?

18. A store needs to buy a batch of TV sets and washing machines. According to market research, it is determined that the purchase amount of TV sets is not less than half of the purchase amount of washing machines. The purchase price and selling price of TV sets and washing machines are as follows:

Purchase price (RMB/set) 18 15

Selling price (RMB/set) 2 16

. (regardless of other expenses except the purchase price)

(2) Which purchase plan will gain the most profit after the store sells the purchased TV sets and washing machines? And get the most profit. (Profit = selling price-purchasing price)

19. RoyceWong, a fruit grower in Baiyu Village, Jiangyou, a "national civilized village" in Mianyang City, harvested 2 tons of loquat and 12 tons of peach. Now it is planned to rent 8 trucks of A and B to transport all these fruits to other places for sale. It is known that one truck of A can hold 4 tons of loquat and 1 ton of peach, and one truck of B can hold 2 tons of loquat and peach respectively. How many schemes are there?

(2) If each truck of Class A has to pay the transportation fee of 3 yuan and each truck of Class B has to pay the transportation fee of 24 yuan, which scheme should fruit grower Wang Can choose to minimize the transportation fee? What's the minimum freight?

2. In 27, in preparation for the 2th anniversary celebration of a county in our city, the garden department decided to use the existing 3,49 pots of A-type flowers and 2,95 pots of B-type flowers with two kinds of gardening shapes ***5 pots placed on both sides of Yingbin Avenue. It is known that 8 pots of A-type flowers, 4 pots of B-type flowers, 5 pots of A-type flowers and 9 pots of B-type flowers are needed to match one kind of shape. < p Please help to design it.

(2) If the cost of matching a style is 8 yuan and the cost of matching a style is 96 yuan, please explain which scheme in (1) has the lowest cost? How much is the lowest cost?

Mobile phone model A, B, C

Purchase price (unit: RMB/unit) 9 12 11

Pre-sale price (unit: RMB/unit) 12 16 13

21. A mobile phone dealer plans to buy three types of mobile phones of a certain brand * *.

(2) find the functional relationship between y and x;

(3) Assuming that all the purchased mobile phones have been sold, the mobile phone dealer will have to spend an additional ***15 yuan in the process of buying and selling these mobile phones.

① Find the functional relationship between the estimated profit P (yuan) and X (department); (Note: estimated profit p = total pre-sale-purchase price-various expenses) ② Find the maximum estimated profit and write down the number of each of the three types of mobile phones to be purchased at this time.

22. Fighting floods and rescuing, transporting materials to dangerous sections, * * * has an original distance of 12 kilometers, and it takes one hour to deliver them. After 5 kilometers have been traveled in the first half hour, what is the speed in the second half hour to ensure timely delivery?

23. A cinema is open to students in summer vacation, and each ticket is 2 yuan. In addition, you can also sell 3 ordinary tickets to 5 yuan each time. If you want to keep the box office income at least 2, yuan each time, how many discount tickets for students should you sell each time on average?

24. The fruit shop bought 1t Chinese fruit, and the purchase price was 7 yuan /kg. The price is set at 1 yuan /kg. After half of the sale, we are going to sell it at a discount in order to sell it out as soon as possible. If the total profit is not less than 2 yuan, then the rest of the fruit can be sold at a discount to the original price.

25. During the Mid-Autumn Festival, apples are very popular. A merchant bought a batch of apples, and the purchase price was 1.5 yuan per kilogram. There was a loss of 6% of apples in the sale. How much should the merchant set the price at least per kilogram to avoid losing money?

26. The headmaster of Sunshine Middle School is going to lead the "city-level three-good students" of the school to travel to Qingdao in the summer vacation. A travel agency said, "If the headmaster buys a full ticket, the rest of the students will enjoy a half-price discount." B travel agency said, "All the staff including the headmaster will enjoy a 6% discount on the full ticket." If the full ticket to Qingdao is 1 yuan.

(1) Set up a travel agency with X students.

27. A coal-using unit has tons of coal, and it burns tons of coal every day. Now it is known that there are 12 tons of coal remaining after three days of coal burning and 72 tons of coal remaining after eight days of coal burning. (1) Find the resolution function between the remaining tons of coal and the number of days of coal burning in this unit; (2) After burning coal for 12 days, how many tons of coal is left? (3) How many days is it expected that the coal will be burned out?

28. A spring with a length of 2cm is fixed at one end and hung with an object at the other end. Within the limit that the length of the spring after extension does not exceed 3cm, the spring will be extended by .5cm for every object with a mass of 1㎏. If the mass of the object is x㎏, the length of the spring is ycm.

(1) Find the functional relationship between Y and X, and draw the image of the function.

(2) What is the maximum mass of the object hung by the spring?

29. When someone lights a candle with a length of 25㎝, it is known that the candle is shortened by 5㎝ per hour, and the remaining length of the candle is y㎝ after xh. (1) Find the functional relationship between y and x. (2) After several hours, the length of the candle is less than 1㎝?

3. A ship sailed from Port A to Port B at a speed of 2km/h, and two hours later, a speedboat sailed from Port A to Port B at a speed of 4km/h.. List the functional relationship between the distance y km traveled by the ship and the speedboat and the time x h, and draw the image of the function in the rectangular coordinate system. Observe the image to answer the following questions: (1) When is the ship traveling in front of the speedboat? (2) When does the speedboat run in front of the ship? (3) Which ship sailed 6km first? Which ship sailed 1km first?

31. A school plans to buy several computers. Now it is known from two shopping malls that each computer of the same model is quoted at 6 yuan, and there is a certain amount for buying more computers.