Jiangyou middle school recruitment

Application problem set of linear inequality in one variable

If the total price does not exceed that of 400 yuan, the candy should not be less than 15kg, what is the maximum quantity of mixed candy B, 8kg of sugar A in 20 yuan, and how many kilograms of sugar B per kg 18 yuan? What's the minimum?

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

In order to reward the students who won the prize in the math contest, a school bought some extracurricular reading materials for them. If each person gives three books, there are still eight left. If the first person gives five books and the last person gets less than three extra-curricular books, assuming that the school buys m extra-curricular books and X students win prizes, please answer the following questions:

(1) m is represented by an algebraic expression containing x;

(2) Understand the number of school winners and the number of books bought after class.

Jingmen City (200 1) has 10 vegetable farmers, and each vegetable farmer can grow 3 mu of vegetable A or 2 mu of vegetable B. It is known that vegetable A can earn 5,000 yuan per mu and vegetable B can earn 8,000 yuan per mu. If the total income is not less than 1.56 million yuan, how should the staff be arranged?

(200 1 Shaanxi) Taxi starting price 10 yuan (i.e. 5 kilometers to meet domestic demand 10 yuan). After reaching or exceeding 5km, increase the price by 1km (the part less than 1km is counted as 1km).

(Chongqing, 2002) 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. There are two taxi teams, Team A and Team B. Team A has three fewer cars than Team B. If all the cars of Team A are lined up, each car will take five people, but there are not enough cars, each car will take six people, and some cars are not full. If all the buses of Team B are arranged, each bus will take 4 people. If it is not enough, each bus will take 5 people. If some buses are not full, then Team A has a taxi ().

a . 1 1 b . 10 c . 9d . 8。

(200 1 Jingzhou) On the weekend, a company decided to organize 48 employees to take a boat trip to the nearby water park. First, the company sent a person to find out the rent of the ship. The rent list that this person saw is as follows:

Number of people per ship (person) rent (yuan)

Big ship 5 3

Ship No.3, No.2

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

(200 1 Anhui) An engineering team wants to recruit two types of workers 150, and the monthly wages of the two types of workers are 600 yuan and 1000 yuan respectively. At present, the number of Class B workers is required to be not less than twice that of Class A. When asked how many people are recruited for each of the two jobs, the monthly salary can be the least.

A certain plant is suitable to grow in mountainous areas with the temperature of 18℃ ~ 22℃. It is understood that for every elevation increase of 100 meters in mountainous areas, the temperature drops by 0.6℃, and now the average temperature at the foot of the mountain is 22℃. Where is the mountain suitable for this plant (assuming that the average elevation at the foot of the mountain is 0m).

If the total price is not more than 400 yuan, the candy is not less than 15kg, the candy A in 20 yuan is 8kg, and the candy B is several kilograms per kilogram 18 yuan, what is the maximum quantity of mixed candy B? What's the minimum?

When shopping malls buy m pieces of a certain commodity, each piece will be increased by 65% of all the goods sold according to the purchase price in 30 yuan, and then the price will be reduced by 10%, so that each piece can 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 of this batch of goods is not less than 25%, what should be the price of the remaining goods?

(200 1 Anhui) An engineering team wants to recruit two types of workers 150, and the monthly wages of the two types of workers are 600 yuan and 1000 yuan respectively. At present, the number of Class B workers is required to be not less than twice that of Class A. When asked how many people are recruited for each of the two jobs, the monthly salary can be the least.

A company went to the fruit base to buy some high-quality fruits to express condolences to medical workers. The fruit base has adopted two sales schemes for customers who buy more than 3000kg (including 3000kg).

Scheme A: Each kilogram of 9 yuan is delivered from the base to the door; Scheme B: Each kilogram of 8 yuan is transported back by the customer by car. It is understood that the transportation fee for renting a car from the base to the company is 5000 yuan.

(1) Write the functional relationship between the payment amount y (yuan) and the fruit quantity x (kg) of the two procurement schemes of the company, and write 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 why.

(Jiamusi) Company A deals in two commodities, A and B. The purchase price of each commodity is 6.5438+0.2 million yuan, and the selling price is 6.5438+0.45 million yuan. The purchase price of each commodity is 80,000 yuan, and the price is 6,543.8+0,000 yuan. Their purchase price and price are always the same. Now I'm going to buy 20 yuan each for A and B, and the funds used are not less than 60 yuan.

(1) What purchasing schemes does the company have?

(2) What kind of procurement scheme can the company adopt to obtain the maximum profit? What is the maximum profit?

(3) Use the maximum profit obtained in (2) to buy again. Please write the purchase plan directly to get the maximum profit.

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

(1) The annual rent per mu of water surface is 500 yuan, and the water surface needs to be rented for the whole mu;

② At the beginning of the year, 4 kg of crab fry and 20 kg of shrimp fry can be mixed into each mu of water surface;

(3) The price of crab seedlings per kilogram is 75 yuan, and the feeding cost is 525 yuan, and the income can be obtained in that year 1 400 yuan;

④ The price per kilogram of shrimp is 15 yuan, the feeding cost is 85 yuan, and the annual income is 160 yuan.

(1) lease n mu of water, and the annual rent is _ _ _ _ _ _ _ _ _ _ _ _ _;

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

(3) Uncle Li has 25,000 yuan, and he is going to borrow no more than 25,000 yuan from the bank for mixed culture of crabs and shrimps. As we all know, the annual interest rate of bank loans is 8%. How many acres of water does Uncle Li have to rent and borrow from the bank, so that the annual profit can exceed 35,000 yuan?

The owner of Shuangrong Clothing Store (Harbin) went to the factory to buy two kinds of clothes, A and B. If he bought 9 pieces of A clothes and 10 pieces of B clothes, he would have to 1 8 10 yuan. If you buy 12 pieces of A-type clothes and 8 pieces of B-type clothes, you need 1 880 yuan.

(1) How much is each piece of clothing A and B?

(2) If you sell 1 piece of A-type clothing, you can get 18 yuan, and if you sell 1 piece of B-type clothing, you can get 30 yuan. According to the market demand, the clothing store owner decided that the number of type A clothing is twice that of type B clothing, and there can be up to 28 pieces of type A clothing, so that the total profit after all the clothes are sold is not less than 699 yuan. How to purchase goods?

In order to expand its business, a company in Henan decided to buy six machines to produce some kind of piston. There are two kinds of machines A and B to choose from. The price of each machine and the number of pistons produced by each machine are shown in the following table. After the budget, the cost of buying the machine this time can't exceed 340 thousand yuan.

Price of Party A and Party B (RMB 10,000/set) 75-day output per set (set) 10060

(1) According to the company's requirements, how many purchasing schemes can there be?

(2) If the daily production capacity of six machines purchased by the company cannot be less than 380, which scheme should be chosen to save money?

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

Purchase price (RMB/set) 1800 1500 selling price (RMB/set) 2000 1600.

It is planned to purchase 100 TV sets and washing machines, and the store can raise funds at most 1800 yuan.

(1) Could you please help the store calculate how many kinds of purchase plans there are? (excluding other expenses except the purchase price)

(2) After the store sells the purchased TV sets and washing machines, which purchase scheme will get the most profit? And get the maximum profit. (Profit = selling price-buying price)

RoyceWong, a fruit grower in Baiyu Village, Jiangyou, a "national civilized village" in Mianyang City, harvested 20 tons of loquat and 0/2 tons of peach/kloc. At present, it is planned to rent eight A-class and B-class trucks to transport all these fruits to other places for sale. It is known that a Class A truck can hold 4 tons of loquat and 1 ton of peach, and a Class B truck can hold 2 tons of loquat and peach respectively.

(1) How does RoyceWong arrange for A and B trucks to be transported to the sales place at one time? How many schemes are there?

(2) If the transportation cost of each class A truck is 300 yuan and the transportation cost of each class B truck is 240 yuan, which scheme does the fruit farmer choose to have the smallest transportation cost? What's the lowest freight?

In 2007, a county in our city prepared for the 20th anniversary celebration, and the garden department decided to use the existing 3490 pots of A-type flowers and 2950 pots of B-type flowers, with two gardening styles, totaling 50 pots, and put them on both sides of Yingbin Avenue. It is known that matching a style requires 80 pots of A-type flowers and 40 pots of B-type flowers, and matching a style requires 50 pots of A-type flowers and 90 pots of B-type flowers.

(1) The extracurricular activity group of Class 9 (1) in a school undertook the design of this gardening modeling collocation scheme. How many matching schemes are there? Please help design it.

(2) If the cost of matching a model is 800 yuan and the cost of matching a model is 960 yuan, please explain which scheme in (1) has the lowest cost? How much is the minimum?

Mobile phone models a, b and c

Purchase price (unit: yuan/department) 90012001100.

Pre-sale price (unit: yuan/department)120016001300

A mobile phone dealer plans to buy 60 mobile phones of a certain brand, including Type A, Type B and Type C, and each mobile phone should buy at least 8, and the purchase price is exactly 6 1 1,000 yuan. Suppose you buy X type A mobile phones and Y type B mobile phones. The purchase price and pre-sale price of the three mobile phones are as follows:

(1) Use the formula containing x and y to express the purchase quantity of Class C mobile phones;

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

(3) Assuming that all the purchased mobile phones have been sold, the mobile phone dealers need to spend 1500 yuan in the process of buying and selling these mobile phones.

(1) Find the functional relationship between the expected profit p (yuan) and x (part); (Note: Estimated profit p = total pre-sale amount-purchase price-various expenses) ② Find the maximum estimated profit and write down how many mobile phones you bought at this time.

Flood fighting and emergency rescue, transporting materials to dangerous sections, the whole journey is 1 .20km, and it needs to be delivered1hour. After driving 50 kilometers in the first half hour, what is the speed in the second half hour to ensure timely delivery?

A cinema is open to students in summer vacation, with each ticket to 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?

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 were lost in the sales. Merchants should at least set the price per kilogram so as not to lose money.

The headmaster of Sunshine Middle School is going to lead the school's "three excellent students at the municipal level" to travel to Qingdao in the summer vacation. A travel agency said that "if the principal buys a full ticket, the rest of the students will enjoy a half-price discount." B Travel Agency said that "all staff members, including the person in charge, will enjoy a 60% discount on all tickets." If the full ticket to Qingdao 1, 000 yuan.

(1) Suppose the number of students is X, the fee charged by travel agency A is Y yuan, and the fee charged by travel agency B is Y yuan. Write the expense expressions of the two travel agencies respectively.

(2) Regarding the number of students X, which travel agency is more favorable?

A household coal company has tons of coal and burns tons of coal every day. It is now known that there are 102 tons left after three days of coal burning and 72 tons left after eight days of coal burning. (65,438+0) Find the resolution function between the remaining tons of coal and the days of burning coal. (2) How many tons of coal are left after burning coal 12 days? (3) How many days is the coal expected to burn out?

A 20 cm long spring with one end fixed and the other end hung with an object. Within the limit that the extension length of the spring does not exceed 30cm, the spring will extend by 0.5cm for each object with the 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 an object suspended by a spring?

Someone lit 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 after xh is y㎝. (1), find the functional relationship between y and x (2), and after several hours, the length of the candle is less than 10㎝?

A ship sails from port A to port B at a speed of 20km/h, and two hours later, a speedboat sails from port A to port B at a speed of 40km/h ... List the function relationship between the distance y km traveled by the ship and the speedboat and the time x h, and draw the image of this function in the rectangular coordinate system. Observe the image and answer the following questions: (1) When is the boat in front of the speedboat? (2) When does the speedboat run in front of the boat? (3) Which ship sailed 60 kilometers first? Which ship passed 100km first?

A school plans to buy a batch of computers, and now it is learned from two shopping malls that each computer of the same model is quoted at 6000 yuan, and there is a certain discount for buying more computers. The preferential conditions of a shopping mall are: the first piece is charged at the original price, and the rest is 15% off; The preferential terms of Mall B are: 20% off each set.

(1) Write down the relationship between the charges of two shopping malls and the number of computers purchased;

(2) Under what circumstances is it more favorable to buy in the mall?

(3) Under what circumstances is it more favorable to go to Mall B?

(4) Under what circumstances do two shopping malls charge the same?

Red Star Company wants to recruit type A and type B workers 150, and the monthly salary of type A and type B workers is 600 yuan and 1000 yuan respectively. At present, the number of type B workers is required to be not less than twice that of type A workers, so when recruiting type A workers, what is the minimum monthly salary? What is the monthly salary at this time?

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, 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?

Someone asked the teacher how many students there were in his class. The teacher said, "Half of the students are studying math, one quarter are studying music, one seventh are studying foreign languages, and less than six students are playing football on the playground." How many students are there in this class?

A chemical plant in our city has 290 kilograms of raw materials A and 2 12 kilograms of raw materials B. It is planned to produce 80 products A and B with these two raw materials. It takes 5 kilograms of raw materials A and 1.5 kilograms of raw materials B to produce a product A; It takes 2.5 kg of raw material A and 3.5 kg of raw material B to produce a product B. Can the existing raw materials in this chemical plant ensure the smooth production? If so, how many schemes are there? Please design it.

In order to reward the students who won the prize in the math contest, a school bought some extracurricular reading materials for them. If each person gives three books, there are still eight left. If each person gives five books in front, the last person gets less than three extra-curricular books; Suppose the school bought M extracurricular books and X students won prizes. Please answer the following questions: (1) use an algebraic expression containing x to represent m; ⑵ Ask about the number of school winners and the number of books purchased after class.

When the price of a refrigerator sold in a shopping mall is 2 190 yuan and the monthly power consumption is 1kw, the price of a refrigerator sold in a shopping mall is 10% higher than that of a refrigerator, but when the power consumption is 0.55 kW that day, the shopping mall will discount the sales of a refrigerator. If only the price and power consumption are considered, it is worthwhile for consumers to buy at least a few discounts. (service life 10 year, 365 days per year, and the electricity charge per kilowatt hour is calculated in 0.4 yuan).

A company has 50 employees. In order to improve economic benefits, we decided to introduce a new production line and transfer some employees from existing employees to the new production line. After investigation, it was found that the monthly per capita output value of employees who stayed in the original production line increased by 40%; The monthly per capita output value of employees working in the new production line is three times that of the original, and X people are assigned to work in the new production line.

(1) Fill in the blank: if the per capita output value of employees before division of labor is RMB, the per capita output value of employees who remain in the original production line after division of labor is RMB, and the total output value is RMB; The monthly per capita output value of employees working in the new production line is yuan, and the monthly total output value is yuan;

(2) After the division of labor, the total monthly output value of employees staying in the original production line shall not be lower than that of the original production line before the division of labor; Moreover, the monthly output value of the new production line is not less than half of the monthly output value of the production line before division of labor. Q: What range should the number of people be transferred?

Since the beginning of this year, most parts of Guangdong have been short of electricity. In order to encourage citizens to save electricity, power companies have adopted the method of charging monthly electricity consumption. If the function image of a household's monthly electricity bill y (yuan) and electricity consumption x (degrees) is a broken line (as shown in the figure), the following problems can be solved according to the image:

(1) Write the functional relationship between Y and X when 0≤x≤ 100 and x≥ 100 respectively;

(2) Using the function relation, explain the charging standard adopted by the power company;

(3) If the user uses 62 kWh a month, how much should he pay? If the user pays 105 yuan a month, how many kwh does the user use this month?

A highway toll station has m (m > 0) Vehicles queue up to wait for the toll to pass. Assuming that the traffic volume (the number of cars passing through the toll booth every minute) is unchanged, the charging speed of each charging window is also unchanged. If you open a toll window, it takes 20 minutes to charge all the cars in line and the cars coming behind. If you open two charging windows at the same time, it only takes 8 minutes to charge all the cars waiting in line and the cars coming behind. If all the cars waiting in line for charging are required to pass within 3 minutes, and the cars coming to the next station are also required to pass at any time, how many charging windows should be opened at least at the same time?

In order to strengthen students' awareness of traffic safety, a middle school and the traffic police brigade jointly held the activity of "I will be a small traffic police for one day", and sent some students to traffic intersections on Sunday to help the traffic police maintain traffic order. If four people are arranged at each intersection, there are still 78 people left. If there are 8 people at each intersection, there will be less than 8 people at the last intersection, but not less than 4 people. How many students will be assigned to this middle school? How many traffic intersections are on duty?

In order to improve the production and living environment of urban and rural people, our city has invested a lot of money to control the pollution of Zhupi River and established a comprehensive sewage treatment plant in the suburbs. There are tons of sewage to be treated in the reservoir, and the sewage flowing into the reservoir from the urban area is increasing at a fixed flow rate of tons per hour. If it takes 30 hours to treat sewage at the same time, it takes 10 hour to treat sewage at the same time. If the sewage is required to be treated within 5 hours, it must be at least.