Mathematics problems in the first grade of junior high school

1. There are 90 workers in the workshop, and each person can produce 24 nuts or 15 bolts every day. If a bolt is matched with two nuts, how many people should be assigned to produce bolts and how many people should produce nuts to make the bolts and nuts match each other?

2. 8 rounds of middle school students' football league in a certain district (that is, each team needs to play 8 games). 3 points for winning a game, 1 point for drawing a game, and 0 point for losing a game. In this football league, the teams in the men's division have twice as many matches as those in the negative position, and * * * will get 17 points. Do you know how many games the men's division team won?

3. 10 years ago, the mother was six times older than her son; 10 years later, the mother is twice as old as her son.

It is known that a ship has a deadweight of 500 tons and a volume of 1000 cubic meters. At present, there are two kinds of goods to be loaded, those with a volume of 7 cubic meters per ton and those with a volume of 2 cubic meters per ton. How can we make full use of the ship's load and volume?

A city has a population of 420,000. It is planned that after one year, the urban population will increase by 0.8% and the rural population will increase by 1. 1%, so that the population of the whole city will increase by 1%. What is the current urban and rural population of this city?

6. Party A and Party B practice running. If Party B runs 10 meter first, Party A will catch up with Party B in 5 seconds; If you let B run for 2 seconds first, then A will catch up with B in 4 seconds. Find the speed of a and b ..

Last year, the total revenue of a company exceeded the total expenditure by 500,000 yuan. This year, the total revenue increased by 65,438+00%, and the total expenditure was saved by 20%. The total revenue this year is 654.38 billion yuan more than the total expenditure. Find out the total income and total expenditure last year.

8. Wang Chengbao contracted 25 mu of land, and planted two kinds of greenhouse vegetables, eggplant and tomato, this spring, which cost 44,000 yuan, including eggplant 1.7 million yuan per mu and net profit of 2,400 yuan. Planting tomatoes cost 1800 yuan per mu and earned a net profit of 2600 yuan. How much did Uncle Wang make?

9. Xiaoming and Liang Xiao walk in opposite directions from A and B, which are 20 kilometers apart. After the two-hour meeting, Xiaoming returned to his original place, and Xiao Liang continued to move towards A. When Xiaoming returned to A, Xiao Liang was 2 kilometers away from A and asked about their speed.

10.the Indian ocean tsunami at the end of 2004 touched the hearts of people all over the world. An international medical rescue team used two raw materials, A and B, to prepare nutritional products for postoperative patients. Each gram of raw material A contains 0.5 units of protein and 0.5 units of iron 1 unit, and each gram of raw material B contains 0.7 units of protein and 0.4 units of iron. If patients need 35 units of protein and 40 units of iron per meal, then raw materials A and B contain 0.5 units of iron per meal.

1 1 has a two-digit number, and the sum of its two digits is 1 1. Switch the single digits of this two-digit number with the ten digits, and the new number is 63 larger than the original number, and the original two-digit number can be found.

12. A batch of goods is to be transported to a certain place, and the owner is going to rent two kinds of trucks from the automobile transportation company. It is understood that the situation of renting this truck twice in the past is as follows:

The first and second projects

Number of Class A vehicles/2 5 vehicles

Number of Class B vehicles/3 6 vehicles

Cumulative tonnage/ton 15.5 35

At present, three A-class trucks and five B-class trucks of this company are leased, and the goods have just been delivered at one time. If the freight per ton is calculated in 30 yuan, how much freight does the truck have to pay?

13, junior one students travel to a certain place, if each car takes 45 people, then 15 students have no seats; If there are 60 people in each car, there is 1 car. Ask the workers how many students and cars there are.

14. A school held a math contest, and 120 people signed up. Competition results: the average score is 66, the average score of those who pass is 76, and the average score of those who fail is 52. How many students passed and how many failed in the math contest?

15, the distance between Party A and Party B is 20km. A goes from A to B, and B goes from B to A at the same time. Two hours later, they met on the road. After meeting, A returns to A, B still goes to A, A returns to A, and B is still 2km away. Find the speed of A and B. ..

16. The distance between Party A and Party B is 60 kilometers. A and B ride bicycles from two places respectively. If A leaves half an hour before B and B walk 2 kilometers more than A every hour, they will walk exactly the same distance when they meet. Find the speed of a and b riding bicycles.

17. It is known that the sum of the original prices of two commodities is 200 yuan. Due to market changes, the price of commodity A decreased by 65,438+00%, while the price of commodity B increased by 65,438+00%. After the price adjustment, the sum of the unit prices of commodity A and commodity B increased by 5% compared with the sum of the original unit prices. Find the original unit price of a and b goods.

18, a class of students went to Beishan 18 km for an outing. There is only one car, so it needs to be divided into two groups. Group A takes the bus first, and Group B walks. When the bus arrives at A, Group A gets off and walks, and the bus returns to Group B. Finally, the two groups arrive at Beishan Station at the same time. Given the speed of 60 km/h and the walking speed of 4 km/h, find the distance from point A to Beishan Station.

19, the number of gymnastics teams and basketball teams in a school is 5:6, the number of volleyball teams is 2 times less than that of gymnastics teams, and the sum of the number of basketball teams and gymnastics teams is 3 times equal to 42 people. How many people are there in each of the three teams?

20. 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. Ask everyone how many grams they need.

2 1. A shopping mall plans to allocate 90,000 yuan to buy 50 TV sets from a manufacturer. It is known that this manufacturer produces three different models of TV sets, the ex-factory price is 1500 yuan, 2 100 yuan per set, and 2,500 yuan per set. (1) If the shopping mall buys 50 TV sets of two different models at the same time, and it costs 90,000 yuan, please study the shopping plan of the shopping mall;

(2) If a shopping mall sells a first-class TV set with a profit of 150 yuan, a second-class TV set with a profit of 200 yuan and a third-class TV set with a profit of 250 yuan, which purchase scheme is the most profitable?

(3) If the mall is going to buy 50 TV sets of three different models at the same time with 90,000 yuan, please forget the purchase plan.

22. A clothing factory wants to produce a batch of sportswear of the same model. It is known that a certain fabric can be made into 2 tops or 3 pairs of pants every 3 meters. At present, this fabric is 600 meters long. Please help me design how to distribute the cloth, so that the sportswear can be complete and not wasted. How many sets of sportswear can you produce?

23. A storefront decoration can be completed in 8 days if two decoration groups, A and B, are invited at the same time, and the cost of the two groups needs to be paid ***3520 yuan; If you ask group A to do it alone for 6 days, and then ask group B to do it alone 12 days, you need to pay ***3480 yuan for both groups. Q:

(1) How much does the store pay for each group to work alone for one day?

(2) It is known that it takes 12 days for group A to complete alone, and it takes 24 days for group B to complete alone. Which group is invited alone, and the store pays less for it?

(3) If the store can make a profit in 200 yuan every day after renovation, how do you think to arrange the construction and use the store for operation? Tell me your reasons. (You can directly use the known conditions in (1)(2))

The equation (group) is above, and the inequality (group) is below, but I think 40 questions have been added.

35 ~ 50 minutes, isn't it a little less?

1, a math test, *** 16 multiple-choice questions, the grading standard is: 6 points for one question, 2 points for one wrong question, and no points for failure to answer. A student has 1 unanswered questions. He hopes that his score will not be lower than 70. How many problems should he correct at least?

2. An English book has 98 pages. Zhang Li studied for a week (7 days), but Li Yong finished it in less than a week. Li Yong reads three pages more than Zhang Li every day. How many pages does Zhang Li read every day? (The answer is rounded)

3. An engineering team wants to recruit two types of workers 150, and the monthly wages of the two types are 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 asking how many people are recruited for both types, can the monthly salary be the least?

4. The original price of a commodity is 800 yuan. When selling, the price tag is 1200 yuan. If the profit margin is not less than 5%, what is the maximum discount you can give?

5. There are 100 workers in an aquatic product breeding and processing factory, and each worker catches 60 kilograms of aquatic products every day on average, or 50 kilograms of aquatic products caught on the processing day. It is known that direct selling of aquatic products can make a profit per kilogram of 7 yuan, and sales of refined aquatic products can make a profit per kilogram 17 yuan. Suppose x workers are arranged to complete aquatic products every day.

(1) Use the algebraic expression containing x to express the profit obtained by the daily arrangement of this factory:

(2) If all refined aquatic products and unprocessed aquatic products are sold in one day, the factory profit will be 46 160 yuan. How many people do refined aquatic products? How many people should be arranged to process aquatic products in order to maximize the profit of this factory?

6. Under normal circumstances, retailers should generally consider the discount factor when they may carry out promotional activities in the future when pricing goods. If the purchase price of a brand computer is 5,000 yuan, you can still get a profit no less than that of 400 yuan if you get a 10% discount for future promotion. What should be the initial selling price of this computer at least?

7. Autumn outing in the second grade, renting a number of 48-seat buses, just full; If you rent a 64-seat bus, you can rent less 1 car. One car is not full, but you know more than half. It is known that 250 yuan rents 48 buses and 300 yuan rents 64 buses. What kind of bus should you rent more economically?

8. A bunch of toys were given to several children. If each child gives 3 yuan, give the remaining 3 yuan. If you give each child 5 yuan, give each child a toy. However, if a child has less than three toys, how many children are there?

9. A town in our city organized 20 vehicles to ship three kinds of navel oranges, A, B and C * * *100t to other places for sale. According to the plan, 20 cars will be transported, each car can only transport the same navel orange, and it must be full. According to the information provided in the following table, solve the following problems:

Navel orange variety A B C

Capacity of each vehicle (ton) 6 5 4

Get (100 yuan) 12 16 10 per ton of navel orange.

(1) Let the number of vehicles carrying A navel orange be, and the number of vehicles carrying B navel orange be, and express y with an algebraic expression containing X; (2) If there are not less than 4 vehicles loaded with navel oranges, how many vehicles are arranged? And write the layout plan; (3) What arrangements should be taken to maximize the profit of this sale? And find the value of the maximum profit.

10. It is known that a clothing factory now buys two kinds of fabrics *** 122 meters from textile mills, which costs 4 180 yuan. It is known that 30 yuan per meter for Class A fabrics and 40 yuan per meter for Class B fabrics.

(1) How many meters do I need for fabrics A and B?

(2) It is planned to produce 80 sets of A and B fashions with these two fabrics. It is known that two kinds of fabrics A and B are needed to make a suit of A or B fashion, as shown in the following table:

Cloth fashion Jiayi

One (meter) 0.6 1. 1

Type B (meter) 0.9-0.4

(1) Set X sets for producing a type of fashion, and find the range of X;

(2) If the price of a fashion model is 100 yuan and the price of a fashion model is 90 yuan, how many sets of two fashion models does this clothing factory produce, and the total profit is the largest? What is the maximum profit?

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

(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?

12. A shopping mall needs to purchase 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:

Classified TV washing machine

Purchase price (RMB/set) 1800 1500

Price (RMB/set) 2000 1600

It is planned to purchase *** 100 TV sets and washing machines, and the store can raise up to 16 1 800 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)

13, 20 10, a county in our city is preparing for the 20th anniversary celebration. The garden department decided to use the existing 3490 pots of Class A flowers and 2950 pots of Class B flowers to arrange 50 gardening shapes on both sides of Yingbin Avenue. It is known that it takes 80 pots of class A flowers and 40 pots of class B flowers to match a model, and 50 pots of class A flowers and class B flowers to match a model.

(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?

14, a group of students took a group photo at the school gate. It is known that it takes 0.6 yuan to develop a negative and 0.4 yuan to develop a photo. Everyone gets a photo, and the average share of money is no more than that of 0.5 yuan. How many students will take part in this photo shoot?

15. Two shops, A and B, sell the same teapot and teacups. Each teapot is priced in 20 yuan, and each teacup is priced in 5 yuan. The preferential measures of the two stores are different: one store buys a teapot and gives a teacup as a gift; Store B charges 92% of the selling price. A customer needs to buy 4 teapots and several (more than 4) teacups. How many drinks do you buy when you go to Jia's shop for a discount?

16. In order to protect the environment, an enterprise decided to buy 10 sets of sewage treatment equipment. At present, there are two kinds of equipment, A and B. The price, monthly sewage treatment capacity and annual consumption of each equipment are as follows:

Type a and type b

Price (ten thousand yuan/set) 12 10

Sewage treatment capacity (ton/month) 240 200

Annual consumption expense (ten thousand yuan/set) 1 1

According to the budget, the funds used by enterprises to purchase equipment are not higher than 6.5438+0.05 million yuan.

(1) Please design several purchasing schemes for this enterprise;

(2) If the enterprise produces 2040 tons of sewage every month, which procurement scheme should be chosen to save money;

(3) Under the condition of (2), if the service life of each equipment is 10 year, and the sewage treated by the sewage plant is 10 yuan per ton, please calculate how many ten thousand yuan the enterprise will save by treating the sewage by itself compared with discharging the sewage to the sewage plant for treatment. (Note: Enterprise sewage treatment expenses include equipment purchase expenses and consumption expenses)

17. Local taxi starting price 10 yuan, fare within 5km 10 yuan). After reaching or exceeding 5km, each additional 1km, 1.2 yuan (less than 1km, the fare increase 1.2 yuan; The part less than 1km is counted as 1km). Now someone takes this taxi from A to B, pay 17.2 yuan. What is the approximate distance from a to b?

18, Wahaha mineral water per bottle 1.2 yuan. Now two shopping malls, A and B, are offering preferential policies: 10% discount for all shopping malls in area A and 20% discount for shopping malls in area B. If you are a consumer, which shopping mall is more suitable?

19, a group of monkeys went to steal peaches together one day. When you divide peaches, if you divide each monkey into three parts, there are 59 left. If each monkey gets five peaches, but a monkey gets less than five peaches. Can you find out how many monkeys and peaches there are?

20. The scoring rules for football matches are: win a game and get 3 points, draw a game and get 1 point, and lose a game and get 0 point. A football team needs to play 14 games in a certain season. Now I have played eight games and lost one, and got 17 points.

(1) How many games did this team win in the first eight games?

(2) How many points can this team score after playing 14?

(3) Through the analysis of the game situation, this team played 14 games and scored no less than 29 points, which can achieve the expected goal. Please analyze, in the next six games, how many times will this team win to achieve the expected goal?

2 1. The owner of Shuangrong Clothing Store 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 18 10 yuan. If you buy 12 pieces of A-type clothes and 8 pieces of B-type clothes, you need 1880 yuan.

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

(2) Selling a type A garment can make a profit 18 yuan, and selling a type B garment can make a profit in 30 yuan. According to the market demand, the clothing store owner decided that the number of type A clothing should be 4 more than that of type B clothing, and the maximum number of type A clothing can be 28, so that the total profit after all the clothing is sold is not less than 699 yuan. How many purchase plans are there? How to purchase goods?

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