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Mathematics examination paper and answer of the first volume of the second day of junior high school
Special topics on the application of binary linear equations

1. Li Minghe's father is years old, and he knows that his father is years younger than his age. If Li Ming is years old, the equation can be _ _ _ _ _ _ _ _ _ _ _.

My mother saved Xiaoming's education savings for six years with 20,000 yuan, and she will get 23,456 yuan after six years. The annual interest rate of this education savings is ().

A.2.86% B.2.88% C.2.84%

3. The sum of two digits of a ten-digit number and a single-digit number is, and after adding these two digits, the result just becomes a two-digit number formed by digital inversion, so this two-digit number is ().

A.B. C. D。

4. In order to encourage residents to save water, our city charges tap water users in sections: if the monthly water consumption does not exceed cubic meters, it will be charged at one yuan per cubic meter; If the monthly water consumption exceeds cubic meters, the excess will be charged at RMB per cubic meter. If a resident pays RMB water fee this month, the household's water consumption this month is _ _ _ _ _ _ _ cubic meters.

5. Oriental Mall sells a commodity with a purchase price of 1980 yuan at 20% of the marked price, and still makes a profit of 10%, then the marked price of the commodity is _ _ _ _ _ _ _ _ _ _ _.

6. A home appliance store sells two TV sets of different brands at a time, one of which earned 12% and the other lost 12%, and the price of the two TVs sold this time is 3080 yuan, so the profit of the store in this transaction is _ _ _ _ _ _ _ _.

7. Wang Chao goes from A to B. If you walk kilometers every hour, you are still kilometers away from B within the specified time;

If you walk thousands of meters per hour, you will arrive a few minutes ahead of schedule. Ask for the time and place designated by both parties.

Distance. (1) If the specified time is small, the equation _ _ _ _ _ _ _ _ _ _ _ _ _.

(2) Let the distance between Party A and Party B be kilometers, and the equation is _ _ _ _ _ _ _ _ _ _ _.

8. A school organized a team member to take part in the voluntary digging and earthmoving work. If each person excavates or transports cubic meters of soil every day, how should the number of people who dig and transport soil be distributed so that the excavated soil can be transported away in time? (Only list equations, not solve them)

9. Mr. Wang took advantage of the holiday to lead the group members to the countryside for social investigation. The original price of each ticket is RMB. Owner A said, "You can get a discount if you take my car." Owner B said, "Students can get a discount when they take my car." Mr. Wang calculated in his mind that the payment is the same no matter which car he takes. Excuse me, how many students did Mr. Wang take?

10. Both Company A and Company B are ready to recruit talents from the society. The recruitment conditions of the two companies are basically the same, but the salary is different as follows: Company A's annual salary 10000 yuan, annual salary 10000 yuan, half a year 10000 yuan, and half a year 10000 yuan. From the perspective of economic income, which company is favorable?

1 1 It is understood that individual clothing sales can be profitable as long as they are higher than the purchase price, but bosses often bid higher than the purchase price. Suppose you want to buy a dress with a price tag of 200 yuan, within what range should you make a counter-offer?

12 one day after class, the teacher copied an application problem on the blackboard as homework. As soon as the teacher left, the naughty Xiao Qiang erased the application questions in the back part, leaving only: "A ship has a tonnage and a cubic meter, and there are two kinds of goods to be transported, of which the tonnage of A goods is cubic meters, and the tonnage of B goods is cubic meters." After returning to the classroom, the students immediately talked about it: the monitor had a brainwave and immediately said, "Students use their imagination to complete and solve problems." Can it be solved? Just try it.

13 in order to make effective use of power resources, the power supply department of a city recently conducted a pilot project for residents to use electricity in peak and valley.

From 8: 00 to 2 1: 00, the electricity consumption is 0.55 yuan per kwh ("peak electricity" price), and from 2 1: 00 to 8: 00 the next day, the electricity consumption is 0.30 yuan per kwh ("valley electricity" price). After Mr. Wang used "Peak Electricity", the electricity consumption in May was 300 degrees. Pay the electricity bill of 650.

14. A middle school needs to get some teaching instruments. Scheme 1: Buy in the store, and each item needs 8 yuan; Option 2: The school does it itself. For each piece of 4 yuan, the rental fee for production tools is 65438 yuan +020 yuan. Equipment is necessary.

(1) Calculate the total cost of the scheme and the scheme respectively;

(2) When how many instruments are purchased, the cost of the two schemes is the same;

(3) If the school needs 50 pieces of instruments, which scheme is cheaper? Please explain the reason.

15. There is a passage in "Arabian Nights": There are a group of pigeons, some of whom are 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 flies from the tree, the number of pigeons under the tree is the whole group;" If one flies down from the tree, there are as many pigeons in the tree as there are under it. " According to this description, please count how many pigeons are on the tree and under the tree. How many pigeons are there in this group?

Liang Xiao wants to buy a walkman and a schoolbag. He found that the prices of the two commodities he liked were the same in the two supermarkets. The sum of the unit prices of walkman and schoolbag is RMB, and the unit price of walkman is less than that of schoolbag.

(1). What is the unit price of Xiao Liang's favorite walkman and schoolbag?

⑵. During May Day, two supermarkets held profit-making activities: 20% discount on all goods in supermarkets; For every full yuan of shopping in the supermarket, the amount of shopping will be returned (less than RMB will not be returned). Shopping rolls are universal. Xiao Liang only has RMB. Can he only buy these two things in one supermarket? If both companies can buy, which one will save more money?

Students from Class 7, Grade 7 17 of a school mail-order 50 math extracurricular books from a publishing house at a price of 7.50 yuan each. According to the regulations of the publishing house, mail order 10 or less (including 10) requires an additional mail order fee of 3 yuan; Mail order 10 copies or more (excluding 10 copies) requires a mail order fee of 15% of the book fee. When remittance is made in the post office, it needs 1 yuan for every 100 yuan remittance. If the remittance is less than 100 yuan, it shall be paid by remittance of 100 yuan.

⑴. After discussion by the class committee, there are two different mail order schemes: the first scheme is to send 10 copies each time and send them in five times; The second scheme is to order 50 copies by mail at one time, and ask for the cost of two different mail order schemes.

(2) If the number of books by mail order is 60 and 70 respectively, please compare the price difference of each book in the above two different mail order schemes, find out the price difference, and explain which scheme is more economical to use by mail order?

18. The ticket prices of tourist attractions are shown in the following table. Guangming junior middle school * * 104 has two classes (1) and (2) people traveling, of which (1) class has less than 50 students and (2) class has more than 50 students. It will save a lot of money if the two classes join forces to buy tickets in a group. How many students are there in each class?

The number of ticket buyers is1~ 50,51~ 100, which exceeds100.

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

19. There are some kinds of instruments available in Beijing and Shanghai, among which Beijing can provide Taiwan Province and Shanghai can provide Taiwan Province. As we all know, Chongqing needs Taiwan Province and Wuhan needs Taiwan Province. The transportation expenses of instruments from Beijing and Shanghai to Chongqing and Wuhan are shown in the following table. The relevant departments plan to transport these bills in RMB. Please design a plan to enable Wuhan and Chongqing to get the necessary instruments, and the freight is just enough. Freight Schedule (Unit:)

destination

Starting point Wuhan Chongqing

Beijing 400 800

Shanghai 300 500

20. A wholesaler wants to transport a batch of seafood from place A to place B, and both the automobile freight company and the railway freight company have started the seafood transportation business. It is known that the transportation distance is kilometers, and the speed of cars and trains is kilometers per hour and kilometers per hour respectively. The charging items and standards of the two freight companies are shown in the following table:

Transportation cost of means of transport (unit price)

Yuan/ton km

Refrigeration fee (unit price)

Yuan/ton hour

Toll (yuan), handling fee and management fee (yuan)

Automobile 2 5 200 0

Train 1.850 1600

(Note: "Yuan/ton kilometer" refers to the freight per ton of goods per kilometer; "Yuan/ton hour" refers to the hourly refrigeration fee for each ton of goods)

(1) If the wholesaler has several tons of seafood to ship, which freight company should he choose to save the freight?

(2) If the wholesaler has tons of seafood to stay far away, which freight company should he choose?

(3) When wholesalers have several tons of seafood, it doesn't matter which one they choose.

……