-Proportional issues and calendar issues.

1, Party A, Party B and Party C have 167 tons. A is 5 tons less than B, and C is 3 tons more than A. How many tons are A, B and C respectively?

2. The vegetable field is 975 hectares, and vegetables, tomatoes and celery are planted. The area ratio of vegetables to tomatoes is 3︰2, and the area ratio of tomatoes to celery is 5︰7. What are the areas of these three vegetables?

3. Villages A, B and C raised 6.5438+0.4 million yuan to run schools. Through negotiation, the proportion of capital contribution of villages A, B and C is 5: 2: 3. Ask them how much ten thousand yuan each should invest.

4. During the construction, the constructors used the concrete of No.1 Middle School, which was made of water, cement, yellow sand and gravel. The weight ratio of these four raw materials is 0.7: 1: 2: 4.7. How many kilograms of water, cement, yellow sand and gravel do you need to mix this concrete?

Xiaoming went out to travel for four days. It is known that the sum of four days is 65. What is four days?

6. Xiaohua randomly finds a number on the calendar, and finds that the sum of it and the five numbers of up, down, left and right is 85, and asks Xiaohua to find the number.

There are three days in the same column on the calendar, and the sum of the dates is 75. What was the first date?

Solve the problem with formula (2)

-distribution problem.

1. team a 15, team b 28. Now 10 cars are transferred to two teams, which makes the number of cars in team A half that of team B. How many cars should be allocated to each team?

There are fewer girls than boys in a class. If the number of girls increases by 3 and the number of boys decreases by 3, then the number of girls equals the number of boys. How many boys and girls are there?

3. There are 85 workers in a workshop, each of whom can process 16 large gears or 10 small gears on average every day. Knowing that two big gears and three small gears are matched, how should we arrange the labor force to make the products just complete?

If a classmate does five math problems every hour, he can finish them at the scheduled time. When he finished the 10 problem, the efficiency of solving the problem increased by 60%, so he not only finished it three hours in advance, but also did six more problems. How many questions does he plan to do? How many hours will it take to finish?

Xiaoli spent 18 yuan in the fruit shop and bought 6 Jin of apples and oranges. It is known that apples are 3.2 yuan per kilogram and oranges are 2.6 yuan per kilogram. How many kilograms of apples and oranges did Xiao Li buy?

6. Warehouse A has 200 tons of coal, and Warehouse B has 80 tons of coal. If warehouse A transports 15 tons per day and warehouse B transports 25 tons per day, how many days does it take for the two warehouses to store coal on average?

7. There are 50 tons of water in two pools, 5 tons in pool A and 8 tons in pool B.. At this time, the water in Pool A is 3 tons less than that in Pool B, so how many tons are there in Pool A and Pool B?

8. A team of 55 people, each digging an average of 2.5 cubic meters of soil or transporting 3 cubic meters of soil every day. In order to arrange the labor force reasonably and transport the excavated soil in time, how should the number of people digging and transporting soil be distributed?

Solve the problem with formula (3)

-profit and loss problem workload and discount.

1. Apply a few kilograms of chemical fertilizer to a wheat field, 6 kilograms per mu, lacking 17 kilograms; The yield per mu is 5 kg, and the yield is 3 kg more. How many acres is this wheat field?

2. The graduates are sitting in the auditorium. 1 There are three people sitting on the bench, but 25 people can't sit down. 1 There are four people sitting on the bench, and just four benches are empty. How many graduates are there? How many benches are there?

3. Pack a batch of goods into a batch of boxes. If each box contains 10, there are 6 pieces left; If each box contains 13 pieces, then a box only contains 1 piece. How many goods and boxes are there respectively?

4. There was a ***20-question math contest, which stipulated that 5 points were deducted for doing one question correctly, and 2 points were deducted for each wrong question or not, and Xiao Jing got 86 points. How many questions did Xiao Jing answer correctly?

5. Road repair, it takes 20 days for Team A to complete it alone, and it takes 12 days for Team B to complete it alone. Now, after four days of independent repair by Team A, how many days will it take for Team A and Team B to complete the joint repair?

6. Some people read a book. On the first day, they read 20 pages; on the second day, they read 14 pages of the whole book; on the third day, they read 13 pages of the whole book; on the fourth day, they just read 25 pages of the whole book. How many pages are there in this book?

7. For a certain coat, the initial installation cost will be increased by 50%, and then it will be sold at a 20% discount, which will generate profits in 80 yuan. How much is this coat?

8. Some clothes are on sale in different seasons. If each piece of clothing is 50% off on the basis of the marked price, it will lose 60 yuan; And if it is sold at a 20% discount, it will earn 120 yuan. What is the list price and cost of this dress?

9. With the change of seasons, a commodity will be sold at a discount. If you sell at a 15% discount on the pricing, you will lose 25 yuan; if you sell at a 10% discount on the pricing, you will earn 20 yuan. What is the price of this commodity?

Solve the problem with formula (4)

-Travel issues.

1. The distance between the two stations is 168km. The local train leaves from Station A at a speed of 36 kilometers per hour, and the express train leaves from bilibili at a speed of 48 kilometers per hour. ..

(1) Two trains leave at the same time, in opposite directions. How many hours did they meet?

(2) The local train starts first 1 hour, and drives in the opposite direction. How many hours does it take for the express train to meet the local train?

Party A and Party B leave from the same place and go to a certain place. A Walk four kilometers an hour. After A left 16 km, B rode his bike to catch up with A at 12 km/h. How many hours will B catch up with A after departure?

3.a and B practice the 50-meter short distance race. A runs 7 meters per second and B runs 6.5 meters per second.

(1) After a few seconds, A leads B 2 meters?

(2) If A lets B run 4 meters first, how many seconds can it catch up with B?

5. The distance between Xiao Ming and Xiao Mei's home is1.8km. One day, Xiao Ming and Xiao Mei set out from their respective homes and headed for each other's home at the same time. The famous dog and Xiaoming set out together. The puppy first ran to meet Xiaomei, then ran back to Xiaoming, and then ran to Xiaomei … between Xiaoming and Xiaomei. Known nicknames are 50m/min, Xiaomei 40m/min and famous dogs 150m/min. How many meters did the puppy run when Xiaoming met Xiaomei?

6.a and B practice running on the 400-meter circular track. A runs 5.5 meters per second and B runs 4.5 meters per second.

(1) B runs first 10 meter, and then A and B start in the same place and direction. How long will it take them to meet for the first time?

(2) B runs 10 meter first, and then A and B start from the same place back to back. How long will it take them to meet for the first time?

(3) How long did Party A and Party B meet for the first time?

(4) How long does it take for A to run 10 meter first, and then B to start from A in the same place and direction?

7. A ship is sailing between two docks. The current speed is 3 kilometers per hour. It takes 2 hours to sail downstream and 3 hours to sail upstream. How to find the distance between two docks?

8. Two people, A and B, are running on a 400-meter-long circular track. If they run in the same direction, they will meet every minute. If they run in the opposite direction, they meet every 40 seconds. It is known that A runs faster than B. What are the speeds of A and B respectively?

9. Two people, A and B, rode bicycles in opposite directions from two places 65 kilometers apart. The speed of A is 17.5km, and the speed of B is 15km. A few hours later, the distance between them was 32.5 kilometers.

10, the car is driving on the expressway at a speed of 72 kilometers per hour. When driving to the silent valley, the driver honked his horn and heard an echo four seconds later. How far is the valley in the car? (The speed of sound is 340 meters per second)

Solve the problem with formula (5)

-Other questions.

1, brain input an article of 1 800 words, it takes 30 minutes for Xiao Ming and 45 minutes for Xiao Hong. Now it is 1 1: 10. If Xiaoming and Xiaohong cooperate, can they finish recording before 1 1: 30? Please explain the reason.

2. The school organizes teachers and students to watch movies. There are 950 students and 27 teachers. The theater ticket office said:

Please design a ticket purchase plan that you think is the most economical and work out how much it costs to buy a ticket.

A shop deals in a commodity. Because the purchase price is reduced by 5% and the selling price remains unchanged, the profit rate is increased from m% to (m+6)%. What is the value of m?

4. A math contest was held in the first day of a school, and 80 people signed up for it. The overall average score of the contest is 63, the average score of passing schools is 72, and the average score of failing students is 48. What is the passing rate of this contest?

5. There is a three-digit number, and its unit number is 1 more than hundred digits, and the ten-digit number is 1 less than half of the one-digit tree word. If the single digit is regarded as hundreds, the hundred digits as tens and the tens as single digits, then the sum of the new number and the original number is 16 165438.

6. One of the six figures is 2. If the number 2 in his single digits is moved to the first place, the order of other digits remains the same, and the new number is the original number. Can you find the original six figures?

7. Dahong and Xiaohong received lucky money of *** 1000 yuan in the New Year. Dahong deposits his lucky money in the bank according to one-year education savings, with an annual interest rate of 1.98%, which is exempt from interest tax; Xiaohong bought his lucky money as a bond with a monthly interest rate of 2. 1.5 ‰, but he had to pay 20% interest tax. After a year, the income of the two people is exactly the same. How much is their lucky money?

8. Pour the water into a rectangular iron box with the length, width and height of 16cm, 10cm and 5cm respectively, and the bottom of the box is 20cm×20cm (filled with water). When the iron box is filled with water, how much does the height of water drop in the rectangular container?

9. The purchase price of a commodity in 800 yuan is 1200 when it is sold. Later, due to the backlog of this commodity, the store was prepared to sell it at a discount, but how much discount should it be to maintain a profit margin of 5%?

10, there is a narrow crossing that allows one-way traffic. Usually, you can pass 9 people every minute. One day, Mr. Wang came to the crossroads. At this time, there are 36 people waiting to pass in front of him (assuming first come, first served, ignoring Mr. Wang's crossing time). It takes seven minutes to get to school after crossing the intersection.

(1) If you make a detour at this time, it will take 15 minutes to get to school. In order to save time, should Mr. Wang choose a detour or a crowded intersection to go to school?

(2) If, with the maintenance of Mr. Wang and others, the order returns to normal in a few minutes (during the maintenance of order, if three people pass through the crossing every minute), Mr. Wang asks how long it will take to maintain order through the crossing six minutes earlier than in crowded situations.

1 1 Try to find out, discuss and answer the questions according to the following situations:

A class organized a spring outing to the scenic spot. Most students go by bus, with an average speed of 24 kilometers per hour. Four students in charge of logistics left the school bus in half an hour, with a speed of 60 kilometers per hour. Two groups of people reached the foot of the mountain at the same time. When they arrived, they found it expensive to go up the mountain by cable car, and they couldn't browse the scenery along the way. So everyone agreed that the big troops would go up the mountain on foot, and the fourth logistics team would be changed to an advance team, taking a cable car up the mountain and holding activities at the top of the mountain.

Fill in the blanks. (3 points for each small question, * * * 24 points)

1. It is known that 4x2n-5+5=0 is a linear equation about x, then n = _ _ _ _ _ _

2. If x=- 1 is the solution of equation 2x-3a=7, then a = _ _ _ _ _

3. When x=______, the sum of algebraic expression x- 1 is opposite to each other.

4. It is known that the sum of x and 3 times of x is 6 less than 2 times of x, and the equation is _ _ _ _ _.

5. In the equation 4x+3y= 1, if y is expressed by the algebraic expression of x, then Y = _ _ _ _ _ _

6. When the purchase price of a commodity in 300 yuan is 60% off the list price, the profit rate is 5%, and the list price of the commodity is _ _ _ _ _ _ _.

7. Given that the sum of three consecutive even numbers is 60, these three numbers are _ _ _ _ _ _.

8. For a job, it takes 6 days for Party A to do it alone, 12 days for Party B to do it alone, and _ _ _ _ _ _ _ days for both parties to do it together.

Second, multiple choice questions. (3 points for each small question, * * * 30 points)

9. Equations 2m+x= 1 and 3x- 1=2x+ 1 have the same solution, then the value of m is ().

A.0 B. 1 C.-2 D

10. The solution of equation 3x =18 is ().

A. One solution is 6 B, and there are two solutions, both of which are 6.

C. No solution D. There are countless solutions

1 1. If the equation 2ax-3=5x+b has no solution, then a and b should satisfy ().

A.a，b≠3 B.a=，b=-3

C.a，b=-3 D.a=，b ≦- 3

12. The equation after converting the denominator of the equation into an integer is ().

13.800 meters on the runway, two people are practicing long-distance running. A runs 300 meters per minute, and B runs 260 meters per minute. They set out in the same place, at the same time and in the same direction, and met for the first time after t minutes, and t equals ().

A. 10 points B. 15 points C.20 points D.30 points.

14. A shopping mall found that the sales in the first quarter of this year increased by 10% in February and decreased by 10% in March, so the sales in March were higher than 1 month ().

A. increase10% B. decrease10% C. neither increase nor decrease D. decrease 1%.

15. in the trapezoid area formula S= (a+b)h, it is known that H = 6cm, A = 3cm and S = 24cm2, then B = () cm.

A. 1

16. It is known that there are 28 people in group A and 20 people in group B. Among the following deployment methods, the one that can make one group less than half of the other group is ().

A. transfer 12 people from group a to group b, and transfer 4 people from group b to group a.

C. transfer 12 people from group b to group a.

D transfer 12 people from group a to group b, or transfer 4 people from group b to group a.

17. The rules of football match are: win a game with 3 points, draw a game with 1 point, lose a game with 0 points, a team played 14 games and lost 5 games, and * * * got 19 points, so the team won () games.

a3 b . 4 c . 5d . 6

18. As shown in the figure, how many weights can be removed from the left plate in Figure A to keep the balance? ( )

A.3 B.4 C.5 D.6

Answer:

1. 1.32.-3 (inching: substituting x=- 1 into the equation 2x-3a=7, get -2-3a=7, get a =-3) 3. (nudge: solve the equation x- 1=- and get x =) the solution is x=525 yuan) 7.18,20,228.4 [pointing: assuming it takes x days to complete, then x(+)= 1 and the solution is x = 4. ∴x=-6, so we should choose B to expand or shrink the numerator and denominator of the fraction by the same factor at the same time by using the properties of the fraction, and the decimal equation becomes an integer equation) 13. C (nudge: When A and B meet again, A runs 800 meters more than B, the equation is 260t+800=300t, and the solution is t = 20) 14.d 15.b (nudge: from the formula S= (a+b)h,

One-dimensional equation exercise (if you can print, print it, if you can't, do the answer in your notebook)

Class name, seat number score

Fill in the blanks

1, fill in the blanks with appropriate numbers or expressions, and explain which property the equation is based on and how it is deformed:

(1) If 2x = 5-3x, then 2x+_ _ _ _ _ _ _ = 5 is based on the equation _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

(2) If -5x = 5y, then x = _ _ _ _ _ _, which is based on the properties of the equation, and both sides of the equation are _ _ _ _ _ _ _ _ _ _ _ _.

2, when, about the equation is a linear equation.

3. The equation about x: (p+ 1)x=p- 1 has a solution, so the value range of p is _ _ _ _ _.

4. Given that 2 is the solution of the equation about, the value of is _ _ _ _ _ _ _ _.

5. The solution of the equation ∣ 2x-6 ∣ = 0 is _ _ _ _ _ _ _.

6. If the purchase price of a commodity is 1 10 yuan and the selling price is 132 yuan, the profit rate of the commodity is _ _ _ _ _ _ _ _.

7. If the sum of the algebraic expression and x- 1 is 0, then the value of x is equal to _ _ _ _ _ _ _.

8. When x=5, the value of the algebraic expression is _ _ _ _ _ _ _ _; Given that the algebraic expression has a value of 5, then x = _ _ _ _ _.

9. It is known that the ship's countercurrent speed is m km/h and the current speed is 2 km/h, so the speed of the ship in still water is _ _ _ _ _ _ _ _.

10, 5 kg of 85% pesticide is prepared into 2% pesticide, and x kg of water is needed.

Column equation: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

1 1. The first group needs 5 hours to harvest a piece of wheat, and the second group needs 7 hours. The first group harvested 1 hour, and then the second group harvested together. These two groups * * * are the same as those that have used the X-hour series equation after harvesting: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

12, the side length of a square is x meters. If one side of a square is reduced by1.2m and the other side by1.5m, the area of the rectangle is reduced by14.4m.. The equation is: _ _ _ _ _ _ _ _ _ _ _.

13. A workshop has received the task of processing X parts, and plans to process 120 parts every day, which can be completed on schedule. However, 40 pieces are actually processed every day, and the result is that the equation is completed six days in advance: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Second, multiple choice questions

1. The following equation is a linear equation, which is ().

(A)(B)(C)(x-3)(x-2)= 0(D)7x+(-3)2 = 3x-2

2. The basis of transforming the equation into 2(x+ 1)-24=3(x-2) is (a) the law of multiplication (b) the basic properties of fraction (c) the properties of equation (d) the law of shift.

3. The circumference of a rectangle is 16cm, and the difference between its length and width is 1cm, so its length and width are () respectively.

A, 3cm, 5cm b, 3.5cm, 4.5cm c, 4cm, 6cm d,10cm, 6cm.

There are only 25 multiple-choice questions in a test paper. Answer one question correctly and get 4 points; Wrong 1 question, get 1 point; If a student does all the questions, he will get 70 points; If he does () correctly.

a、 17 B、 18 C、 19 D、20

Third, the calculation problem

1.0.5x-0.7=6.5- 1.3x 2、 1-2(2x+3)= -3(2x+ 1)

3、2(x-2)-3(4x- 1)= 9( 1-x)

Fourth, the application questions

1. What is the current speed of a ship sailing between docks 80 kilometers apart, 4 hours downstream and 5 hours upstream?

2. A ship travels between Pier A and Pier B, sailing downstream for 3 hours and upstream for 3.5 hours. If the speed of the ship in still water is 26 kilometers per hour, (1) find the current speed; (2) Find the distance between two docks.

There are 70 ostriches and goats in the pasture. Given that the sum of the legs of an ostrich and a goat is 196, how many ostriches and goats are there respectively?

4. A transport team transports a batch of goods, each car is loaded with 8 tons, and the last car is only loaded with 6 tons. If each car is loaded with 7.5 tons, there are 3 tons that can't be loaded. How many cars are there in the convoy? How many tons are there in this shipment?

5. For a two-digit number, the number in the tenth place is twice that in the tenth place. If the number exchanged between the number in the second place and the number in the tenth place is 36 less than the original number, find the original two digits.

6. Eight rounds of middle school football league in a certain district (that is, each team needs to play eight games), winning one game will get 3 points, and drawing one game will get 1 point.

Negative games get 0 points. In this football league, Xiao Ping 'an drew twice the lost game and got 17.

How many games did the team win?

7. There are 42 workers in the packaging factory, and each worker can produce 120 round iron sheets or 80 rectangular iron sheets per hour on average. Two round iron sheets can be combined into a sealed barrel. How to arrange workers to produce round or rectangular iron sheets?

8. A store will increase the cost price of color TV by 50%, and then write "big reward, 20% discount" in the advertisement. As a result, every color TV set made a profit in 270 yuan. What is the cost price of each color TV?

9. The distance between the two stations is 275 kilometers. The local train travels from Station A to bilibili at a speed of 50 kilometers per hour. 1 hour later, the express train leaves bilibili for Station A at a speed of 75km per hour. How many hours after the local train leaves, will you meet the express train?

10. Distribute some books to students. If each person sends out four books, there are still 25 left. If each person distributes five books, there are five books left. How many students are there?

1 1. The train body is 200 meters long. When it passes through the tunnel, the speed is 60 kilometers per hour. It takes 2 minutes to get out of the tunnel from the front to the rear. Find the length of the tunnel.

12, GSM users pay the monthly fee in 50 yuan first, and then pay the phone bill every call 1 minute, while Shenzhou Bank does not pay the monthly fee, but pays the phone bill every call 1 minute, and 0.6 yuan, (1) how many minutes a month, are the two mobile communication charges the same?

(2) How to choose which mobile communication is more economical?

13. A milk processing factory has 9 tons of fresh milk. If you sell fresh milk directly in the market, you can make a profit of 500 yuan per ton; Made into yogurt for sale, the profit per ton can reach 1200 yuan; Made into milk tablets for sale, the profit per ton can reach 2000 yuan.

The production capacity of this factory is: if it is made into yogurt, it can process 3 tons a day; The processed milk tablets can be processed 1 ton every day. Due to the limitation of personnel, the two treatment methods cannot be carried out at the same time. Due to the limitation of temperature, this batch of milk must be sold or processed within 4 days. Therefore, the factory has designed two feasible schemes:

Option 1: make as many pieces of milk as possible and sell the rest directly;

Option 2: Make part of it into milk slices and the rest into yogurt, which can be sold in exactly 4 days.

Which scheme do you think is the most profitable? Why?

14. A seventh-grade student accidentally knocked over the ink bottle while doing his homework, so that he only saw the following words in an homework question: "The distance between A and B is 40 kilometers, the speed of motorcycle is 45 kilometers per hour, and the speed of truck is 35 kilometers per hour." (The black part indicates that some words are covered by ink), please complete this homework problem and solve the equation in parallel.

15. There is a narrow intersection, which can only pass in one direction. Usually, nine people pass through every minute. One day, when Mr. Wang arrived at the intersection, he found that only three people could cross the intersection every minute because of the crowd. At this time, there are still 36 people waiting to pass in front of him (assuming that Mr. Wang's crossing time is ignored). It takes 7 minutes to get to school after crossing the intersection.

(1) If you make a detour at this time, it will take 15 minutes to get to school. From an economic point of view, should Mr. Wang choose to go to school by detour or through a crowded intersection?

(2) If, under the maintenance of Mr. Wang and others, the order returns to normal in a few minutes (during the period of maintaining order, there are still three people crossing the crossing every minute), as a result, Mr. Wang crosses the crossing six minutes earlier than in the crowded situation and asks how long it will take to maintain order.