1. A store has a set of sportswear. If it is sold at a 20% discount on the list price, 20 yuan can still make a profit. It is known that the cost price of this sportswear is 100 yuan. What's the price tag of this sportswear?
Test center: the application of one-dimensional linear equation.
Special topic: sales problems.
Analysis: The price of this sportswear is X yuan.
Equivalence relation: You can still make a profit in 20 yuan by selling at a 20% discount on the list price, that is, 20% discount on the list price-cost price =20 yuan.
Solution: Solution: The price of this sportswear is X yuan.
According to the meaning of the question: 0.8x- 100=20,
Solution: x = 150.
A: The price of this sportswear is 150 yuan. Comments: The key to solving the problem is to understand the meaning of the topic, find out the appropriate equivalence relationship, list the equations according to the conditions given by the topic, and then solve it.
The road from a to b has a flat road and an uphill road. If you ride a bike on a level road 15km/h, uphill 10km/h, downhill 18km/h, it takes 29 minutes from a to b and 25 minutes from b to a, what is the distance from a to b?
Test center: the application of one-dimensional linear equation. Special topic: Travel problem. Analysis: This question first draws the equivalence relation according to the meaning of the question, that is, the distance from A to B is constant, and then lists the equation as10 (2960-x) =18 (2560-x), so as to solve the equation and answer it. Answer: Solution: Ping.
29 minutes = 2960 hours, 25 minutes = 2560,
According to the meaning of the question:10 (2960-x) =18 (2560-x),
Solution: x= 13,
Then the distance from A to B is15×13+10× (2960-13) = 6.5km,
Answer: The distance from A to B is 6.5 kilometers ... Comments: This question mainly investigates the application of linear equation of one variable. The key to solving problems is to master the general steps of solving problems through column equations, that is, ① to find the equivalent relationship according to the meaning of the questions; ② List the equations; ③ Solve the equation.
In 2009, the total water consumption for production and operation in Beijing was 580 million cubic meters, of which domestic water consumption was 60 million cubic meters more than that for production and operation. How many cubic meters are used for production, operation and life respectively?
Test center: the application of one-dimensional linear equation. Special topic: application problem. Analysis: The equivalent relationship is: household water consumption = 3 times of production and operation water consumption +0.6. Solution: Solution: If the production and operation water consumption is X billion cubic meters, the household water consumption is (5.8-x-X) billion cubic meters.
According to the question, it means 5.8-x=3x+0.6.
Solution: x= 1.3,
∴5.8-x=5.8- 1.3=4.5.
A: The production and operation water consumption is 65.438+0.3 billion cubic meters, and the domestic water consumption is 450 million cubic meters. Comments: The key to solving the problem is to find out the meaning of the problem and find the appropriate equivalent relationship. This problem can also be listed according to "the total production, operation and domestic water consumption is 580 million cubic meters".
4. Xiaohua will deposit 100 yuan earned by work-study program in the bank for one year, and take it out of 50 yuan to buy school supplies when it expires, and deposit all the remaining 50 yuan and interest due in the bank for one year. If the annual interest rate of the deposit is reduced to half of the original, the principal and interest and 63 yuan can be obtained after maturity, and the annual interest rate of the first deposit (excluding interest tax) can be calculated.
Test center: the application of one-dimensional linear equation. Special topic: application questions; Analysis: First, the annual interest rate of the deposit is unknown, and then the sum of the principal and interest plus interest for two years MINUS enough money to buy school supplies is equal to the final sum of principal and interest. Solution: If the annual interest rate of the first deposit is X, the annual interest rate of the second deposit is x2, and the sum of the principal and interest of the first deposit is (100+ 100×x) yuan.
In terms of meaning, (100+100× x-50 )× x2+50+100 x = 63,
The solution is x=0. 1 or x=-135 (truncation).
A: The annual interest rate of the first deposit is 10%.
Comments: The key to solving the problem is to understand the general idea of the problem, especially the principal and interest due for the second time is 50+ 100x, and many students will ignore 100x according to the conditions given in the problem.
In 2008 Beijing Olympic Games, China athletes won more than 65,438,000 gold medals, ranking first in the world. Among them, 2 gold medals are more than the sum of silver medals and bronze medals, and 7 silver medals are less than bronze medals. How many gold, silver and bronze medals are there?
Test center: the application of one-dimensional linear equation. Analysis: If the number of silver medals is X, the number of bronze medals is (x+7) and the number of gold medals is x+(x+7)+2, which can be solved according to the equation of *** 100.
Solution: If the number of silver medals is X, then the number of bronze medals is (x+7). The number of gold medals is x+(x+7)+2, (1).
Get x+(x+7)+x+(x+7)+2= 100(3 points).
The solution is x=2 1, (5 points)
So x+7 = 21+7 = 28; 2 1+28+2=5 1
A: The gold medal, silver medal and bronze medal are 565,438+0,265,438+0,28 respectively. (6 points) Comments: Examine the application of linear equations; Getting the equivalent relationship of each medal number is the easy point to solve this problem.
Tianjiao Supermarket and Di Chin Supermarket sell the same goods at the same price. In order to attract customers, both supermarkets implement membership card system. Tianjiao supermarket will issue Tianjiao membership card after purchasing 500 yuan goods, and the re-purchased goods will be charged at 85% of the original price; After purchasing goods from 300 yuan in Di Chin supermarket, we will issue a membership card to Di Chin, and the re-purchased goods will be charged at 90% of the original price. How can customers choose a store to get more discounts?
Test site: the application of one-dimensional linear equation; Application of one-dimensional inequality. Analysis: according to the meaning of the question, we can list the relationship between the expenses of the two supermarkets and the amount of shopping X, and then compare the two sizes to draw a conclusion. Solution: Solution: Let customers spend X yuan on shopping.
When 0≤x≤300, customers are the same when shopping in two supermarkets.
② When 300 < x ≤ 500, customers can get more discounts when shopping in Di Chin supermarkets.
When x > 500, it is assumed that customers can get more discounts when shopping in supermarkets in Di Chin. The solution of 300+0.9 (x-300) < 500+0.85 (x-500) is x < 900.
③ Therefore, when the price is 500 < x < 900, customers can get more discounts when shopping in Di Chin supermarkets. Similarly, they can get:
When x=900, customers shopping in two supermarkets is the same.
⑤ When x > 900, customers can get more discounts when shopping in Tianjiao Supermarket. Comments: This topic mainly examines the application of linear equations and the mastery of linear inequalities.
7. Xiao Wang goes to Xinhua Bookstore to buy books. The bookstore stipulates that 20 yuan can enjoy a 15% discount when buying books after applying for a discount card. After handling the discount card, Wang Mai bought some books, and the price after purchasing the books plus the card fee was less than the original price of these books 10 yuan. What is the original price of these books?
Test center: the application of one-dimensional linear equation. Special topic: application questions; Economic problems. Analysis: Credit card handling fee plus book discount amount should be equal to the original book price plus the saved 10 yuan, and the quantitative relationship can be solved by an equation. Solution: solution: the original price of the book is x yuan.
From the problem: 20+0.85x=x- 10,
Solution: x = 200.
Answer: Xiao Wang bought these books at the original price in 200 yuan. Comments: The key to solving the problem is to understand the meaning of the topic, turn the actual problem into a mathematical problem, then find out the appropriate equivalence relationship according to the conditions given by the topic, list the equations, and then solve them.
8. The railway between A and B is 240 kilometers long. In order to reduce the travel time of 20 minutes, it is necessary to speed up 10k m/h, but under the existing conditions, the speed limit for safe travel is100km/h. Can the speed-up target be achieved?
Test center: the application of one-dimensional linear equation. Special topic: Travel problem. Analysis: the walking distance has not changed before and after the speed increase, and the equation can be solved. Solution: solution 1
Solution: If the speed before the speed increase is x kilometers per hour, it will take 240x hours.
According to the meaning: (x+ 10)( 240x- 2060)=240,
Solution: x 1=-90 (excluding), x2=80,
Because 80 < 100, the speed-up target can be achieved.
Solution 2
Solution: let the growth rate be x km/h, and according to the meaning of the question, get 240x- 10- 240x= 2060, excluding the denominator.
X2- 10x-7200 = 0。
Solution: x 1=90, x2=-80.
After testing, x 1=90 and x2=-80 are the roots of the original equation.
But the speed is negative, so we take x = 90.
Because x = 90 < 100, the speed-up target can be achieved.
9. The overdraft of water source is worrying, and saving water is imminent. In view of the phenomenon that residents waste water, a city has set a water consumption standard of 8m3 per household per month, and the excess is charged at a higher price. The water consumption and water charge of a household for two consecutive months are 1.2m 3 respectively, calculated in 22 yuan; 10m3, 16.2 yuan. How much is the water consumption per cubic meter for residents in this city? What is the charge per cubic meter for the part exceeding the standard?
Test center: the application of one-dimensional linear equation. Special topic: application questions; Economic problems. Analysis: The cost of standard water plus the cost of exceeding the standard is the total cost of this month, which can be solved by equation. Solution: Solution: Let's charge X yuan per cubic meter of standard water, and Y yuan for the part exceeding the standard.
From the topic: 8x+(12-8) y = 22; 8x+( 10-8)y= 16.2，
Solution: x= 1.3, y = 2.9.
Therefore, the standard water consumption of residents in this city is charged at 1.3 yuan per cubic meter, and the excess water consumption is charged at 2.9 yuan.
10. Statistics show that among the 664 cities in China, they can be divided into three categories according to the water resources situation: temporary water shortage cities, general water shortage cities and serious water shortage cities. Among them, the number of cities with temporary water shortage is 50 times less than that with severe water shortage, and the number of cities with general water shortage is twice as much as that with severe water shortage. How many cities are looking for serious water shortage?
Test center: the application of one-dimensional linear equation. Special topic: application questions; Engineering problems. Analysis: the equivalent relationship of this question is: temporary water shortage city+general water shortage city+serious water shortage city =664. List the equations accordingly, and you can get the answer. Solution: Suppose that X cities are seriously short of water.
According to the meaning: (4x-50)+x+2x = 664.
Solution: x = 102.
A: There are cities with severe water shortage 102.
1 1. At present, there are about1280,000 primary and junior high school students in Guangzhou, of which the number of primary school students is twice that of junior high school students (data source: Guangzhou Education Statistics Manual in 2005).
(1) Find the current number of primary school students and junior high school students in Guangzhou;
(2) Suppose that every primary school student needs to pay miscellaneous fees to 500 yuan this year, and every junior high school student needs to pay miscellaneous fees 1 000 yuan, all of which are allocated by the Guangzhou Municipal Government. How much should the Guangzhou Municipal Government allocate for this purpose?
Test center: the application of one-dimensional linear equation. Special topic: engineering problems. Analysis: (1) This question can assume that the number of junior high school students in Guangzhou is x million at present, because the number of primary and junior high school students in Guangzhou is about1280,000, of which the number of primary school students is twice that of junior high school students, and the number of primary school students is 140.
(2) On the basis of (1), get the answer with "Guangzhou municipal government appropriation = number of primary school students ×500+ number of middle school students × 1000". Solution: (1) If the number of junior high school students is X, the number of primary school students is (2x+ 14.
Then x+2x+ 14= 128.
The solution is x=38.
A: There are 380,000 junior high school students and 900,000 primary school students.
(2) 500× 900,000+1000× 380,000 = 830 million yuan, that is, 830 million yuan.
A: The Guangzhou Municipal Government will allocate 830 million yuan for this purpose.
12. Xiaoming went to the stationery store to buy 2B pencils. The shopkeeper said, "If you buy more, I'll give you a 20% discount." Xiao Ming calculated. If you buy 50 pencils, it will be cheaper than the original price. What is the original price of each pencil? Test center: the application of one-dimensional linear equation. Special topic: application questions; Economic problems. Analysis: the equivalence relation is: original price × 50 × (1-80%) = 6. From this, the equations can be listed. Solution: Solution: Let the original price of each pencil be X yuan.
50x( 1-0.8)=6，
Solution: x = 0.6.
Answer: So the original price of each pencil is 0.6 yuan.
13. The comprehensive experimental activity group of Class One, Grade Three, went to two stations, A and B, respectively, to investigate the passenger flow during the "Spring Festival travel rush Peak" last year and the year before last. The picture shows Xiao Ming communicating with two other students after the investigation. According to their conversation, please calculate the passenger flow of stations A and B during the "Spring Festival travel rush fever" last year.
Test center: the application of one-dimensional linear equation. Special topic: reading type. Analysis: The increased percentage multiplied by the cardinal number is the actual number of people, from which the equation can be solved. Solution: Let's assume that the passenger flow at Station A was X and the mileage was (20-x) during the "Spring Festival travel rush Peak" the year before last.
From the meaning of the question: 0.2x+0. 1(20-x)=22.5-20,
Solution: x=5
∴ The passenger flow of Station A last year was: 1.2×5=6 (ten thousand people).
∴ Number of people: 22.5-6= 16.5 (ten thousand people).
A: During the "Spring Festival travel rush Peak" last year, the number of passengers at Station A was 60,000, and the number of passengers was 6.5438+0.65 million.
Read the following dialogue:
Xiaohong's mother: "Shop assistant, please buy me some pears."
Shop assistant: "Little Red Mom, all the pears you bought last time are sold out. We haven't had time to buy them yet. I suggest you buy some new apples this time, which are a little more expensive than pears, but have higher nutritional value. "
Xiaohong's mother: "OK, you are very trustworthy. This time I will spend 30 yuan money like last time. "
Comparing the computer receipts before and after, Ma Hong found that the price per kilogram of apples is 0.5 times that of 65438+ pears, and the weight of apples is 2.5 kilograms lighter than pears.
According to the above conversation and Xiaohong's mother's discovery, try to find out the unit price of pears and apples.
Test center: the application of one-dimensional linear equation. Special topic: reading type. Analysis: If the price per kilogram of pears is X yuan, then the price per kilogram of apples is 1.5x yuan. According to the equivalence relation that the weight of apple is 2.5kg lighter than that of pear, the equation is solved. Solution: If the price per kilogram of pears is X yuan, then the price per kilogram of apples is 1.5x yuan.
Yes: 30x=30 1.5x+2.5,
Solution: x=4,
1.5x=6。
A: The unit prices of pears and apples are 4 yuan/Jin and 6 yuan/Jin respectively.
15. In order to report the school's participation in the city's middle school students' basketball game in time, the reporter of our school's sound of spring studio learned from the captain Wei that the school's * * * team participated in the 16 game with a score of 28 points. According to the regulations, if you win a game, you will earn 2 points, and if you lose a game, you will earn 1 point. However, Tan Xiao forgot how many games were won or lost, so please refer to the above.
Test center: the application of one-dimensional linear equation. Special topic: application questions; Game problem. Analysis: After the team wins, the score plus the lost points should be equal to the total score, and then the equation can be listed to solve the application problem. Solution: Solution: Suppose the team won X games and lost (16-x) games.
From the topic: 2x+( 16-x)× 1=28.
Solution: x= 12,
A: The team won 12 games and lost 4 games.
16. Lenovo Middle School organized junior three students to participate in sports once a week in the first three weeks of this semester, and each of the 400 students in the whole grade only participated in one ball game or track and field event. Suppose that 20% of the students who participate in ball games will participate in track and field activities next time; At the same time, 30% of students who take part in track and field activities will take part in ball games next time.
(1) If the number of people who participated in ball games for the first time and the second time is equal, what should be the number of people who participated in ball games for the first time?
(2) If there are not less than 200 students taking part in ball games for the third time, how many students will take part in ball games for the first time?
Test center: the application of one-dimensional linear equation. Special topic: application problem. Analysis: (1) Let X participate in ball games for the first time, then (400-x) students participate in track and field activities for the first time. According to the students who participate in ball games every time, 20% will participate in track and field activities next time; At the same time, among the students who participate in track and field activities every time, 30% will participate in ball games next time, indicating the number of people who participate in ball games for the second time, and then solving it according to the meaning equation.
(2) On the basis of taking part in ball games for the second time, the proportion of students who take part in ball games each time will be 20% in track and field activities next time; At the same time, among the students who participate in track and field activities every time, 30% will participate in ball games next time, which means that the number of people who participate in ball games for the third time will be solved according to the inequality of topics. Solution: Solution: (1) Suppose the number of people participating in ball games for the first time is X, and the number of people participating in track and field activities for the first time is (400-x).
The classmate who participated in the ball game for the second time was X? ( 1-20%)+(400-x)？ Thirty percent
From the meaning of the question: x=x? ( 1-20%)+(400-x)？ Thirty percent
Solution: x=240
(2)∵ Who is the student who participated in the ball game for the second time? ( 1-20%)+(400-x)？ 30%= x2+ 120，
∴ Who participated in the ball game for the third time: (x2+ 120)? ( 1-20%)+[400-(x2+ 120)]？ 30%= x4+ 180，
∴ x≥80 from x4+ 180≥200,
When x=80, the number of people participating in ball games and track and field activities for the second and third time is an integer.
Answer: (1) There should be 240 students participating in ball games for the first time; (2) There are at least 80 students participating in ball games for the first time.
17. Students from the school's comprehensive practice activity group took a bus to Tianchishan Agricultural College for social investigation. There are two kinds of vehicles available for rent: the first one can take 8 people and the second one can take 4 people. If only a few cars of the first car are rented, four seats will be vacant; If you only rent the second car, it will be three more than the first car, which is just full.
(1) How many students participated in this social survey?
(2) It is known that the rent of the first car is 300 yuan/day, and the rent of the second car is 200 yuan/day. If every student has a seat and the rent is the least, how can I rent a car?
Test center: the application of one-dimensional linear equation. Special topic: application problem. Analysis: (1) Pay attention to the key words: "If you only rent a few first-class cars, four seats will be available; If you only rent the second car, it will be three more than the first car, which is just full. According to the difference between the two sitting methods, the equations are listed and solved.
(2) We should consider different car rental schemes, and then compare them one by one to find the best one. Solution: Solution: (1) Suppose there are ***x students participating in this social survey, then 4( x+48+3)=x,
Solution: x=28
Twenty-eight students took part in the social survey.
(2) Its car rental scheme is as follows
① There are 4 vehicles of the first category and 0 vehicles of the second category;
② 3 vehicles in the first category, and 1 vehicle in the second category;
③ 2 vehicles of the first category and 3 vehicles of the second category;
④ Class I 1 vehicle, and Class II, 5 vehicles;
⑤ The first car has 0 cars and the second car has 7 cars.
Through comparison, it can be seen that the first type rents 3 vehicles, and the second type rents 1 vehicle, with the lowest cost.
Its cost is 1 100 yuan.
18. The price of bread bought by the shopkeeper from the bakery is 65438+ 0.0 yuan per loaf. If the bread can't be sold, 0.2 yuan will return to the factory that day. In a month (30 days), the small shop sells 80 loaves of bread every day for 20 days, and sells 50 loaves of bread every day for the rest 10 days, and the small shop owner makes a net profit in 600 yuan. if
Test center: the application of one-dimensional linear equation. Special topic: economic issues. Analysis: according to the meaning of the question, the number of buns he entered should be between 50 and 80; The equivalent relationship is: (20× purchase quantity+10×50)× profit per transaction-(purchase quantity -50)× 10× compensation per transaction = 600; You can get the answer by listing the solutions of the equation. Solution: solution: let this number be X.
Judging from the meaning of the question: (20x+500 )× (1-0.6)-(x-50 )×10× (0.6-0.2) = 600,
Solution: x = 50.
So this number is 50.
19. Xiaogang found that the sum of the unit prices of his favorite walkman and schoolbag was 452 yuan, and the unit price of the walkman was four times less than that of the schoolbag. 8 yuan, ask for the unit price of Xiaogang's favorite walkman and schoolbag.
Test center: the application of one-dimensional linear equation. Special topic: application questions; Analysis: The key words of this question are "The sum of the unit price of the walkman and the schoolbag is 452 yuan, and the unit price of the walkman is 4 times less than that of the schoolbag by 8 yuan", that is, the unit price of the walkman = the unit price of the schoolbag × 4-8. Solve the equation according to this equivalence relation. Solution: If the unit price of the walkman is X yuan, the unit price of the schoolbag is (452-x) yuan.
Column equation: x=4(452-x)-8,
Solution: x = 360.
When x=360, 452-x = 92.
20.( 1) The purchase price of a commodity is 400 yuan, and the price is 600 yuan. When it is sold at a discount, the profit rate is 5%. Then, at what discount is this commodity sold?
(2) A chemical fertilizer factory produced 500 tons of chemical fertilizer in April last year. Due to poor management, the output decreased by 65,438+00% in May. Since June, the output has increased month by month, reaching 648 tons in July. What is the average growth rate of output in June and July?
Test site: the application of one-dimensional linear equation; Application of quadratic equation in one variable. Special topic: the problem of growth rate; Economic problems. Analysis: (1) Assuming that the commodity is sold at a discount of X, the equation can be obtained according to the relationship between purchase price, price tag and profit;
(2) Let the average growth percentage of the output of this factory in June and July be X, and solve the listed equation according to the increase or decrease of the output. Solution: Solution: (1) Let this product be sold at X discount.
600x=400( 1+5%)，
You can get X = 0.7.
(2) Let the average growth rate of the output of this factory in June and July be X 。
If the output in May is 500( 1- 10%)=450, then it is 450( 1+x) in June and 450 (1+x) = 648 in July.
( 1+x)2= 648450= 1.44，
1+x= 1.2，
x=20%。
2 1. A stationery is sold in a shopping mall, and each piece can make a profit in 2 yuan. In order to support poor mountainous areas, it is now sold to mountain schools at a discount of 30% of the original selling price, and each piece is profitable in 0.2 yuan (profit = selling price-purchasing price). What is the purchase price of each piece of this stationery?
Test center: the application of one-dimensional linear equation. Special topic: sales problems. Analysis: The equivalence relation is: 30% off the selling price-purchase price = profit 0.2, subdivided into: (purchase price+2) × 70% off-purchase price = profit 0.2. According to this equivalence relation, the equation can be solved. Solution: Let the purchase price of each stationery be X yuan.
According to the question: 70%? (x+2)-x=0.2
Solution: x=4
A: The purchase price of each piece of this stationery is 4 yuan.
In recent years, the level of educational technology and equipment in Yibin has improved rapidly, especially the modern equipment with computer as the core has made a breakthrough. The number of computers per 100 people in primary and secondary schools is in the leading position in the province, and the total number of primary and secondary schools in the city has increased from 1996 in 2000 to 1040. If the number of computers added each year from 1997 to 2000 is the same as that of the previous year and continues to increase at this rate, what will be the total number of computers equipped in primary and secondary schools in Yibin by 2003?
Test center: the application of one-dimensional linear equation. Special topic: the problem of growth rate. Analysis: First, according to the number of computers in 1996+the number of computers increased in four years * * = the number of computers in 2000, the annual growth is obtained, and then the total number of computers equipped in primary and secondary schools in Yibin in 2003 is 1 1600.
Then:1040+(2000-1996) x =11600,
The solution is x=2640,
∴ In 2003, the total number of computers in primary and secondary schools in Yibin was 1 1600+(2003-2000) × 2640 = 19520 (units).
A: In 2003, the total number of computers in primary and secondary schools in Yibin was 19520.
23. An enterprise produces a product, the cost of each product is 400 yuan, and the sales price is 5 10 yuan. In order to further expand the market, the enterprise decided to reduce the sales price and cost at the same time. Through market research, it is predicted that the sales price of this product will decrease by 4% and the sales will increase by 65,438+00% in the next quarter, thus realizing the sales profit (sales profit = sales price).
Test center: the application of one-dimensional linear equation. Special topic: application questions; Analysis of economic problems: There are many words in this topic, so it is necessary to examine the topic clearly and find the equivalence relationship: the sales profit (sales profit = sales price-cost price) remains unchanged, assuming that the cost price of each product is reduced by X yuan, then the sales price of each product is 5 10( 1-4%) yuan, and it is sold (65438+). The new sales profit is [510 (1-4%)-(400-x)] × (1+10%) m yuan, while the original sales profit is (510-400). Just do an equation.
[5 10( 1-4%)-(400-x)]×m( 1+ 10%)= m(5 10-400)，
Solve this equation X = 10.4.
A: The cost price of this product should be reduced by 10.4 yuan.
24. In order to encourage China Olympic Team to achieve good results in the 2008 Olympic Games, Shuguang Sports Equipment Factory presented a batch of soccer balls to China Olympic Team. If each football team gets one, six balls are missing. If every two people get one, there are six balls left. How many footballs are there?
A player was very happy after receiving the football, so he carefully studied the black and white blocks on the football (pictured). The results show that the black block is pentagonal, the white block is hexagonal, the black and white are on the sphere, and the black block is *** 12. How many white squares are there?
Test center: the application of one-dimensional linear equation. Special topic: application problem. Analysis: (1) According to the meaning of the question, we can know that there are two constants in this question, the total number of football players and the total number of football players. Both of these constants need the number of football players, so the first question can use the total number of football players as the equation of the equation relationship;
(2) The second problem can be solved by the relation that the number ratio of black blocks to white blocks is 3: 5. Solution: Solution: (1) There are x soccer balls.
Then there is: x+6=2(x-6),
∴x= 18；
Therefore, there are 18 soccer balls;
(2) Let the white block have y blocks,
Then 3y=5× 12,
∴y=20，
So there are 20 pieces in the white square.
25.3 12 Arbor Day, 170 Seventh-grade students participated in voluntary tree planting activities. If boys can dig three tree pits a day and girls can plant seven trees a day, then only one tree will be planted in each tree pit. How many boys and girls are there in this grade?
Test center: the application of one-dimensional linear equation. Special topic: engineering problems. Analysis: If there are X boys in this grade, there will be (170-x) girls, so boys can dig 3 tree pits on average and girls can plant 7 trees on average (170-x). Then according to each tree pit, list the equations and solve them.
According to the meaning of the question: 3x=7( 170-x),
Solution: x= 1 19,
170-x=5 1。
Answer: Boys in this grade are 1 19, so girls are 5 1.
26. In order to save energy, a unit charges electricity according to the following regulations every month: the electricity consumption does not exceed 140 kwh, and it is charged at 0.43 yuan per kwh; If it exceeds 140 degrees, the excess will be charged at 0.57 yuan per degree. If the average electricity bill charged by Mexican consumers in April is 0.5 yuan per kWh, how much should consumers pay in April?
Let the total power consumption be x degrees: [(x-140) * 0.57+140 * 0.43]/x = 0.5.
0.57 times -79.8+60.2 = 0.5 times
0.07x= 19.6
x=280
Step by step: 140*0.43=60.2
(280- 140)*0.57=79.8
79.8+60.2= 140
27. The ratio of delivery personnel to sales personnel in the home appliance department of a shopping mall is 1: 8. Due to the obvious increase in the purchase of home appliances this summer, the manager of the home appliance department transferred 22 people from the sales staff to deliver the goods. Results The ratio of delivery staff to sales staff was 2: 5. How many delivery staff and sales staff are there in the home appliance department of this shopping mall?
Suppose there are x delivery people and 8X sales people.
(X+22)/(8X-22)=2/5
5*(X+22)=2*(8X-22)
5X+ 1 10 = 16X-44
1 1X= 154
X= 14
8X=8* 14= 1 12
The home appliance department of this shopping mall used to have 14 delivery staff and 1 12 sales staff.
28. We are now promoting a product with a price reduction of 65,438+00%. In order to keep the sales amount unchanged, how many percent will the sales volume increase over the original price?
Assumption: increase by x%
90%*( 1+x%)= 1
Solution: x = 1/9
Therefore, the sales volume increased by11.11%compared with the original price.
29. The sum of the original unit prices of commodities A and B is 100 yuan. Due to market changes, a commodity decreased by 65,438+00%. B After the price adjustment of commodities rose by 5%, the sum of the unit prices of the two commodities rose by 2%. What are the original unit prices of A and B respectively?
If the original unit price of commodity A is X yuan, then B is100-X.
( 1- 10%)X+( 1+5%)( 100-X)= 100( 1+2%)
The result x = one in X=20 yuan.
100-20=80 B
30. The number of people in Workshop A is 30 less than 4/5 of Workshop B. If 10 people are transferred from Workshop B to Workshop A, then the number of people in Workshop A is 3/4 of Workshop B. Find the original number of people in each workshop.
There are x people in workshop B. According to the equality of the total number, the equation is listed as follows:
X+4/5X-30 = X- 10+3/4(X- 10)
X=250
So the number of people in Workshop A is 250*4/5-30= 170.
Description:
The left side of the equation is adjusted first, and the right side of the equation is adjusted later.
Summary report of teaching assistant's work 1
I have felt my responsibility since I became a teaching assistant in the Faculty of Scie