Application example of one-dimensional linear inequality in the first volume of the seventh grade (preferably with an answer)

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Seven-grade math application problem 70 reward points Answer: 70 | Solution time: 2010-1711:03 | Questioner: Dragon Warrior 000.

............................, urgent note (it is best to give no less than 20 points for those who meet the requirements, and be willing to give 100 points). ..............

The best answer is 1. In order to save energy, a unit collects electricity charges 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

2. The ratio of delivery staff to sales staff 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.

3. Now a commodity is reduced in price 10% for promotion. 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.

4. 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

5. 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.

6.A rides a bike from place A to place B, and B rides a bike from place B to place A, both of which move at a constant speed, so that they can start at eight o'clock in the morning at the same time. By morning 10, they were still 36 kilometers apart, and by noon 12, they were 36 kilometers apart. How can we find the distance between a and b? (Equation)

Let the distance between a and b be x.

x-(x/4)=x-72

x=288

Answer: The distance between A and B is 288.

7. The length of car A and car B is 180m. If two trains travel relatively, it takes * * *12s from the time when the front meets the rear; If driving in the same direction, it takes 60 seconds from the front of car A to the rear of car B, and the speed remains unchanged. Find the speed of a car and b car.

The sum of the speeds of the two vehicles is [180 * 2]/12 = 30m/s.

Let the speed of a be x, then the speed of b is 30-X.

180*2=60[X-(30-X)]

X= 18

That is, the speed of car A is 18m/s and the speed of car B is12m/s..

8. Two candles of the same length, the thick one can burn for 3 hours and the thin one can burn for 8/3 hours. When the power goes out, two candles are lit at the same time, and when the phone calls in, they are blown out at the same time. Thick is twice as long as thin. Find out when the power went out.

Suppose the blackout time is X.

Let the total length be 1, then the coarse firing is 1/3 and the fine firing is 3/8.

1-X/3=2[ 1-3X/8]

X=2. Four

Is the power failure 2. Four hours.

9. A factory produced 2300 machines this year, which was 25% higher in the first half of the year and 25% lower in the second half 15%. How many machines were produced in the second half of this year?

Solution: If X production units are set in the second half of the year, [2300-X] units will be produced in the first half of the year.

According to the meaning of the question:1-15% x+1+25% 2300-x = 2300.

Solution: 93 1

A: 93 1 set will be produced in the second half of the year.

10. A rides a bicycle from place A to place B, and B rides a bicycle from place B to place A, both of them are moving at a high speed. You should know that they set off at 8 am at the same time, and by 10 in the morning, they are still 36 kilometers apart, and by noon 12, they are 36 kilometers apart. What's the distance between a and b? ]

Let the distance between a and b be x.

x-(x/4)=x-72

x=288

A: The distance between A and B is 288 meters.

1 1. The fast horse walks 240 miles every day, and the slow horse walks 150 miles every day. Slow horse goes first 12 days. How many days can a fast horse catch up with a slow horse?

The slow horse left 150 days, the fast horse left for 240 days, and the slow horse left first 12 days, that is to say, the distance between the slow horse and the fast horse was150×12 =1800 Li before departure, and then the fast horse set off. This is the fast horse's catch-up speed in a day. The difference between the fast horse and the slow horse is 1800 Li, and the fast horse catches up with 90 Li a day, so 1800÷90=20 days is the number of days when the slow horse catches up with the fast horse.

12. It is known that five A-type machines are full of 8 boxes of products a day, and four B-type machines are full of 1 1 box of products a day, leaving 1. Each type A machine produces 1 product more than type B machine every day. How many products are there in each box?

Let's assume that there are x products in each box.

5 Type A machines: 8x+4

7 B model: 1 1x+ 1.

Because (8x+4)/5 = (11x+1)/7+1.

So: x= 12

So each box contains 12 products.

13. Father and son work in the same factory. It takes my father 30 minutes to walk from home to the factory, and my son only 20 minutes to walk this way. The father left five minutes earlier than his son. How many minutes can he catch up with his father?

Let the total length be "1", then the speed of the father is: 1/30, and the speed of the son is: 1/20.

Let the catch-up time be x.

Father left five minutes early: 1/30*5= 1/6.

x[ 1/20- 1/30]= 1/6

X= 10

That is, the time for my son to catch up is: 10 minutes.

14.200 parts need to be processed. First, A worked alone for five hours, and then worked with B for four hours before finishing the task. It is known that A processes 2 more parts per hour than B. How many parts do A and B process per hour?

Solution: Let B process (x-2) pieces per hour, then A processes X pieces per hour.

According to the total workload such as work efficiency and doubling time:

[(X-2)+X]*4+5X=200

[2X-2]*4+5X=200

8X-8+5X=200

13X=200+8

13X=208

X=208/ 13

X = 16...A.

16-2= 14 (pieces) ... b

A: Then A processes 16 pieces per hour, and B processes 14 pieces.

15. The total length of a bridge is 1000 meters. A train crosses the bridge. It takes 1 minute for the train to cross the bridge completely. The whole train stayed on the bridge for 40 seconds. Find the speed and length of the train.

1 min =60 seconds

If the length of the train is x meters, you can get it according to the meaning of the question.

The speed of the train is (1000+x)/60.

Therefore [(1000+x)/60] * 40 =1000-2x.

The solution is x= 125.

( 1000+x)/60 =( 1000+ 125)/60 = 1 125/60 = 18.75

So the train speed is 18.75 meters per second and the length is 125 meters.

16. Each worker in a workshop can produce 12 bolts or 18 nuts. Each bolt shall be equipped with two nuts. There are currently 28 workers. How to allocate the number of workers so that the daily output just matches?

Solution: Assuming that X individuals are designated to produce bolts, then (28-x) individuals produce nuts.

Because each bolt should have two nuts, the number of bolts is twice as much as the number of nuts.

2× 12x= 18(28-x)

X= 12, so 28-x=28- 12= 16.

That is, 12 people should be allocated to produce bolts and 16 people to produce nuts.

17. Put the sugar in several small squares, 1 square contains 1 grain, the second square contains 2 grains, the third square contains 4 grains, and the fourth square contains 8 grains ... and so on, starting from several squares, there are 448 grains in three consecutive squares?

It is known that sugar is equivalent to a geometric series An with a common ratio of 2, an = 2 (n- 1).

It is required to start from several cells and there are 448 * * * in three consecutive cells. Let the number of sugar in this cell be An, and sum the formula according to the equal proportion series.

[an( 1-2 3)]/( 1-2)= 448，an = 64 = 2 (n- 1)，N=7。

So from the seventh grid, there are 448 * * * in three consecutive grids.

18.200 parts need to be processed. First, A worked alone for five hours, and then worked with B for four hours before finishing the task. It is known that A processes 2 more parts per hour than B. How many parts do A and B process per hour?

Solution: Let B process (x-2) pieces per hour, then A processes X pieces per hour.

According to the total workload such as work efficiency and doubling time:

[(X-2)+X]*4+5X=200

[2X-2]*4+5X=200

8X-8+5X=200

13X=200+8

13X=208

X=208/ 13

X = 16...A.

16-2= 14 (pieces) ... b

A: Then A processes 16 pieces per hour, and B processes 14 pieces.

19. There are 30 tourists, of whom 10 knows neither Chinese nor English. Three people know three times as much English as Chinese. How many people know English but don't know Chinese?

If X people know Chinese, then the number of people who speak English is 3X+3.

Those who know English and Chinese must be greater than or equal to 30- 10.

3X+3+X & gt； = 30- 10 (greater than or equal to)

Those who know English must not exceed 30- 10, that is, less than or equal to.

3X+3 & lt； = 30- 10

17/4 <= X & lt= 17/3

X=5 people (X must be an integer)

Then 3X+3= 18 people.

There are 18+5-20=3 people who know both English and Chinese.

20. The store sells two sets of clothes, each set 135 yuan. According to the cost, a profit of 25%, a loss of 25%. Will the two sets make a profit or lose money?

The store sells two sets of clothes, each set 135 yuan. According to the cost, a profit of 25%, a loss of 25%. Will the two sets share profits or losses?

Let the cost of the first set be x.

X*[ 1+25%]= 135

X= 108

Profit: 135- 108=27 yuan.

The cost of setting up the second group is y.

Y[ 1-25%]= 135

Y= 180

Loss: 180- 135=45 yuan.

So, total loss, loss: 45-27= 18 yuan.

2 1. The cylindrical barrel for drinking water has an inner diameter of 25 cm and an inner wall height of 35 cm. There is a glass with an inner diameter of 6 cm and an inner wall height of 10 cm. How many glasses does it take to put a bucket of drinking water in this glass?

A cylindrical barrel for drinking water has an inner diameter of 25 cm and an inner wall height of 35 cm. There is a glass with an inner diameter of 6 cm and an inner wall height of 10 cm. How many glasses does it take to put a bucket of drinking water in this glass?

Assumption: X-ray glasses are needed.

3 * 3 * 3. 14 * 10 * X = 5 * 5 * 3. 14 * 35

X = 5*5*35/3*3* 10

X = 9.7

A: I need 10 glasses.

22. Ask two workers to make billboards. The master worked alone for four days and the apprentice worked alone for six days. Now the apprentice does 1 day first, and then two people cooperate. Upon completion, 450 yuan will be awarded * * *. If the remuneration is calculated according to the amount of work completed by everyone, how should it be distributed?

Let the total workload be X, the master's efficiency be x/4, the apprentice's efficiency be x/6, and the total efficiency be 5x/ 12. If the apprentice does x/6 in one day, then the time they * * * complete together is 5x/6 divided by 5x/ 12 to get 2 days, which means that it takes 3 days in total.

23. In the second quarter, a canteen saved 3,700 kilograms of coal, including 20% more in May and 25% more in June. How many Jin of coal was saved in the canteen in June?

Solution: Let's save X kilograms in April.

x+( 1+20%)x+( 1+20%)x+25% *( 1+20%)x = 3700

x+ 1.2x+ 1.2x+0.25 * 1.2x = 3700

3.7x=3700

x= 1000

June = April *( 1+20%)( 1+25%)

Then it is equal to:

1000 * (1+20%) * (1+25%) = 3700 (kg)

After investigation, it conforms to the meaning of the question.

A: The canteen saved 3,700 kilograms of coal in June.

24. Father and son work in the same factory. It takes the father 30 minutes to walk from home to the factory, the son only 20 minutes, and the father leaves five minutes earlier than the son. How many minutes can he catch up with his father?

Father and son work in the same factory. It takes the father 30 minutes to walk from home to the factory, the son only 20 minutes, and the father leaves five minutes earlier than the son. How many minutes can he catch up with his father?

Let the total length be "1", then the father's speed is 1/30, and the son's speed is 1/20.

Let the catch-up time be x.

Father left five minutes early: 1/30*5= 1/6.

x[ 1/20- 1/30]= 1/6

X= 10

That is, the time for my son to catch up is: 10 minutes.

25. A team is 450 meters long and moves at a speed of 90/ min. A person takes things from the beginning to the end and will be right back. He is twice as fast as the whole team. How long does it take this person to go back and forth?

90/ min is 90 meters per minute? The following is 90m/min =1.5m/s calculated at the speed of 90m/min.

The time from beginning to end is t,

1.5t+2x1.5t = 450t =100s.

The time from tail to head is t 1.

1.5t+450 = 2x1.5tt = 300 seconds.

So it takes a total of 400 seconds.

Last week, my mother bought some boxes of milk with 36 yuan in the supermarket. Today, she came to this supermarket again and found that every box of milk she bought last time was sold to 0.3 yuan. So my mother spent 36 yuan to buy this kind of milk, and found that she bought four more boxes than before. What is the original price of this milk?

If the original price is X yuan, then the current price is (X-0.3) yuan.

36 divided by X=36 divided by (X-0.3)-4.

It is troublesome to solve this problem. Usually it can't be solved upstairs.

My method: the original price is X yuan, and the current price is (X-0.3) yuan.

36/X times 0.3=4 times (X-0.3)

10.8=4X squared-1.2x.

2.7=X(X-0.3)

X= 1.8

27.a and B run on a 400-meter-long circular track. The speed of A is 360m/min, and that of B is 240m/min.

(1) The two men ran in the same direction at the same time. How many laps did they run when they first met?

(2) When two people run in the same place and direction at the same time, when they meet for the first time after a few seconds?

1, suppose: two people meet after x minutes.

(360-240)x=400

120x=400

x=400/ 120

x= 10/3

Two people ran (360+240)* 10/3/400=5 laps.

2、

It should be: "Two people run in opposite directions at the same time."

Suppose: two people meet in x minutes.

(360+240)x=400

600x=400

x=400/600

x=2/3

2/3 minutes =40 seconds

28. Two trains, A and B, are running in opposite directions. The speed of the train is 60 kilometers per hour, and the length is 150 meters. Train B has a speed of 75 kilometers per hour and a length of 120 meters. How long does it take for two cars to meet from front to back?

It can be assumed that train A is stationary, so the speed of train B relative to train A is 60+75 =135 km/h; The two cars went from the front to the rear 150+ 120=270 meters =0.27 kilometers.

Then the required time t=0.27/ 135=0.002 hours.

29. On the expressway, a car with a length of 4m and a speed of 1 10km/h is ready to overtake a truck with a speed of 12m. How many seconds does it take for the car to mourn the truck from the beginning? (accurate to 1 sec)

Suppose it takes t seconds. Suppose that the distance traveled by the car during that period is S1= 30.56t (110km/h = 30.56m/s), and the truck S2 = 27.78t (100km/h = 27.78m/s). That is, after substituting s 1=s2+20, t=7.2 seconds.

30. The car is driving on the highway at a speed of 72 kilometers per hour, heading for the silent valley. The driver honked his horn and heard an echo four seconds later. How far is the car from the valley? (Sound travels at a speed of 340 meters per second)

=(340+20)*4/2-20*4=640 (m)

Where 20 is the speed of the car 20m/s = 72km/h.

The speed of sound waves is 340 meters per second.

The vehicle speed is 72km/h = 20m/s.

The sound wave propagates 340*4= 1360m in 4 seconds.

Car 4 seconds 20*4=80m.

Suppose the car is x meters away from the valley when it hears the sound.

2x= 1360-80。

x=640

3 1. A math exam, which consists of 25 multiple-choice questions. Scoring standard stipulates: if you choose the right one, you will get 4 points; if you don't choose or choose the wrong one, you will get 1 point. Xiaolan got 85 points in the final exam. How many questions did he answer correctly?

Set the x question correctly.

4x-(25x) =85

5x= 1 10

x=22

Answer 22 questions correctly.

32. Fill a cylindrical bottle with a bottom diameter of 5cm and a height of 18cm with water. Then pour the water in the bottle into a cylindrical glass bottle with a bottom diameter of 6cm and a height of 10cm and fill it with water. Can it be completely filled? If not, how high is the water level in the bottle? If it is not full, find the distance from the water surface in the cup to the mouth of the cup.

1. Solution: Fill a cylindrical bottle with a bottom diameter of 5cm and a height of 18cm with water. The volume of water is v1=18 * π (5/2) 2 = (225/2) π =1658.

A cylindrical glass bottle with a bottom diameter of 6cm and a height of 10cm can hold water with a volume of v2 =10 * π (6/2) 2 = 90 π;

Obviously v1> V2, so it can't be fully loaded. There is 22.5π water left in the first cylindrical bottle.

Assume that the water level in the first bottle is higher than Xcm, and establish the following equation:

X*π(5/2)^2=22.5π

The solution is X=3.6.

So the water level in the first bottle is still 3.6 cm high.

33. There are 45 people in a class. People who can play chess are 3.5 times as many as those who can play Go. The number of people who can't play either game is 5, and the number who can only play Go is 5.

Solution: Suppose there are X people who can only play Go.

According to the meaning of the question, there are the following equations:

(45-5-5-X)+5=3.5(X+5)

40-X=3.5X+ 17.5

X=5

So there are five people who can only play Go.

A: Only five people can play Go.

34. A test paper has 25 questions, and each question gives 4 answers. Choose 4 points for each question correctly, and choose no wrong deduction 1 point. A classmate said he got 7 1 point, B classmate said he got 62 points, and C classmate said he got 95 points. Which student do you think is right? Please provide a justification for the answer.

Student C is right for the following reasons:

Solution: suppose a classmate gets n points and chooses the right X question, then the one who doesn't choose or chooses the wrong one is 25-X;

Then the score n = 4x-1* (25-x) = 5x-25 = 5 (x-5).

So obviously, no matter how many questions are answered correctly, the score is always a multiple of 5;

So among the three students, only C is right.

35. The prices of bananas in the fruit wholesale market are as follows

The number of bananas purchased does not exceed 20 kg but does not exceed 40 kg.

Price per kilogram 6 yuan 5 yuan 4 yuan

Zhang Qiang bought 50kg bananas twice (the second time was more than the first time), and * * * paid 264 yuan. How many Jin of bananas did Zhang Qiang buy for the first time and the second time respectively?

Suppose the number of bananas bought is x and y, respectively.

Then there is the equation.

6x+5y=264

x + y=50

X= 14 y=36。

The average is 264/50, which is greater than that of 5 yuan. So it can only be a combination of unit price 6 and 5 or 6 and 4. Two equations are solved. The result is clear at a glance.

I write so much first, I hope the landlord will adopt it, and I will update it quickly.

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