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
1) 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.
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.
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 is 5%, the sum of the unit prices of the two commodities will increase 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
The number of people in workshop A is 30 less than 4/5 of that in 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 that in 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.
A rides a bike from place A to place B, and B rides a bike from place B to place A, both of which advance at a constant speed. You should know that they leave at 8: 00 a.m. at the same time, at 10 in the morning, they are still 36 kilometers apart, and at noon 12, they are 36 kilometers apart. How to 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.
1.A and B are both 180m in length. If two trains are driving relatively, it takes * * *12s from the moment when the front and rear meet; 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..
Two candles of the same length, the thick one can burn for 3 hours and the thin one can burn for 8/3 hours. Light two candles at the same time when there is a power failure, and blow them out at the same time when there is a call. Thick is twice as long as thin, and you can find the time of power failure.
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.
Selected problems in the application of linear equations with one variable
Equations in the calendar
1, the sum of three consecutive odd numbers is 387. Find these three odd numbers.
2. Draw a box (3╳3) containing 9 numbers on the calendar at will, and then add the 9 numbers in the box, and the result is 90. Try to find the number among these nine numbers.
3. For three digits, the sum of the numbers on the three digits is 17, the number on the hundredth digit is 7 larger than the number on the tenth digit, and the number on the single digit is 3 times that on the tenth digit. Find these three numbers.
4. Given that the sum of three consecutive odd numbers is greater than the sum of two identical even numbers 15, find three consecutive odd numbers.
5. The sum of three consecutive even numbers is 18. Find their products.
6. There are two numbers, the first number is 4 less than the second number, and the second number is exactly 4 times the first number. Find these two numbers.
7. Now my brother's age is exactly my brother's age, and my brother's age is my brother's age nine years ago. How old is my brother now?
8. Divide 55 into four numbers. If the first number adds 1, the second number subtracts 1, the third number multiplies by 2, and the fourth number divides by 3, all the numbers are the same. What are these four numbers?
9. 1998 A person's age is exactly equal to the sum of the figures of his birth year. How old was this man in 2003?
10, Xiaohua attended Japanese training for 8 days, and these 8 days add up to 100. When did Xiaohua finish the training?
1 1. The sum of the dates of the day before, the day after and the day before Xiaoming's birthday this year is 78. When is Xiaoming's birthday this year?
Mr. Wang will attend a three-day training. These three days are exactly in a vertical row of the calendar and the three numbers are connected. The sum of these three days is 36. Do you know when Mr. Wang will attend the training?
13, Xiaoming and Xiaohong play games. Xiao Ming took out a calendar and said; "I drew a square in 2╳2 with my pen, and the sum of their numbers is 76. Do you know what numbers I circled? " Can you help Xiaohong solve it?
14, the sum of three consecutive even numbers is 36. Find their products.
15, two digits, four times as many as ten digits. If you switch one digit and ten digits, the new number is 54 larger than the original number, so find the original two digits.
16, and the sum of three consecutive odd numbers is 75. Find these three numbers.
17, a two-digit number, where the ten digits are A and the one digit is B. If the ten digits and the one digit of this two-digit number are reversed, the original number will be subtracted, and the difference is 72. Find this two-digit number.
18. Circle the number 2╳2 with a square on the calendar, and the total is 64. What is the date of these four days?
19. If a square is used to circle the number 3╳3 on the calendar, the total is 126, then what is the date of these 9 days?
20. If today is Monday, what day is it after 2004?
2 1. There are two students, A and B. A said to B, "If you give me your pen, my pen is twice as big as yours." B said to A, "If you give me one of your pens, I will have as many as you." How many pens do you each have?
22. There are two digits, and ten digits are more than single digits 1. After the two numbers are reversed, the number obtained is 36 less than the original number. Find the original number.
23. The difference between one seventh of a number and five is the smallest positive integer. What's this number?
24. Two-digit numbers. The tenth digit is smaller than the second digit 1. The sum of the numbers in the tenth and second places is one fifth of this two-digit number. Find this two-digit number.
25. Xiaogang, a junior one student in a middle school, 13 years old, is a sheep. Coincidentally, Xiaogang's grandfather is also a sheep, and the sum of their ages is 86. Can you work out grandpa Xiaogang's age?
26. The sum of three consecutive even numbers is greater than the largest one 10. What are these three consecutive even numbers? What's their total number?
I'm getting fat.
1. Cast three cylindrical parts with a diameter of 2 cm and a height of 16 cm with round steel with a diameter of 4 cm. How long does it take to cut round steel?
2. There is a cubic copper block with a side length of 4 cm, which should be melted and cast into a cuboid copper block with a length of 2 cm and a width of 4 cm. What is the height of copper block after casting (excluding loss)?
3. A factory forged a cylindrical bottle with a diameter of 60 mm and a height of 20 mm, and then poured the water in the bottle into a cylindrical glass with a bottom diameter of 6 cm and a height of 10 cm. 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.
4. Fill all the water in a cylindrical bucket with a diameter of 40 cm and a height of 60 cm filled with water into another cylindrical bucket with a half diameter of 30 cm. What is the height of water at this time?
5. A cuboid iron block with a length of 9 cm, a width of 7 cm and a height of 3 cm and a cubic iron block with a side length of 5 cm are fused into a cylinder with a base diameter of 20 cm, and the height of the cylinder is required (π is 3. 14).
6. Circle a rectangle with a 5.2-meter-long iron wire, so that the length is 0.6 meters more than the width. What is the length and width of this closed rectangle?
7. A cylindrical bucket with a diameter of 1.2 m and a height of 1.5 m is filled with water, and the water is poured into a square iron box with a bottom length of1m. When the iron box is filled with water, how many meters does the water height in the bucket drop?
8. The length-width ratio of the rectangle is 5: 3, and the length-width ratio is 12 cm. Find out the length and width of this rectangle respectively.
9. The small cylinder is 8 cm in diameter and 6 cm in height. The diameter of a large cylinder is 10 cm, and its volume is 2.5 times that of a small cylinder. What is the height of the big cylinder?
10. Forging a cylindrical blank with a radius of 5 cm and a height of 8 cm, how long should the round steel with a radius of 4 cm be cut?
1 1. It is known that the weight of soybean after germination can be increased by 3.5 times. Now we need 100 kg of soybean sprouts. How many kilograms of soybeans should be used?
12. The circumference of the rectangle is 36 cm. If the length is reduced by 4 cm and the width is increased by 2 cm, the rectangle becomes a square. Find the side length of a square.
13. Use a cylindrical oil reservoir with a bottom radius of 5 cm, and soak the oil with steel balls. If 546π grams of steel balls are fished out, how many centimeters will the liquid level drop? (1 cubic centimeter steel ball 7.8g)
14. forging a cylindrical blank with a diameter of 70 mm and a height of 45 mm, how many millimeters should the round steel with a diameter of 50 mm be cut?
15. A machine factory wants to forge a blank with a cylinder with a diameter of 20 mm and a height of 40 mm above and a cylinder with a diameter of 60 mm and a height of 20 mm below. How long does a round steel with a diameter of 40 mm need?
16. Enclose a rectangle with a 20cm iron wire (1), so that the length ratio of the rectangle is 2.6cm wider. At this time, how many centimeters is the length and width of the rectangle? (2) Make the length and width of the rectangle equal. How long is the side of the square at this time?
17. There is a cylindrical iron block with a bottom diameter of 20 cm and a height of 26 cm. Forging it into a cuboid blank. If the rectangular body length is 10π cm and the width is 13 cm, find the height of the cuboid.
Discounted sales
Commodity profit = commodity price-commodity cost price
Commodity profit rate =
=
Discounted sales of goods stipulate clearly marked sales.
1. The purchase price of goods is 400 yuan, and the price is 600 yuan. When the store asks for a discount, the profit rate is not less than 5%. What is the lowest discount for this product?
2. The purchase price of a commodity is 1600 yuan, which is sold at 20% of the marked price, and the profit rate is 10%. What's its list price?
3. The purchase price of a kind of sports equipment is 1.200 yuan, and it is sold at a 10% discount on the basis of the marked price of 1.800 yuan. The purchase price of a treadmill is 2000 yuan, and the marked price is 3200 yuan, with a 20% discount. Which product has higher profit margin?
4. For a batch of goods, Party A will reduce the original price by 10 yuan, with 10% of the selling price as the capital, and Party B will reduce the original price by 20 yuan, with 20% of the selling price as the capital. If they have the same amount of capital, ask for the original price.
5. The price of a commodity in 780 yuan, in order to make small profits but quick turnover, is sold at 10% of the selling price and then returned to 30 yuan as a gift certificate. At this time, the profit is still 65,438+00%. What is the purchase price of this commodity?
If a store sells a color TV at a 10% discount on the list price, it can still make a profit of 20%. If the purchase price of color TV is 2400 yuan, what is the price of color TV?
7. The price of a commodity is 165 yuan. If the price is reduced by 10% (that is, the discount is 10%), the profit can still be 10% (relative to the purchase price). What is the purchase price of the goods?
8. The purchase price of a commodity is 2000 yuan, and the price is 3000 yuan. The store requires a discount at the selling price, and the profit rate is not less than 5%. What's the lowest discount for salespeople to sell this product?
9. After a commodity is purchased, the retail price is set at 900 yuan per piece. In order to adapt to the market competition, the store reduced the price by 10% of the retail price and sold it in 40 yuan, with a profit of 10% (relative to the purchase price). What is the purchase price of this commodity?
10, a shop assistant sells two coats at the same time, each for 135 yuan. If calculated according to the cost, one of them will make a profit of 25% and the other will lose 25%. Did the clerk lose money or make money this time?
1 1. Eggs in the market are priced by quantity. A vendor bought a batch of eggs at a price of 0.24 yuan each, but accidentally damaged 12 eggs in the process of selling. The remaining eggs were sold at a price of 0.28 yuan each, making a profit 1 1.2 yuan. How many eggs did the vendor buy at first?
12, a school is going to organize a trip for teachers and students, including 22 teachers. There are two travel agencies, A and B, with the same pricing and favorable conditions. A travel agency said that teachers are free and students charge 20% off; Travel agency b said that all teachers and students should get a 15% discount. After accounting, the actual charges of both parties are the same. How many students will take part in the tour?
13.A Shareholders sold two kinds of stocks, A shares sold 1500 yuan with a profit of 20%, and B shares also sold 1500 yuan with a loss of 20%. Is this shareholder a profit or a loss in this transaction? How much profit or loss?
14. A store bought a bell product of 100 and a bell product of 80 from the wholesale department of a company, and spent 2800 yuan. When the store retails, the price of each A bell product will increase by 15%, and the price of each B bell product will increase by 10%. In this way, after all products are sold, the income of * * * will be 366.
15. Due to the change of seasons, a certain 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?
16. A set of furniture was sold at the cost price plus 60%. Later, under preferential conditions, the price was reduced by 72% to get 6336 yuan. What's the price of this furniture? How much money can this set of furniture make after it is sold?
17, a commodity is priced at 226 yuan, and now it can be sold at a 30% discount, and it can still make a profit 13%. What's the purchase price of this clock?
18, Xiao Zhang, a self-employed individual, can still make a profit of 20% by selling a commodity at a 10% discount on the basis of the marked price. If the purchase price of a commodity is 24 yuan per piece, what is the list price of each piece?
19, the purchase price of a commodity is 3000 yuan, and the price is 4500 yuan.
(1) The store requires a discount on the selling price, with a profit of not less than 5%. What is the lowest discount for this product?
(2) If the market sales situation is not good, the store requires a discount at a loss. What is the lowest discount for selling this product?
(3) If the product causes a large inventory, the store requires a loss discount of no more than 5%. What is the lowest discount for selling this product?
"Project Hope" benefit performance
1.There are 90 students in Class A and Class B. After the mid-term exam, Class A will be transferred to Class B with 4 students. At this time, the number of students in Class A is 80% of that in Class B. How many students are there in the first two classes of the mid-term exam?
2. A set of books is divided into upper, middle and lower volumes. It takes 40% of the total printing time to print the first volume, 36% of the total printing time to print the intermediate volume and 24 days to print the second volume. How many days did it take to print a complete set of books?
3. The school carried out tree planting activities. Class A and Class B planted 3 1 tree, of which Class A planted twice as many trees as Class B. How many trees do you want to plant in each class?
4. Hong Guang Garment Factory wants to produce a batch of certain student clothes. It is known that every 3 meters of cloth can be made into two coats or three pairs of trousers, and one coat and one pair of trousers are a set. It is planned to use this 600-meter-long cloth to produce student clothes. How much cloth should be used to produce coats and trousers respectively? * * * How many sets can you produce?
5. There are 100 workers in a workshop, and each worker can add 18 bolts or 24 nuts on average every day. In order to match the bolts and nuts processed every day (one bolt and two nuts), how should the workers who process bolts and nuts be distributed?
In the math activity group of our school, there are two fewer girls than boys. If the number of girls increases by 3 and the number of boys decreases by 1, then the number of girls is 3 more than that of the whole group, thus finding the original number of boys and girls.
7. Granary A, B and C store 80 tons of grain. It is known that the grain storage ratio of warehouse A and warehouse B is 1: 2, and that of warehouse B and warehouse C is 1: 2.5. How many tons are stored in warehouses A, B and C respectively?
8. Before 1 1 round of National Football League A, a team remained unbeaten (including unbeaten and draw) and scored 23 points. According to the rules of the game, win a game and get 3 points, draw a game 1 point, and lose a game and get 0 point. Please stay here 165438.
9. Three students, A, B and C, donated books to Hope Primary School in poor areas. It is known that the ratio of books donated by them is 7: 5: 8, and * * * donated 200 books. How many books did each of the three students donate?
10, a school held a seventh-grade math competition, with 80 participants, with an average score of 63, 72 for students who passed, and 48 for students who failed. How many students passed?
1 1. A school organized an activity attended by 100 people. It is necessary to divide the participants into two groups. As we all know, the number of people in the first group is twice that of the second group. How many people are in each group?
12. Before Group A 1 1 round (match), Team W remained unbeaten in a row, with 23 points. According to the rules of the game, the team scored 3 points in one game and drew 1 point. So how many games did the team win?
13. A batch of dormitories. If each dormitory has 1 person,1person has nowhere to live. If there are 3 people in each dormitory, 10 rooms are unoccupied. How many dormitories and people are there?
14, teachers and students *** 100 people go to plant trees, each teacher plants 2 trees, each student plants 1 tree on average, and one * * species 1 10 tree. How many teachers and students are there?
15, a school organized a spring outing for students. If you rent several 45-seat buses, 15 people have no seats. If you rent the same number of 60 buses, there will be an extra 1 bus, and the rest will be full. It is understood that the daily rent for renting 45 buses is 250 yuan, and the daily rent for renting 60 buses is 300 yuan. What kind of bus is more economical?
16, a, b and c villages will jointly build a canal, and the plan requires labor 176 people. Because the population of each village is different, it is reasonable to share it according to the ratio of 2: 3: 6. How many laborers are sent to each of the three villages?
17. Three workshops in a factory 180 people. The number of people in the second workshop is three times that in the first workshop, exceeding 1 person. The number of people in the third workshop is half of that in the first workshop, less than 1 person. How many people are in each of the three workshops?
18, Pool A and Pool B * * * store 40 tons of water, and Pool A fills 4 tons. After Pool B produces 8 tons of water, the water in the two pools is exactly equal. How many tons of water do you want from Pool A and Pool B?
19, female students in mathematics extracurricular group account for the whole group, and after adding 4 female students, they account for the whole group. How many people are there in the math extracurricular group?
20. Divide a piece of land with an area of 1600 square meters into two parts, so that their area ratio is 3: 5, and find the area of each part.
2 1. One team has 108 hectares of forest farm and 54 hectares of pasture. Now it is necessary to cultivate a new fruit tree and turn some pastures into forest farms, so that the pasture area only accounts for 20% of the forest farm area. What is the pasture area of the forest farm?
Can you catch up with Xiaoming?
1, A and B practice 100 meter race. A runs 7 meters per second and B runs 6.5 meters per second. If A lets B run first 1 sec, how many seconds can A catch up with B?
2. Party A and Party B are 285 meters apart and walk in opposite directions. A walks 8 meters per second from A and 6 meters per second from B. If A walks 12 meters first, how many seconds will it take for A and B to meet?
3. Two planes, A and B, fly in opposite directions from two airports 750km apart at the same time, and arrive at the same midway airport half an hour later. If the speed of a plane is 0.5 times that of 65438+B plane, find the speed of B plane. ..
4. Two trains, A and B, are144m long and180m long. Car A travels 4 meters more per second than car B. The two trains run in opposite directions, and it takes 9 seconds from meeting to staggering. What is the speed of the two cars?
From a to b, the sea is 40 kilometers closer than the land. In the morning 10, a ship sailed from A to B. In the afternoon 1, a car sailed from A to B. They arrived at B at the same time. The speed of the ship is 24 kilometers per hour, and the speed of the car is 40 kilometers per hour. So how many kilometers is the land and sea distance from A to B?
6. A group of students went off-campus for military training. They walked at a speed of 5 kilometers per hour and walked 18 minutes. The school had to send an urgent notice to the captain. The correspondent started from the school and rode his bike to catch up with the students at a speed of 14 km/h. How long will it take the correspondent to catch up with the students?
7. Mine blasting In order to ensure safety, the person who lit the fuse should be moved to a safe area 3000 meters away before blasting. The burning speed of the fuse is 0.8 cm/s, and the speed of people leaving is 5 m/s. How many centimeters does the fuse need at least?
8. Xiao Ming and Xiao Li set out from school to watch sports games on the playground at the same time. Xiaoming walks 80 meters every minute. He walked to the playground and waited for five minutes before the game started. Xiaoli walks 60 meters every minute. When she entered the playground, the game had already started for 3 minutes. How far is it from school to playground?
9. It takes four hours for a ship to sail between two docks, but after four and a half hours of countercurrent, it is still 8 kilometers short, and the current is 2 kilometers per hour. What's the distance between the two docks?
10, A and B are 360 kilometers apart. Car A leaves from A at a speed of 72 kilometers per hour. Twenty-five minutes later, the B train departs from B at a speed of 48 kilometers per hour. After the two cars meet, they continue to drive at the original speed, so when the distance between the two cars is 120 km, the A car starts from a *.
1 1, and the distance between Station A and bilibili is 5 10 km. A local train goes from Station A to bilibili at a speed of 45 kilometers per hour. After the local train had been running for two hours, another express train traveled from bilibili to Station A at a speed of 60 kilometers per hour. How many hours after the express train leaves?
12. A ship travels downstream from A for 9 hours, and it takes 1 1 hour to reach A. Given the current speed of 2 km/h, find the speed of the ship in still water.