Analysis and solution method 1: Assuming that there are X people * * * at the beginning, the total amount of sugar in the two methods remains unchanged, which is 5x+ 10=4× 1.5x-2, and the solution is x= 12, then these sugars * * have12× 5+.
Method 2: After the number of people increases by 1.5 times, each person is divided into 4 pieces, which is equivalent to the original number, and each person is divided into 1.5×4=6 pieces.
With these candies, each person is divided into five pieces, with the extra 10, the less each divided into six pieces and the less two pieces, so the total number of people at the beginning is (10+2)÷(6-5)= 12, so * * has/kloc-.
Two children, A and B, each have a bag of sweets, and each bag of sweets is less than 20. If A gives B a certain amount of sweets, A has twice as many sweets as B. If B gives A the same amount of sugar, A has three times as much sugar as B. So, how many sweets are there in A and B?
According to the meaning of the question, the total amount of sugar should be a multiple of 3 or a multiple of 4, that is, a multiple of 12, because each bag of two bags of sugar does not exceed 20, so the total amount of sugar does not exceed 40. So the total amount of sugar can only be 12, 24 or 36.
If the total amount of sugar is an odd multiple of 12, then the sugar of A is an odd multiple of 12÷(3+ 1)×3=9. Then after giving B the same amount of sugar twice, the sugar of A is 12.
In other words, odd plus even equals even, which is obviously impossible. Therefore, the total amount of sugar cannot be an odd multiple of 12.
Then two children, A and B, can only have even multiples of 12, that is, 24 sweets.
3. There are 42 students in Class A and 48 students in Class B. It is known that in a math exam, the scores are graded according to the percentage system. Results The total math scores of all classes are the same, and the average scores of all classes are integers, and the average scores are higher than 80. How much is the average score of Class A higher than that of Class B?
Solution 1: Because the average score of each class is an integer, the total scores of the two classes are equal, so the total scores are multiples of 42 and 48, so it is a multiple of [42,48] = 336.
Because the average score of Class B is higher than 80, the total score should be higher than 48×80=3840.
Because it is graded according to the percentage system, the average score of Class A will not exceed 100, so the total score should not be higher than 42× 100=4200.
Between 3840 and 4200, only 4032 is a multiple of 336, so the total score of both classes is 4032.
Then the average score of Class A is 4032÷42=96, and that of Class B is 4032÷48=84.
So the average score of Class A is 96-84= 12 higher than that of Class B. 。
Method 2: The average score of Class A is 42 = Class Average × 48, that is, Class A Average × 7 = Class B Average × 8. Because 7 and 8 are reciprocal, the average score of class A is 8 times of a certain number, and the average score of class B is 7 times of a certain number. And because the average scores of the two classes are above 80, they are not higher than 100.
So the average score of Class A is higher than that of Class B 12×(8-7)= 12.
4. A township hydropower station collects electricity charges by households. The specific provisions are: if the monthly electricity consumption does not exceed 24 degrees, it will be charged at 9 cents per degree; If it exceeds 24 degrees, the excess will be charged at 20 points per degree. It is known that family A paid 90.6 points more than family B in a certain month (electricity consumption is calculated by the whole degree). How much did A and B pay respectively?
Analysis and solution If the electricity consumption of both parties exceeds 24 degrees, the difference between their electricity charges should be an integer multiple of 20 cents;
If the electricity consumption of both parties does not exceed 24 degrees, the difference between them should be an integer multiple of 9 cents.
Now 96 points is neither an integer multiple of 20 points nor an integer multiple of 9 points, so the household electricity consumption of A exceeds 24 degrees, and that of B does not exceed 24 degrees.
Assume that household A uses 24+X kWh, household B uses 24-y kWh, 20x+9y=96, x=3 and y = 4.
That is, the electricity consumption of household A is 27 kWh, and that of household B is 20×9= 180 = 1 yuan 8, and that of household A 180+96=276 =2 yuan 7.6.
That is, Party A and Party B each pay 76 cents for electricity in 2 yuan and 65438+80 cents for electricity in 0 yuan.
5. The number of spring outing in primary and secondary schools is an integer multiple of 10. When traveling, the staff of the two schools do not take a car, and each car is as full as possible. It is now known that if both schools rent a coach car with a seat of 14, they need to rent 72 such cars; If both schools rent 19 coaches, the second primary school rents 7 more coaches than the first primary school. How many people will take part in this spring outing?
The analysis and solution assume that the number of spring tourists in the second primary school is m and the number of spring tourists in the first primary school is n, and take19× 6+65438 ≤ m-n ≤19× 8-1,that is, 18, which shows that the second primary school rents seven more vans than the first primary school.
It is also known that two schools need to rent a 14-seat van.
1. A cuboid bunker is 4m long, 2m wide and 0.5m deep. If the yellow sand weighs 1.4 tons per cubic meter, how many tons does it weigh?
2. It is known that a rectangular tin tank with a length of 18 decimeter and a width of 10 decimeter can hold 1620 liters of water. How deep is this tank?
3. A cuboid plastic box with medicine, 0.6m long, 0.25m wide and 0.5m deep. If you put the whole box of medicine into a small bottle with a capacity of 400ml each, how many bottles should this box contain at least?
4. A cubic billet is 6 cm long and forged into rectangular steel with a cross section of 3 cm long. How many meters is steel?
5. A cuboid oil drum with a bottom area of 18 square decimeter can hold 43.2 kilograms of oil. If the weight of each liter of oil is 0.8 kg, what is the height of the oil drum?
6. In a glass jar with a length of 25cm and a width of 20cm, there is a cubic iron block with a length of10cm. At this time, the water depth is 15 cm. If this iron block is taken out of the jar, how many centimeters is the water depth in the jar?
7. A cuboid fuel tank with a square bottom and a side length of 6 decimeters measured from the inside. It contains 144 liters of oil. As we all know, the depth of the oil inside is half that of the oil tank. How many decimetres is this oil tank?
8. One room 1200 wooden floor, 40 cm long, 20 cm wide and 2 cm thick. How many square meters is this room? How many cubic meters of wood does it take to spread out this room?
9. A section of rectangular steel, with a length of1.6m and a cross section of 4cm square. It weighs only 7.8 grams per cubic centimeter. How much does this square steel weigh?
10. Make an uncovered cuboid oil drum with iron sheet. The length and width are 4 decimeters and the height is 6 decimeters. How many square decimetres is the iron sheet? Put gasoline in a barrel, and each liter of oil weighs 0.82 kg. How many kilograms of gasoline can this barrel hold?
1 1. Forge a cubic billet with a length of 0.6 meters into rectangular steel with a cross section of 0.09 square meters. How long is forged steel? (Equation solving)
12, a cuboid glass tank, measuring 40 cm long and 25 cm wide from the inside, and the water depth in the tank is 12 cm. After a stone is immersed in water, the water surface rises to 16 cm, and the volume of the stone is found.
13. Make 12 cuboid iron chimneys, each section is 2m long, 4m wide and 3m high. How many square meters of iron do you need at least?
14. The floor of Xiao Min's room is rectangular. It is 5 meters long and 3 meters wide, and has a 2 cm thick wooden floor. How many cubic meters of wood do you need at least?
15, a coal truck, viewed from the inside, is 2.5m long and1.8m wide, and the loaded coal is 0.6m high, with an average weight of1.5t per cubic meter. How many tons of coal does this truck carry?
16. rectangular iron drum without cover, with square bottom, 4m side length and 1m height. How much iron does it take to make such a barrel? How many liters of water can this barrel hold?
17. The stadium is paved with 37.5 cubic meters of cinder on a straight runway with a length of 100 meter and a width of 7.5 meters. How thick can cinder be spread?
18, rectangular children's swimming pool, 40m long,14m wide and1.2m deep. How many square bricks with an area of 16 square decimeter should be pasted on the wall and bottom of the pool now?
19, cuboid container, bottom area 16 square decimeter, water height 6 decimeter. Now put an iron block with a volume of 24 cubic decimeters. How high is the water surface at this time?
20. Stack 2 100 cubes with a side length of 1 cm into a cuboid. Its height is 10 cm, and its length and width are greater than its height. What is the circumference of its bottom?
2 1, rectangular iron sheet, 32 cm long, cut a square with a length of 4 cm at its four corners, then fold it and weld it into a rectangular iron sheet box without a cover. It is known that the volume of this iron box is 768 cubic centimeters. What is the area of this iron?
22. The area of a rectangle is 24 cm, and its length and width are all whole centimeters. How many kinds of rectangles are there?
23. Class 5 (1) has no more than 50 students. When studying in groups, according to the different teaching contents, they can be divided into 3 people in each group, 4 people in each group, 6 people in each group and 8 people in each group. All kinds of points are just finished. There may be () students in this class or () students.
24. Party A, Party B and Party C borrow books from the library. Party A comes every six days, Party B comes every eight days and Party C comes every nine days. If we meet in the library on March 5, when will we go to the library next time?
25. Gardeners planted a tree every 4 meters on both sides of a highway, and planted 74 trees in a row. Now it's time to plant a tree every 6 meters. So, how many trees don't need transplanting?
26. Uncle Zhang sold fruit all day. When counting money at night, he found that a stack of banknotes in his hand was all two yuan and five yuan. Zhang divided the pile of money into two piles with equal amounts. In the first pile, the amount of five yuan and two yuan is equal, and in the second pile, the number of five yuan and two yuan is equal. Do you know how much money there is at least in this pile of money?
27. The fifth-grade students in bright primary school are divided into groups of 786, all of whom have just finished their studies. How many students are there in Grade Five?
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1: There are 90 ping-pong balls in the sporting goods. If every two are packed in a box, can they be packed properly? If you pack a box every five, can you finish it? Why?
90#2=45 boxes
90#5= 18 boxes
Answer: If every two are packed in a box, that's right.
An An's mother [Department Head Level 4] An An's mother [Department Head Level 4] went to TA's house to see the questions that Ta had answered. Tribal charm: 1 rank 0/ 100 Quick question intelligence: rank 4 150 1/200 1 square vitality: 65438+
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And:
1 A workshop can produce 120 class a parts, 100 class b parts or 200 class c parts every day. Class A, Class B and Class C can be selected respectively, and 1 part constitutes a set. Now it is required to produce the most complete set of products within 30 days. How many days does it take to produce three parts, A, B and C?
A math book is 6.25 yuan and a Chinese book is 5.86 yuan. Two books and one * * *, how much is it?
A watermelon weighs 4.86 kg and a cantaloupe weighs 3.5 kg. How many kilograms is a watermelon heavier than a cantaloupe?
A kind of wool costs 48.36 yuan per kilogram. How much is 3 kilos? Buy 0.6 kg?
A professional sericulture group raises 2 1 silkworm, and a * * * produces cocoons 1240 kg. How many kilograms of cocoons are produced per piece on average?
6 Xiaohong has read the story book for 5 days, reading 12 pages every day, and has not finished reading 38 pages. How many pages are there in this book? (Draw a line segment)
7. Three bags of flour and three bags of rice in the canteen. Flour is 25 kg per bag and rice is 50 kg per bag. How many kilograms of flour and rice are shipped?
The militia used 250 bullets for the first time, 320 bullets for the second time, and the third time was less than the sum of the previous two times 180. How many bullets were used for the third time?
9 The school bought 45 boxes of colored chalk, and white chalk bought 15 boxes more than colored chalk. How many boxes of chalk do I buy?
10. An empty basket weighs 2 kilograms, and there are 32 kilograms of peanuts in the basket. How many times the weight of the basket containing peanuts is that of the empty basket?
1 1. The grain store sent two truckloads of flour, each with 80 bags of 25 kilograms. How many kilograms of flour did this grain shop send? (Answer in two ways)
12 and 3 students went to the vegetable garden to collect cabbage, and they were divided into four groups, each group 1 1 person, with an average of 45 kilograms per person. A * * * How many kilograms of cabbage?
13 chemical fertilizer plant plans to produce 7200 tons of chemical fertilizer, which has been produced for four months, with an average of 1200 tons of chemical fertilizer per month, with 800 tons remaining per month. How many months will it take to complete the production?
14. The plastic factory plans to produce 1300 plastic modules and 780 plastic modules in 6 days. According to this calculation, how many days will it take to produce the rest?
15. Li Shifu produced 252 parts in four hours in the morning, and worked at this speed for three hours in the afternoon. How many parts does Li Shifu produce on this day?
16 cement plant plans to produce 3600 tons of cement, which will be completed in 20 days. In fact, it produces 20 tons more than planned every day. How many days does it actually take to complete the task?
17. A pile of 3.6 tons of coal is planned to burn 10 day. After improving the stove, it saves 0.06 tons per day compared with the original plan. How many days can this pile of coal burn now?
18.A and B are 420km apart. A to B plan to take a bus for 7 hours. In fact, its speed is more than planned 10 km. How many hours will it actually arrive?
Xiao Qiang came back to school from home. If he walks 50 meters every minute, 12 minutes to go back to school. If he walks 10 meter per minute, he can go back to school a few minutes earlier.
20. Build a 6.4-kilometer-long expressway, with 1.2 kilometers per month for the first three months and 1.4 kilometers per month for the rest. How many months will it take to complete?
9. Xiaoming spent 10.2 yuan on stationery, bought six pencils at 0.45 yuan each, and bought ballpoint pens for the rest. How many can he buy for each 2.5 yuan?
10. The garment factory originally planned to make 120 suits, each with 4.8m cloth. After improving the cutting method, each set saves 0.3 meters of cloth. How many sets of clothes can be made from the original cloth now?
1 1. A story book, originally 576 words per page, 25 pages. The second edition, with smaller words, only needs 18 pages. How many words are arranged on each page now than before?
12. A passenger train and a freight train leave from Party A and Party B at the same time. The speed of passenger trains is 80 kilometers per hour, and that of freight trains is 60 kilometers per hour. Five hours later, two trains met. How many kilometers is the railway between A and B?
13. Two engineering teams open1500m tunnel at the same time. Construction team A starts from one end and digs 14m every day. Construction team B starts from the other end and digs 16m every day. How many days can the tunnel be dug?
14. Party A and Party B type a 7000-word manuscript at the same time. Party A types 600 words per hour, and Party B types 200 words more than Party A. How many hours does it take to complete the task?
15. After school, Xiao Ming and Xiao Qiang walk in opposite directions at the school gate. Xiaoming walks 70 meters per minute, and Xiao Qiang walks 68 meters per minute. How many meters are they apart after 5 minutes?
16, the distance between a and b is 630 kilometers. Two hours after the bus departs from A, the truck departs from B. It is known that the speed of the bus is 65 kilometers per hour and the speed of the truck is 60 kilometers per hour. A few hours after the van left, it met the bus.
17, the machine tool factory used to know that each machine tool used steel 1.02 tons. After the improved design, each machine tool saves 0. 12 tons compared with the original machine tool. How many machine tools can be made now?
18, Xiaoming bought six pencils and four exercise books, each with 0.68.
1: There are 90 ping-pong balls in the sporting goods. If every two are packed in a box, can they be packed properly? If you pack a box every five, can you finish it? Why?
90#2=45 boxes
90#5= 18 boxes
A: If every two are packed in a box, they can be packed accurately. If every five are packed in a box, it can also be packed accurately. Because 90 is divisible by 5.
There are 57 balls in the sporting goods store, and every three balls are packed in a box. Can they be properly packed?
57#3+ 19 cases
A: I can just finish it.
3: A and B type a document of 10000 words, A type 1 15 words per minute, and B type 135 words per minute. How many minutes will it take?
10000 # (115+135) = 40 points.
A: It will be completed in 40 minutes.
4. Grade five students plant trees, 13 or 14. Each group has just finished. How many students took part in planting trees in grade five?
13X 14= 192 people
Answer: At least 192 people participated in tree planting in the fifth grade.
Although the following questions belong to practical problems, they are related to equations. I solved it with equations.
5: Two cars go back and forth from one place. One car has a speed of 365,438+0 kilometers per hour, and the other car has a speed of 44 kilometers per hour. How many minutes later, the two cars are 300 kilometers apart?
Equation:
Solution: Two cars meet after X point.
3 1X+44X=300
75X=300
X=4
4 hours =240 minutes
Answer: After 240 minutes, the distance between the two cars is 300 kilometers.
6: Two engineering teams will excavate a tunnel with a length of119m, and two teams will carry out construction from both ends. Team A digs 4 meters every day, while Team B digs 3 meters every day. How many days does it take to dig the tunnel?
Solution: Set X days to dig tunnels.
3X+4X= 1 19
7X= 1 19
X= 17
Answer: 17 days, the tunnel was dug.
7. School chorus and dance team 140 people. There are six times as many people in the chorus as in the dance team. How many people are there in the dance team?
Solution: There are X people in the dance team.
6X+X= 140
7X= 140
X=20 people
A: There are 20 people in the dance team.
From here on, this is not an equation problem.
8. The two brothers walked from home to the gym at the same time, with a length of 1300m. My brother walks 80 meters per minute, and my brother rides his bike to the gym at a speed of180 meters per minute, and will be right back. On the way, he met his brother. How many minutes did my brother walk?
1300x2 = 2600m 2600#( 180+80)
=2600#260
= 10 point
Answer: At this time, my brother left 10 minutes.
At 9 o'clock on Children's Day, Mr. Wang bought 360 biscuits, 480 sweets and 400 fruits, made a beautiful gift package and distributed it to the children as gifts. How many gift packages can he make at most?
360+480+400= 1240
Answer: You can make at most 1240 small gift packages.
10: Naughty bought 40 balloons and invited his classmates to blow them at home. In order to share the balloons equally, how many students should be invited to blow them? Naughty not to participate.
40#2=20 people 40#4= 10 people 40#5=8 people.
40#8=5 people 40#@0=4 people 40#20=2 people.
A: There are six ways to invite students, namely: 20, 10, 5, 8, 4 and 2.
1 1: trapezoidal corn field with upper bottom 15m, lower bottom 24m and height 18m. There are 9 corn plants per square meter on average. How many corn can be planted in this field?
( 15+24)x 18 # 2 = 35 1 m2
35 1X9=3 195 strain
A: This land can grow 3 159 maize plants.
12: The number of students in a class is less than 100. When waiting in line, there is just one more person in each row of 5, 4 or 3 people. How many people are there in this class?
5X4X3=60 people 60+ 1=6 1 person
A: There are 6 1 person in this class.
13: Wang Yue has a box of chocolate candy. The number of chocolates every 7, 5 and 3 is 1. How many chocolates are there in this box?
7X5X3= 105 capsules 105+ 1= 106 capsules.
There are at least 106 chocolates in this box.
14: There is a rectangular tunnel with a length of 15 m and a width of 1.2 m in Chenguang Community, which needs to be paved with square bricks. The designer prepared a square brick with a side length of 30 cm. Please calculate: how many such bricks are needed? If each square brick is 3 yuan, how much will it cost to build this tunnel?
15m = 150 decimeter 1.2m = 12 decimeter 30cm =3 decimeter.
150x12 =1800 square decimeter 3X3=9 square decimeter.
1800#9=200 yuan 200X3=600 yuan.
Answer: We need 200 such square bricks, and we need 600 yuan.
15: There are two parallelogram experimental fields with the same area. One is 70 meters long, 45 meters high and the other is 90 meters long. What's your height?
70x 45 = 3 150 m2 3 150 # 90 = 35m。
A: The height is 35 meters.
16: A batch of steel pipes are piled into a pile, with the bottom layer 10, the top layer 1 less 1 less, and the top layer 1 less. How many steel pipes are there in this batch?
10-5+ 1=6 floors (10+5)X6#2
= 15X6#2
=90#2
=45 pieces
A: There are 45 steel pipes in this batch.
1. Two cars, A and B, drive in opposite directions from AB respectively.