1. There are some candies, 5 pieces per person is 10 pieces more; if the current number of people increases to 1.5 times the original number, then 4 pieces per person will be 2 pieces less. Ask about these candies** *How many pieces are there?
Analysis and solution method 1: Suppose there are We get x=12, so these candies are 12×5+10=70 pieces.
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 of people. Each person is divided into 1.5×4=6 pieces.
With these candies, each person is divided into 5 pieces, which is 10 pieces more, and each person is divided into 6 pieces, 2 pieces less, so the total number of people at the beginning is (12)÷(6-5)=12 people, then ***There are 12×5+10=70 pieces of candy.
2. Two children A and B each have a bag of sugar, each bag contains less than 20 sugar particles. If A gives B a certain amount of sugar, A’s sugar will be twice the number of B’s sugar particles. ; If B gives the same amount of sugar to A, A’s sugar will be three times the number of sugar particles B has. Then, how many sugar particles do two children A and B have?
Analysis and solution From the meaning of the question, we know whether the total number of sugars should be a multiple of 3 or 4. That is, it is a multiple of 12. Since the two bags of sugar do not exceed 20 pieces each, the total number does not exceed 40 pieces. Therefore, the total number of sugars can only be 12, 24 or 36 capsules.
If the total number of sugars is an odd multiple of 12, then "after B gives A the same amount of sugar", A's sugar is an odd multiple of 12÷(3+1)×3=9. Then in After A gives B twice the "same amount of sugar", A's sugar will be an odd multiple of 12÷(2+1)×2=8.
In other words, an odd number plus an even number equals an even number, which is obviously impossible. Therefore, the total number of sugars cannot be an odd multiple of 12.
Then the candy that two children A and B can only have is an even multiple of 12, which is 24 pieces.
3. There are 42 students in Class A and 48 students in Class B. It is known that in a certain mathematics examination, papers were graded according to a hundred-point system. As a result, the total mathematics scores of each class were the same. The average scores are all integers, and the average scores are all higher than 80 points. So how many points is the average score of Class A higher than that of Class B?
Analysis and solution method 1: Because the average score of each class is an integer , and the total scores of the two classes are equal, so the total score is both a multiple of 42 and a multiple of 48, so it is a multiple of [42, 48] = 336.
Because the average score of Class B is higher than 80 points, the total score should be higher than 48×80=3840 points.
And because the examination is based on a hundred-point system, the average score of Class A will not exceed 100 points, so the total score should not be higher than 42×100=4200 points.
The number between 3840 and 4200 that is a multiple of 336 is only 4032. Therefore, the total score of both classes is 4032 points.
Then the average score of Class A is 4032÷42=96 points, and the average score of Class B is 4032÷48=84 points.
So the average score of Class A is 96-84=12 points higher than the average score of Class B.
Method 2: The average score of Class A × 42 = the average score of Class B × 48, that is, the average score of Class A × 7 = the average score of Class B × 8. Because 7 and 8 are mutually prime, so the average score of Class A The average score of Class B 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 both classes exceed 80 points and are not higher than 100 points, this number can only be 12.
So the average score of Class A is 12×(8-7)=12 points higher than the average score of Class B.
4. A hydropower station in a certain township charges electricity bills on a per-household basis. The specific regulations are: if the monthly electricity consumption does not exceed 24 kilowatt hours, it will be charged at 9 cents per kilowatt hour; if it exceeds 24 kilowatt hours, the excess will be charged at 9 cents per kilowatt hour. The charge is 2 cents per degree. It is known that in a certain month, House A paid 9.6 cents more for electricity than House B (electricity consumption is calculated in whole units). How much did House A and House B pay each?
Analysis and Solution If A and B both consume more than 24 kilowatt-hours of electricity, then the difference in their electricity bills should be an integer multiple of 2 cents;
If A and B both If the electricity consumption does not exceed 24 kilowatt-hours, then the difference in electricity bills between the two should be
It is an integral multiple of 9 cents.
Now 90.6 cents is neither an integer multiple of 2 cents nor an integer multiple of 9 cents, so the electricity consumption of House A exceeds 24 kilowatt-hours, and the electricity consumption of House B does not exceed 24 kilowatt-hours. ．
Suppose House A uses 24+x kilowatt hours of electricity, and House B uses 24-y kilowatt hours of electricity. There are 20x+9y=96, so x=3 and y=4.
That is, House A uses 27 kilowatt-hours of electricity and House B uses 20 kilowatt-hours of electricity. Then House B should pay an electricity bill of 20×9=180 cents=1 yuan and 8 jiao, and House A pays 1896=276 Cent = 2 yuan, 7 cents and 6 cents.
That is, A and B each pay an electricity bill of 2 yuan, 7 cents and 6 cents, and 1 yuan and 8 cents.
5. The number of people attending the spring outings of Primary School No. 1 and Primary School No. 2 is an integral multiple of 10. People from the two schools do not share a car when traveling, and each car should be filled as much as possible. Now we know that if both schools rent 14-seat coaches, then the two schools will need to rent a total of 72 such buses; if both schools rent 19-seat coaches, the second primary school will have more than the first primary school. Rent 7 such cars. How many people are participating in this spring outing from the two schools?
Analysis and Interpretation Assume that the number of people in the spring outing of the second small school is m, and the number of people in the spring outing of the small school is n. It is known that there are 7 more 19-seat vans rented by two small ones than by one small one. Therefore, 19×6+1≤m-n≤19×8-1, that is, 115≤m-n≤151.
It is also known that the two schools *** need to rent a 14-seater van
1. A rectangular sand pit, 4 meters long, 2 meters wide and 0.5 meters deep. If every cubic meter The yellow sand weighs 1.4 tons. How many tons does the yellow sand weigh?
2. A rectangular iron water tank is 18 decimeters long and 10 decimeters wide. It is known that this water tank can hold up to 1620 liters of water. How deep is this water tank?
3. A rectangular plastic box containing potion is 0.6 meters long, 0.25 meters wide, and 0.5 meters deep. If this entire box of potion is put into a small bottle that can hold 400 ml each, How many bottles of potion can be contained in this box?
4. A cube steel billet with an edge length of 6 decimeters is forged into a square steel cuboid with a cross-section of 3 centimeters on a side. How many meters long is the steel?
5. A rectangular oil drum has a bottom area of ??18 square decimeters and can hold 43.2 kilograms of oil. If each liter of oil weighs 0.8 kilograms, what is the height of the oil drum in decimeters?
6. In a glass jar 25 cm long and 20 cm wide, there is a cube iron block with an edge length of 10 cm. At this time, the water depth is 15 cm. If the iron block is removed from the jar Take it out, how deep is the water in the tank?
7. A rectangular fuel tank has a square bottom and a side length of 6 decimeters measured from the inside. There are 144 liters of oil inside. It is known that the depth of the oil inside is half the depth of the fuel tank. How many decimeters is the depth of the fuel tank?
8. There are 1,200 wooden floors 40 cm long, 20 cm wide and 2 cm thick in a room. How many square meters does this room occupy? How many cubic meters of wood do you need to pave this room?
9. A rectangular steel section is 1.6 meters long and has a square cross-section with a side length of 4 centimeters. Each cubic centimeter just weighs 7.8 grams. How much does this square steel weigh?
10. Use iron sheets to make a cuboid oil drum without a cover. The length and width are 4 decimeters and the height is 6 decimeters. How many square decimeters of iron sheet are used? Put gasoline in a barrel. Each liter of oil weighs 0.82 kilograms. How many kilograms of gasoline can this oil barrel hold?
11. A cube steel billet with an edge length of 0.6 meters is forged into a rectangular steel material with a cross-section of 0.09 square meters. How long is the forged steel material? (Use equations to answer)
12. A rectangular glass tank is 40 cm long and 25 cm wide when measured from the inside. The water depth in the tank is 12 cm. After a stone is immersed in water, the water level rises to 16 cm. Find the volume of the stone.
13. To make a 12-section rectangular iron chimney, each section is 2 meters long, 4 decimeters wide and 3 decimeters high. How many square meters of iron should be used at least?
14. The floor of Xiao Min’s room is rectangular.
It is 5 meters long, 3 meters wide, and has a 2 cm thick wooden floor. How many cubic meters of wood are needed?
15. A coal truck is 2.5 meters long and 1.8 meters wide from the inside. The height of the coal loaded is 0.6 meters. The average coal weight per cubic meter is 1.5 tons. How many tons of coal is loaded in this truck? ?
16. A rectangular iron bucket without a lid. The bottom is a square with a side length of 4 decimeters and a height of 1 meter. How much iron sheet does it take to make a bucket like this? How many liters of water can this bucket hold?
17. The stadium is paved with 37.5 cubic meters of cinder on a straight track 100 meters long and 7.5 meters wide. How thick can cinder be spread?
18. A rectangular children's swimming pool is 40 meters long, 14 meters wide and 1.2 meters deep. How many square tiles with an area of ??16 square decimeters are needed to be pasted on the four walls and bottom of the pool?
19. A rectangular container has a bottom area of ??16 square decimeters and a height of 6 decimeters of water. Now put an iron block with a volume of 24 cubic decimeters. How high is the water level at this time?
20. Use 2100 cubes with an edge length of 1 cm to form a cuboid. Its height is 10 cm, and the length and width are both greater than the height. What is the circumference of its base?
21. A rectangular iron sheet, 32 cm long, cut off 4 cm squares from its four top corners, and then fold it and weld it into a rectangular iron box without a lid. It is known that the volume of this tin box is 768 cubic centimeters. What is the original area of ??this iron sheet?
22. The area of ??a rectangle is 24 centimeters, and its length and width are both whole centimeters. How many types of such rectangles are there?
23. The number of students in Class 5 (1) shall not exceed 50. When studying in groups, according to different teaching content, they can be divided into 3 students per group, 4 students per group, 6 students per group, and 6 students per group. 8 people, all kinds of dividing methods are just finished. This class may have students ( ) or ( ).
24. A, B, and C go to the library to borrow books. A goes every 6 days, B goes every 8 days, and C goes every 9 days. If they go to the library on March 5 The three of them met in the library. When will the next time they all go to the library?
25. Garden workers planted a tree every 4 meters on both sides of a section of road, and planted 74 trees in one day. Now we need to plant a tree every 6 meters. So, how many trees do not need to be transplanted?
26. Uncle Zhang sold fruits for a day. When he was counting money at night, he found that the stack of banknotes on hand were two-yuan and five-yuan notes. Uncle Zhang divided the pile of money into two piles with equal numbers. The first pile contained the same number of five yuan and two yuan, and the second pile contained the same number of five yuan and two yuan. Do you know how many dollars this stack of banknotes contains?
27. The fifth-grade students of Guangming Primary School are divided into groups of 7, 8 or 6 and line up to do exercises. They all happen to be divided. How many students are there in the fifth grade?
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1: There are 90 table tennis balls in the sporting goods. If two are put into a box every two, can they be filled exactly? If every five are put into a box, can they be filled exactly? Finished? Why?
90#2=45 boxes
90#5=18 boxes
Answer: If every two are packed into one box, can it be correct?
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1 A certain workshop can produce 120 parts of type A, 100 parts of type B, or 200 parts of type C every day. Take 3 parts of A, B and C respectively. One, two or one can be used as a set. It is now required to produce the largest number of complete sets of products within 30 days. How many days should each of the three parts A, B, and C be arranged for production?
A mathematics reading book costs 6.25 yuan, and a Chinese reading book costs 5.86 yuan. How much does two books cost per ***?
A watermelon weighs 4.86 kilograms, and a cantaloupe weighs 3.5 kilograms.
How many kilograms more does a watermelon weigh than a cantaloupe?
4 A kind of wool costs 48.36 yuan per kilogram. How much yuan should you pay to buy 3 kilograms? How about buying 0.6kg?
A professional sericulture group raised 21 spring silkworms and produced 1,240 kilograms of cocoons in one day. On average, how many kilograms of cocoons are produced per cocoon?
6 Xiaohong read a storybook for 5 days, reading 12 pages every day, and there were still 38 pages left. How many pages does this book have? (Draw a line segment diagram)
7. The canteen brought 3 bags each of flour and rice. Each bag of flour weighs 25 kilograms and each bag of rice weighs 50 kilograms. How many kilograms of flour and rice are shipped?
The militiamen used 250 rounds of bullets for the first time, 320 rounds for the second time, and 180 rounds less than the previous two times combined for the third time. How many rounds of bullets were used for the third time?
9 The school bought 45 boxes of colored chalk, and bought 15 more boxes of white chalk than colored chalk. How many boxes of chalk should I buy per ***?
10. An empty basket weighs 2 kilograms. Put 32 kilograms of peanuts into the basket. How many times does the basket of peanuts weigh more than the empty basket?
11. The grain store transported two trucks of flour, each truck containing 80 bags of 25 kilograms each. How many kilograms of flour does this grain store transport? (Answer in two ways)
12. The third-grade students went to the vegetable garden to collect cabbage. They were divided into 4 groups, with 11 people in each group. Each person collected an average of 45 kilograms. How many kilograms of cabbage can be harvested per day?
13 Fertilizer factory plans to produce 7,200 tons of fertilizer. It has been in production for 4 months. The average monthly production of fertilizer is 1,200 tons. The remaining monthly production is 800 tons. How many months will it take to complete the production?
14. The plastic factory planned to produce 1,300 plastic modules and produced 780 pieces in 6 days. Based on this calculation, how many days will it take to complete the remaining production?
15. Master Li produced 252 parts in 4 hours in the morning, and worked for another 3 hours in the afternoon at this rate. How many parts does Master Li produce on this day?
16 The cement plant plans to produce 3,600 tons of cement and it will take 20 days to complete. The actual production is 20 tons more per day than planned. How many days does it actually take to complete the task?
17. A pile of 3.6 tons of coal is planned to be burned for 10 days. After improving the stove, it saves 0.06 tons per day than the original plan. How many days can this pile of coal be burned now?
18. Places A and B are 420 kilometers apart. A bus is scheduled to travel from place A to place B for 7 hours. I actually traveled 10 kilometers per hour more than originally planned. How many hours did it actually take to arrive?
Xiaoqiang returns to school from home. If he walks 50 meters per minute, he will return to school in 12 minutes. If he walks 10 meters more per minute, how early can he return to school?
20. To build a 6.4-kilometer-long road, the average construction is 1.2 kilometers per month in the first three months, and the remaining 1.4 kilometers per month. How many months will it take to complete?
9． Xiao Ming spent 10.2 yuan on stationery and bought 6 pencils at 0.45 yuan each. The remaining money bought ballpoint pens at 2.5 yuan each. How many pens can he buy?
10. The garment factory originally planned to make 120 suits, with each suit using 4.8 meters of fabric. After improving the cutting method. Each suit saves 0.3 meters of cloth. How many suits can be made from the original cloth?
11. A storybook originally had 576 words per page and 25 pages. When reprinting, the font size was reduced and only 18 pages were required. How many more words are there on each page now than before?
12. A passenger bus and a freight train depart from two places A and B opposite each other at the same time. The passenger bus travels 80 kilometers per hour and the freight train travels 60 kilometers per hour. After 5 hours, the two vehicles meet.
How many kilometers is the railway between A and B?
13. Two engineering teams are working together to dig a 1,500-meter tunnel at the same time. Engineering team A starts working at one end and digs 14 meters per day. Engineering team B starts working at the other end and digs 16 meters per day. How many days will it take for the tunnel to be dug?
14. A and B type a 7,000-word manuscript at the same time. A types 600 words per hour, and B types 200 words more per hour than A. How many hours will it take to complete the task?
15. Xiao Ming and Xiao Qiang walk in opposite directions at the school gate after school. Xiao Ming 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 passenger car leaves from A, the truck drives in the opposite direction from B. It is known that the passenger car travels 65 kilometers per hour, and the truck travels 65 kilometers per hour. Travel 60 kilometers per hour. How many hours after the truck drove out did it meet the passenger car?
17. The machine tool factory originally knew that each machine tool uses 1.02 tons of steel. After improving the design, each machine saves 0.12 tons than before. How many machine tools can now be manufactured using the steel used to manufacture 300 units?
18. Xiao Ming bought 6 pencils and 4 exercise books, each exercise book cost 0.68
1: There are 90 table tennis balls in the sporting goods, if two are packed in a box , can it be filled exactly? If every five boxes are packed, can it be filled exactly? Why?
90#2=45 boxes
90#5=18 boxes< /p>
Answer: If you put one box every two, it can be completely filled. If you put one box every five, it can be completely filled. Because 90 is divisible by five.
2: There are 57 rubber balls in the sports store, and every three balls are packed in a box. Can they be packed completely?
57#3+19 boxes
Answer: It can be completely filled.
3: Two people, A and B, type a 10,000-word document. A types 115 words per minute and B types 135 words per minute. How many minutes can it take to finish typing?
10000# (115+135) = 40 points
Answer: You can finish the game in 40 minutes.
4: The fifth-grade students planted trees, and the groups of 13 or 14 people were divided into groups. How many fifth-grade students participated in tree planting?
13X14=192 people
Answer: There are at least 192 people in fifth grade participating in tree planting.
Although the following questions are application questions, they are related to equations. I used equations to answer them.
5: Two cars are traveling in opposite directions from one place. One car travels 31 kilometers per hour, and the other car travels 44 kilometers per hour. After how many minutes, the two cars will be 300 kilometers apart?
< p>Equation:Solution: Two cars meet after X time.
31X+44X=300
75X=300
X =4
4 hours = 240 minutes
Answer: After 240 minutes, the two vehicles will be 300 kilometers apart.
6: The two engineering teams will** *A 119-meter-long tunnel is excavated at the same time, and the two teams are working on it from both ends. Team A digs 4 meters every day, and team B digs 3 meters every day. How many days will it take to dig through the tunnel?
Explanation: Assume that the tunnel is dug after Dig the tunnel.
7: There are 140 people in the school chorus and dance team. The number of the chorus team is 6 times that of the dance team. How many people are there in the dance team?
Solution: Suppose the dance team has X people
6X+X=140
7X=140
X=20 people
Answer: There are 20 people in the dance team.
It’s not an equation problem from here on.
8: Two brothers go from home to the gymnasium at the same time. The road is 1300 meters long. The brother walks 80 meters per minute. , the younger brother rode a bicycle at a speed of 180 meters per minute to the gymnasium and returned immediately. He met his elder brother on the way. How many minutes had the elder brother walked?
1300X2=2600 meters 2600#(1880)
1300X2=2600 meters 2600#(1880)
p>
=2600#260
=10 points
Answer: My brother left for 10 minutes.
9:: Children’s Day , Teacher Wang bought 360 biscuits, 480 candies, and 400 fruits, and made exquisite small gift bags to give to the children as gifts. How many small gift bags can be made at most?
3648400=1240
Answer: Up to 1240 small gift bags can be made.
10: Naughty bought 40 balloons and invited classmates to come home to compete in blowing balloons. In order to divide the balloons equally, Naughty should Invite a few classmates to compete in blowing balloons? Naughty people will not 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
Answer: There are 6 ways to invite classmates, namely: 20 people, 10 people, 5 people, 8 people, 4 people, 2 people .
11: A trapezoidal corn field, with an upper base of 15 meters, a lower base of 24 meters, and a height of 18 meters. On average, 9 corn plants are planted per square meter. How many plants can be planted in this land in one day? Corn?
(15+24)X18#2=351 square meters
351X9=3195 plants
Answer: This land can grow 3159 corn plants.
12: The number of students in a certain class is less than 100. When lining up, there are exactly one more student in each row of 5, 4 and 3. How many students are there in this class?
5X4X3 =60 people 61=61 people
Answer: There are 61 people in this class.
13: Wang Yue has a box of chocolate candies, 7, 5, 3 each time The number of chocolate candies is 1. How many chocolate candies are there in this box?
7X5X3=105 pieces 105+1=106 pieces
Answer: There are at least 106 chocolate candies in this box. .
14: There is a rectangular corridor 15 meters long and 1.2 meters wide in Chenguang Community that needs to be paved with square tiles. The designer has prepared square tiles with a side length of 30 cm. Please calculate: How many square tiles are needed? How many square bricks are there? If each square brick costs 3 yuan, how much will it cost to pave this corridor?
Yuan?
15 meters = 150 decimeters 1.2 meters = 12 decimeters 30 centimeters = 3 decimeters
150X12=1800 square decimeters 3X3=9 square decimeters
1800#9 = 200 blocks 200 In a quadrilateral experimental field, one base is 70 meters long and the height is 45 meters, and the other base is 90 meters long. How many meters is the height?
70X45=3150 square meters 3150#90=35 meters
Answer: The height is 35 meters.
16: A batch of steel pipes are stacked in a pile. There are 10 steel pipes on the bottom layer. One less steel pipe is placed on each upper layer, and 5 steel pipes are placed on the upper layer. This How many steel pipes are there in the batch?
10-5+1=6 layers (15)X6#2
=15X6#2
=90# 2
=45 pieces
Answer: There are 45 steel pipes in this batch.
1. Two cars A and B are traveling towards each other from AB