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1. It is known that the price of a table is 10 times that of a chair, and it is also known that a table is 288 yuan more expensive than a chair. How much is a table and a chair?
Think about solving problems:
According to the known conditions, a table is 288 yuan more than a chair, which is exactly (10- 1) times the price of a chair, so the price of a chair can be obtained. According to the price of chairs, we can get the price of a table.
Solution:
Price of a chair: 288? (10- 1)=32 (yuan)
Price of a table: 32? 10=320 (yuan)
A table 320 yuan, a chair 32 yuan.
2. Party A and Party B walked across two places at the same time. Four hours later, they met four kilometers from the midpoint. A is faster than B. How many kilometers is A faster than B per hour?
Think about solving problems:
According to the meeting at 4 kilometers from the midpoint and the speed of A is faster than that of B, we can know that A walks 4 more than B? 2 kilometers, I know that after four hours of meeting. You can work out how many kilometers A is faster than B per hour.
Solution:
4? 2? 4=8? 4=2 km
A: A is 2 kilometers faster than B per hour.
Li Junhe Zhang Qiang bought the same kind of pencils with the same money. Li Jun asked for 13 pencils, Zhang Qiang asked for 7 pencils, and Li Jun gave Zhang Qiang 0.6 yuan money. How much is each pencil?
Think about solving problems:
According to the fact that two people spent the same money to buy the same kind of pencil, Li Jun asked for 13 and Zhang Qiang asked for 7, which means that everyone should get it (13+7)? Two, and Li Jun wanted 13, three more than he deserved, so he gave Zhang Qiang and 0.6 yuan money to get the price of each pencil.
Solution:
0.6? [ 13-( 13+7)? 2]=0.6? [ 13? 20? 2]=0.6? 3=0.2 (yuan)
A: Every pencil is 0.2 yuan.
At 8 o'clock in the morning, two buses A and B leave from two stations at the same time, in opposite directions. After a while, two buses reached both sides of a river at the same time. Because the bridge over the river is being repaired, vehicles are forbidden to pass. The two cars need to exchange passengers and then return to their respective departure stations by the same route. When they arrived at the station, it was already 2 pm. Car A travels 40 kilometers per hour and car B travels 45 kilometers per hour. How many kilometers are there between these two places? (The exchange time is omitted)
Think about solving problems:
According to the fact that two cars leave two stations at 8: 00 am and return to the original station at 2: 00 pm, the travel time of the two cars can be calculated. According to the speed and driving time of the two cars, the total distance traveled by the two cars can be calculated.
Solution:
2 pm is 14 pm.
Round trip time: 14-8=6 (hours)
Distance between the two places: (40+45)? 6? 2=85? 6? 2=255 km
Attendant: The distance between the two places is 255 kilometers.
The school organized two extracurricular interest groups to go out for activities. The first group walked 4.5 kilometers per hour, and the second group walked 3.5 kilometers per hour. 1 hour later, the first group stopped to visit an orchard, which took 1 hour, and then chased the second group. How long will it take to catch up with the second group?
Think about solving problems:
When the first group stopped to visit the orchard, the second group did more [3.5-(4.5-3.5)]? Kilometers, that is, the first group to catch up. It is also known that the first group is faster than the second group every hour (? 4.5-3.5) kilometers, from which we can find out the time to catch up.
Solution:
Distance between the first group and the second group: 3.5-(4.5-? 3.5)=3.5- 1=2.5 (km)
Time taken for the first group to catch up with the second group: 2.5? (4.5-3.5)=2.5? 1=2.5 (hours)
A: The first group can catch up with the second group in 2.5 hours.
6. There are two warehouses, A and B, and each warehouse stores 32.5 tons of grain on average. The tonnage of grain stored in warehouse A is 5 tons less than that in warehouse B. How many tons of grain are stored in warehouse A and warehouse B respectively?
Think about solving problems:
According to the fact that the tonnage of grain stored in warehouse A is 5 tons less than that in warehouse B, we can know that if the tonnage of grain stored in warehouse A increases by 5 tons, the tonnage of grain stored in warehouse B is 4 times that of warehouse B, and the total grain storage will also increase by 5 tons. If the tonnage of stored grain in warehouse B is regarded as 1 times, the total tonnage of stored grain is (4+ 1) times, from which the tonnage of stored grain in warehouse A and warehouse B can be calculated.
Solution:
B stored grain: (32.5? 2+5)? (4+ 1)=(65+5)? 5=70? 5= 14 (ton)
A warehouse stores grain: 14? 4-5=56-5=5 1 (ton)
Warehouse A stores 5 1 ton of grain, and warehouse B stores 14 ton of grain.
Team A and Team B are repairing a 400-meter-long highway. Team A completed four days from east to west and team B completed five days from west to east. Team a repairs more than team b every day 10 meter. How many meters do Team A and Team B repair every day?
Think about solving problems:
According to the fact that Team A repairs10m more than Team B every day, it can be considered that if Team A repairs for 4 days and Team B repairs for 4 days, the total length will be reduced by 410m, and the length at this time is equivalent to Team B (4+5). From this, we can get the number of meters repaired by team B every day, and then get the number of meters repaired by the two teams every day.
Solution:
B number of meters maintained every day:
(400- 10? 4)? (4+5)=(400-40)? 9=360? 9=40 (meters)
How many meters do Team A and Team B repair every day: 40? 2+ 10=80+ 10=90 (m)
A: Two teams repair 90 meters every day.
8. The school bought 6 tables and 5 chairs and paid 455 yuan. As we all know, every table is more expensive than every chair. 30 yuan, what's the unit price of each desk and chair?
Think about solving problems:
As we all know, every table is more expensive than every chair. 30 yuan, if the unit price of a table is as much as that of a chair, the total price will be reduced by 30? 6 yuan, the total price at this time is equivalent to the price of (6+5) chairs, from which the unit price of each chair can be obtained, and then the unit price of each table can be obtained.
Solution:
Price per chair:
(455-30? 6)? (6+5)=(455- 180)? 1 1=275? 1 1=25 (yuan)
Price per table: 25+30=55 yuan.
Every table 55 yuan, every chair 25 yuan.
9. A train and a local train leave from A and B respectively at the same time. The express train is 75 kilometers per hour and the train is 65 kilometers per hour. When we met, the express train traveled 40 kilometers more than the local train. How many kilometers is it between A and B?
Think about solving problems:
According to the known speed of the two cars, the speed difference can be found, and according to the speed difference between the two cars and the distance between the express train and the local train, the travel time of the two cars can be found, and then the distance between Party A and Party B can be found.
Solution:
(7+65)? [40? (75- 65)]= 140? [40? 10]= 140? 4=560 km
A: The distance between A and B is 560 kilometers.
10. A glass company consigned 250 boxes of glass, and the contract stipulated that the freight for each box was 20 yuan. If a box is damaged, it will not only pay the freight, but also compensate 100 yuan. At the time of settlement after delivery, * * * paid the freight 400 yuan. How many cases of glass were damaged during the consignment?
Think about solving problems:
According to the known consignment of 250 cases of glass, the freight for each case is 20 yuan, and the total freight payable can be calculated. According to the damage of each box, not only do you not pay the freight, but you also pay compensation of 100 yuan. The difference between the known payable amount and the actual paid amount is several yuan (100+20), that is, several boxes are damaged.
Solution:
(20? 250-4400)? ( 10+20)=600? 120=5 (box)
A: Five cases are damaged.
1 1. Miss Wang has a box of pencils, such as 1 for two students, two for three students, three for four students and four for five students. How many pencils are there in this box?
Think about solving problems:
According to the meaning of the question, the conditions in the question can be transformed into: two students, three students, four students and five students are short of one. Therefore, it is a required question to find the least common multiple of 2, 3, 4 and 5 and then subtract 1.
Solution:
The least common multiple of 2, 3, 4 and 5 is 60.
60- 1=59 (branch)
There are at least 59 pencils in this box.
12. the first and second squadrons of grade five are going for a spring outing 20 kilometers away from the school. The first squadron walks 4 kilometers per hour, and the second squadron rides bicycles, traveling every hour 12 kilometers. Two hours after the first squadron leaves, the second squadron leaves. How many hours after the second squadron leaves, can it catch up with the first squadron?
Think about solving problems:
Because squadron one started two hours earlier than squadron two? 2 kilometers, and the second squadron is (12-4) kilometers per hour more than the first squadron, so that we can find the time when the second squadron catches up with the first squadron.
Solution:
4? 2? ( 12-4)=4? 2? 8 = 1 (hour)
Answer: The second squadron 1 hour can catch up with the first squadron.
13. A pile of coal shipped from the factory will burn 1500 kg a day, one day ahead of schedule. If we burn 1000 kg a day, we will burn one more day than planned. How many kilograms is this pile of coal?
Think about solving problems:
According to the known conditions, the difference between the total amount of coal burned before and after is (1500+ 1000) kg, which is caused by the difference of (1500- 1000) kg per day. From this, the number of days of planned combustion can be calculated, and then the amount of this pile of coal can be calculated.
Solution:
Days of coal burning originally planned: (1500+ 1000)? ( 1500- 1000)=2500? 500=5 (days)
Weight of this pile of coal: 1500? (5- 1)= 1500? 4=6000 kg
This pile of coal is 6000 kilograms.
14. Mom sent Xiaohong to the store to buy five pencils and eight exercise books, and gave Xiaohong 3.8 yuan money according to the price. As a result, Xiaohong bought 8 pencils and 5 exercise books and got back 0.45 yuan. How much is a pencil?
Think about solving problems:
The total number of pencils and notebooks that Xiaohong intends to buy is equal to the total number of pencils and notebooks actually bought. The change is 0.45 yuan, which means that (8-5) pencils are counted as (8-5) exercise books, with a difference of 0.45 yuan. From this, we can find out how much the unit price of exercise books is more expensive than pencils. Judging from the total amount of money, eight exercise books are more expensive than eight pencils, leaving (5+8) pencils. Then you can work out the price of each pencil.
Solution:
How much is each exercise book more expensive than each pencil: 0.45? (8-5)=0.45? 3=0. 15 (yuan)
Eight exercise books are more expensive than eight pencils: 0. 15? 8= 1.2 (yuan)
Price of each pencil: (3.8- 1.2)? (5+8)=2.6? 13=0.2 (yuan)
A: Every pencil is 0.2 yuan.
15. The father is 45 years old and the son 15 years old. How many years ago, the father's age was 1 1 times that of his son?
Think about solving problems:
The age difference between father and son is (45- 15) years. When the father's age is 1 1 times the son's age, the difference between them is exactly (1 1- 1) times the son's age, so that we can know how old the son is. I also know that my son is 15 years old this year, and the difference between the two ages is what I want.
Solution:
(45- 15)? (1 1- 1)=3 (year)
15-3= 12 (year)
A: Before 12 years ago, the father's age was 1 1 times that of his son.
16. A road construction team undertook the task of building roads. It was originally planned to repair 720 meters a day, but it was actually repaired 80 meters more than the original plan, so that the actual repair difference 1200 meters can be completed three days in advance. What is the total length of this highway?
Think about solving problems:
Repair 720 meters every day as planned, so the actual advance length is (720? 3- 1200) meters. According to the repair of 80 meters per day, the number of days of repair can be found, and then the total length of the road can be found.
Solution:
Days of repair: (720? 3- 1200)? 80=960? 80= 12 (days)
Total length of highway: (720+80)? 12+ 1200=800? 12+1200 = 9600+1200 =10800 (m)
Answer: The total length of this highway is 10800 meters.
17. A shoe factory produced 1800 pairs of shoes, which were packed in 12 cartons and 4 wooden cases respectively. If there are as many shoes in 3 cartons and 2 wooden cases, how many pairs of shoes are there in each carton and each wooden case?
Think about solving problems:
According to the known conditions, we can find the number of 12 cartons converted into wooden cases. First, we can work out how many pairs are packed in each carton, and then we can work out how many pairs are packed in each carton.
Solution:
12 carton is equivalent to wooden case quantity: 2? ( 12? 3)=2? 4=8 (pieces)
Even number of shoes in wooden box: 1800? (8+4)= 18000? 12= 150 (double precision)
Even number of shoes in a box: 150? 2? 3= 100 (double precision)
A: Each carton can hold 100 pairs of shoes, and each wooden box can hold 150 pairs of shoes.
18. A batch of sand and cement was brought into a construction site, with twice as many bags of sand as cement. Use 30 bags of cement and 40 bags of sand every day. After a few days, all the cement was used up, leaving 120 bags of sand. How many bags of sand and cement are there?
Think about solving problems:
According to the known conditions, 30 bags of cement are used every day, 30? Two bags of sand can be used up at the same time.
. But now only 40 bags of sand are used every day, even less (30? 2-40) bags, thus accumulating 120 bags of sand. Therefore, according to the number of less sand bags used in 120 bag, the service days can be calculated. Then you can get the total number of bags of sand and cement.
Solution:
Days when cement is used up: 120? (30? 2-40)= 120? 20=6 (days)
Total number of cement bags: 30? 6= 180 (bag)
Total number of sandbags: 180? 2=360 (bag)
Answer: 180 bags of cement and 360 bags of sand are brought in.
19. The school bought five thermos bottles and 10 teacups, and * * * used 90 yuan money. The price of each thermos is four times that of each teacup. How much is each thermos and teacup?
Think about solving problems:
According to the calculation that the price of each thermos is four times that of each teacup, the price of five thermos can be converted into the price of 20 teacups. In this way, the 90 yuan money for five thermos bottles and 10 teacups can be regarded as the money for 30 teacups.
Solution:
Price of each teacup: 90? (4? 5+ 10)=3 (yuan)
Price of each thermos: 3? 4= 12 (yuan)
A: each thermos 12 yuan, each teacup 3 yuan.
20. The sum of two numbers is 572, and one of them is 0 of several digits. After removing 0, it is the same as the second addend. What are these two numbers?
Think about solving problems:
It is known that several digits of an addend are 0. If 0 is removed, it will be the same as the second addend. It is known that the first addend is 10 times of the second addend, so the sum of the two addends is 572 times of the second addend.
Solution:
The first addend: 572? ( 10+ 1)=52
The second addend: 52? 10=520