28*0. 1=2.8 (yuan) (5.5-2.8)/(1-0.1) = 3 (Zhang) 28-3=25 (Zhang) (/= divide by * = multiply).
Question 2: There are 50 RMB * * with total face value 1 16 yuan. As we all know, one yuan is more than two yuan. How many RMB are there in three denominations?
Question 3: There are 400 movie tickets from 3 yuan, 5 yuan and 7 yuan, with a value of 1920 yuan, among which 7 yuan and 5 yuan have equal tickets. How many movie tickets are there for each of the three prices?
Question 4: Two kinds of cars are used to transport goods. Each car contains 18 boxes, and each car contains 12 boxes. Now there is a 18 car, worth 3024 yuan. If each case is cheap in 2 yuan, the goods are worth 2520 yuan. Q: How many cars are there?
Question 5. A truck can transport ore 20 times a day in sunny days and 12 times a day in rainy days. Transportation 1 12 times a day, with an average of 14 times a day. How many days are it rainy these days?
Question 6. A batch of watermelons has been delivered and will be sold in two categories, the large one in 0.4 yuan and the small one in 0.3 yuan. In this way, these watermelons are worth 290 yuan. If the price per kilogram of watermelons is reduced by 0.05 yuan, this batch of watermelons can only be sold in 250 yuan. Q: How many kilograms is the watermelon?
Question 7. In the darts competition, it is stipulated that each player gets 65,438+00 points, and each player misses the target and gets 6 points. Each player throws 10 times and scores * * * 152 points, in which player A scores more than player B 16 points. Q: How many times did each player win?
Question 8. There are 20 questions in the math contest. Every time he answers a question correctly, he gets 5 points. If he answers a wrong question, he will not only get no points, but also deduct 2 points backwards. Xiaoming got 86 points in this competition. Q: How many questions did he answer correctly?
1. solution: x sheets of 1 element and (28-x) sheets of 1 angle.
x+0. 1(28-x)=5.5
0.9x=2.7
x=3
28-x=25
A: There are three Zhang Yiyuan bills and 25 dimes.
2. Solution: Let 1 element have X, 2 yuan (x-2) and 5 yuan (52-2x).
x+2(x-2)+5(52-2x)= 1 16
x+2x-4+260- 10x = 1 16
7x= 140
x=20
x-2= 18
52-2x= 12
A: There are 20 1 yuan, 8 18 in 2 yuan and 2 12 in 5 yuan.
3. Solution: 7 yuan and 5 yuan have X pieces, and 3 yuan has (400-2x) pieces.
7x+5x+3(400-2x)= 1920
12x+ 1200-6x = 1920
6x=720
x= 120
400-2x= 160
A: 3 yuan has 160 and 7 yuan and 5 yuan have 120.
4. Answer: Total cargo: (3024-2520)÷2=252 (boxes)
There are x buses and (18-x) cars.
18x+ 12( 18-x)= 252
18x+2 16- 12x = 252
6x=36
x=6
18-x= 12
Answer: Bus No.6, 12.
5. Solution: Days = 1 12÷ 14=8 days.
It rained on day X.
20(8-x)+ 12x = 1 12
160-20x+ 12x = 1 12
8x=48
x=6
There are six rainy days.
6. Solution: Watermelon number: (290-250)÷0.05=800 kg.
There is a big watermelon x kg.
0.4x+0.3(800-x)=290
0.4x+240-0.3x=290
0. 1x=50
x=500
There are 500 kilograms of big watermelons.
7. Solution: A: (152+ 16)÷2=84.
B: 152-84=68 points.
Set armor x times
10x-6( 10-x)=84
10x-60+6x=84
16x= 144
x=9
Set b to y times.
10y-6( 10-y)=68
16y= 128
y=8
A: Nine times for A and eight times for B. ..
8. Answer: Suppose he answered question X correctly.
5x-2(20-x)=86
5x-40+2x=86
7x= 126
x= 18
A: He got it right 18.
1.The distance between a and b is 465 kilometers. It takes * * * 7 hours for a car to travel from A to B at a speed of 60km/h, and then speed up 15km/h to arrive at B. How many hours have you been driving at a speed of 60 km/h?
2. There are several chickens and rabbits in the cage, which are *** 100 feet. If the chicken is replaced by a rabbit and the rabbit is replaced by a chicken, it will have 92 feet. How many rabbits and chickens are there in the cage?
Spiders have eight legs, dragonflies have six legs and two pairs of wings. Cicada has six legs, 1 pair of wings. At present, there are 18 of these three kinds of bugs, with 1 18 legs and 20 pairs of wings. How many bugs are there in each species?
4. In the activity of learning from Lei Feng, students * * * did 240 good deeds, senior students each did 8 good deeds, junior students each did 3 good deeds, with an average of 6 good deeds. How many students are there in this activity?
5. A class of 42 students participated in tree planting, with an average of 3 trees planted by boys and 2 trees planted by girls. As we all know, boys have 56 more trees than girls. How many boys and girls are there?
Answer:
1. solution: suppose it travels at a speed of 60 kilometers per hour for x hours.
60x+(60+ 15)(7-x)=465
60x+525-75x=465
525- 15x=465
15x=60
x=4
A: I drove at 60 kilometers per hour for four hours.
2. Solution: When rabbits are replaced by chickens, each rabbit loses two feet.
( 100-92)/2=4,
There are four rabbits.
(100-4*4)/2=42 pieces.
A: There are 4 rabbits and 42 chickens.
3. Solution: Set 18 Spider, Y Dragonfly and Z Cicada.
Three bugs * * *18, get:
X+y+z = 18 ... one type.
There are 1 18 legs, so:
8x+6y+6z = 1 18 ...
With 20 pairs of wings, you must:
2y+z = 20...c type
Where b -6*a gives:
8x+6y+6z-6(x+y+z)= 1 18-6 * 18
2x= 10
x=5
There are five spiders,
Then 18-5= 13 dragonflies and cicadas.
Then change z to (13-y).
Substitute it into type C, and you get:
2y+ 13-y=20
y=7
There are seven dragonflies.
There are 65438 cicadas +08-5-7 = 6 cicadas.
There are five spiders, seven dragonflies and six cicadas.
4. Solution: The students did 240 good deeds, with an average of 6 good deeds per person.
That means there are 240/6=40 of them.
There are x students in Datong University and (40-x) students in primary school.
8x+3(40-x)=240
8x+ 120-3x=240
5x+ 120=240
5x= 120
x=24
40-x= 16
A: There are 24 students in Datong University and 0/6 students in primary school/KLOC.
5. solution: there are x boys and 42-x girls.
3x-2(42 x)= 56
3x+2x-84=56
5x= 140
x=28
42-x= 14
A: Boys are 28 and girls are 14.
Grazing problem
1. In a pasture, the grass grows at a constant speed every day, and every cow eats the same amount of grass every day. 17 cows can eat grass in 30 days, 19 cows can eat grass in 24 days. At present, a group of cows have sold four cows after eating for six days, and the remaining cows will eat up the grass in two days. How many cows did this group of Niu Yi people have before four cows were sold?
17×30=5 10 (head) 19×24=456 (head) (5 10-456)÷(30-24)=9 (head) 30.
2. A reservoir flows in 4 cubic meters of water every minute. If you turn on five faucets, you can finish the water in the pool in two and a half hours; If you turn on eight faucets for 1.5 hours, the water in the pool will be exhausted. Now turn on the tap of 13 and ask how long it will take to drain the water in the pool (each tap drains the same amount of water every hour).
3. There are three warehouses A, B and C, and the amount of chemical fertilizer stored in each warehouse is the same. Warehouse A uses a belt conveyor, 12 workers, and it takes 5 hours to empty warehouse A; Warehouse B uses a belt conveyor with 28 workers, and it takes 3 hours to empty warehouse B; There are two belt conveyors in Warehouse C. If it takes two hours to empty Warehouse C, how many workers are needed at the same time (the function of belt conveyors is the same, each worker delivers the same amount of fertilizer per hour, and belt conveyors and workers deliver fertilizer everywhere at the same time)?
1×5=5 (Taiwan Province) 12×5=60 (person) 28×3=84 (person) 1×3=3 (Taiwan Province) 84-60=24 (person) 24 ÷ (.
4. Fast, medium and slow three cars set off from the same place at the same time and chased a thief riding in front along the same highway. It took the three cars 6 minutes, 10 minutes and 12 minutes to catch up with the thief. Now we know that the speed of express train is 24 kilometers per hour, and the speed of bus is 20 kilometers per hour. What's the speed of the local train? .
Olympic Special Topic-Weighing Ball
1 There are 4 piles of balls with the same appearance, with 4 balls in each pile. It is known that three piles are genuine and one pile is defective. Each quality ball weighs 10g, and each quality ball weighs11g.. Please weigh it with a balance and find out the defective pile.
There are 27 balls with the same appearance, and only one ball is defective, which is lighter than the genuine one. Please weigh it with the balance only three times (no weight) to find out the defective ball. 20 7
3. According to 10 balls with the same appearance, only one ball is defective. Please weigh it three times with the balance to find out the defective products.
There are 12 balls with the same appearance, and only one ball is defective. Only use the balance to weigh it three times. Can you find out the defective products?
Olympic Special Topic-Pigeon Cage Principle
1. A certain group * * * has 13 classmates, at least two of whom have birthdays in the same month. Why?
2. Any four natural numbers, in which the difference between at least two numbers is a multiple of 3. Why is this?
3. There are 15 socks of the same color and size mixed in the box. How many socks can you take out of the box at least to ensure three pairs of socks (socks are left and right)?
Olympic theme-restoration problem
1. Someone went to the bank to withdraw money. The first time, he took more than half of the savings in 50 yuan, and the second time, he took more than half of the remaining 100 yuan. At this point, there is 1250 yuan left in his passbook. What was his initial deposit?
There are 26 bricks, and the two brothers are scrambling to pick them. The younger brother is in front of them. Just after laying bricks, my brother came. My brother saw that my brother picked too much, so he took half of it himself. The younger brother thought he could do it, so he took half from him. My brother wouldn't let me, so he had to give him 5 pieces, so my brother picked 2 pieces more than his brother. How many pieces was my brother going to choose at first?
Olympic theme-train crossing the bridge
1. A 300-meter-long train crosses the bridge at a speed of 1080 meters per minute. It takes 3 minutes to get off the bridge from the front to the rear. How long is this bridge?
2. Someone walks at a speed of 2 meters per second. A train came behind, which took 10 seconds longer than him. As we all know, this train is 90 meters long. Find the speed of the train.
3. On the circular track, when two people run clockwise, they meet every 12 minutes. If the speed of two people is the same, one of them will run counterclockwise and meet every 4 minutes. How many minutes does it take each person to run a lap?
4. A 300-meter-long train passes through a 940-meter-long bridge at a speed of 1080 meters per minute. How many minutes does it take to get off the bridge from the front to the rear?
It takes 40 seconds for a train to cross a 530m bridge and 30 seconds for a 380m cave at the same speed. What is the speed/second and total length of this train?
6. The distance between telephone poles along the railway is 40 meters. When a passenger is in a running train, it is exactly 2 minutes from seeing the first pole to seeing the fifth/kloc-0 pole. How many kilometers does the train travel per hour?
7. A man was standing by the railway. After hearing the whistle of the nearest train, the train passed in front of him in 57 seconds. It is known that the train whistle is1360m away from him; The speed of sound is 340 meters per second. What is the speed of the train? (Numbers are reserved as integers)
How many seconds does it take for a 450-meter-long truck to cross a 570-meter-long iron bridge at a speed of 12 meters per second?
8. At present, two trains run in the same direction at the same time. /kloc-After 0/2 seconds, the express train will overtake the local train. The express train runs18m per second, and the local train runs10m per second. If two trains travel in the same direction at the same time, the express train will overtake the local train in 9 seconds, and find the body length of the two trains.
9. Li Minghe Zhang Yi practiced running on the 300-meter circular track. Li Ming runs 5 meters per second, and Zhang Yiran runs 3 meters per second. Both of them started from the starting point and went in the same direction. How many meters did Zhang Yi run when Li Ming caught up with Zhang Yi for the first time after departure?
The speed of three cars is 10. The fast, medium and slow cars start from the same place at the same time and catch up with the cyclist in front along the same highway. The three cars caught up with the cyclist in 6 minutes, 10 minutes and 12 minutes respectively. Now we know that the express train is 24 kilometers per hour and the bus is 20 kilometers per hour, so how many kilometers per hour is the local train? (choose to do the problem)
1 1 On the circular runway with a circumference of 400 meters, there are two points, A and B, which are 100 meters apart. A and b run away from each other at the same time. After they met, B immediately turned and ran in the same direction as A. When A ran to A, B just ran to B. If A and B ran at the same speed,
Olympic theme-average problem
Final exam 1, Cai Chen scored 89 points in political language, mathematics, English biology, 9 points in political mathematics, 84 points in Chinese English, 86 points in political English, and English was more than Chinese 10.
The fruit shop mixes 2 kilograms of crisp candy, 3 kilograms of fruit candy and 5 kilograms of milk candy into assorted candy. Known crisp candy is 4.40 yuan per kilogram, fruit candy is 4.20 yuan per kilogram, and milk candy is 7.20 yuan per kilogram. Q: How much is the assorted candy per kilogram?
There are two cotton fields, A and B, with an average yield per mu1.85kg.. A has 5 mu of cotton fields, with an average yield of 203 kg per mu. B Average yield per mu of seed cotton in cotton field170kg. B How many acres of cotton fields are there?
It is known that the sum of eight consecutive odd numbers is 144. Find these eight consecutive odd numbers. Xinhua primary school subscribed to a batch of China Youth Daily. If there are three digits, the remainder is 1. Five plots of land, and the rest are two; Seven pieces of land, and the rest is two pieces. How many copies of The Year of China did xinhua primary school subscribe to? This shop sold 1026 meter cloth in three days. The sales volume of the second day is twice that of the first day; On the third day, it sold three times as much as the next day. How much rice cloth do you want to sell in three days?
1. fractional elementary arithmetic: find1/3+115+1/35+1/63+1/99+65438.
Simple method:
1/3= 1×( 1/3)= 1/2( 1- 1/3)
1/ 15 =( 1/3)×( 1/5)= 1/2( 1/3- 1/5)
1/35=( 1/5)×( 1/7)= 1/2( 1/5- 1/7)
1/63 =( 1/7)×( 1/9)= 1/2( 1/7- 1/9)
1/99 =( 1/9)×( 1/ 1 1)= 1/2( 1/9- 1/ 1 1)
1/ 143=( 1/ 1 1)×( 1/ 13)= 1/2( 1/ 1 1- 1/ 13)
So1/3+115+1/35+1/63+1/99+1/. + 1/2( 1/5- 1/7)+ 1/2( 1/7- 1/9)+ 1/2( 1/9- 1/ 1 1)+ 1/2( 1/ 1 1- 1/ 13)
Common factor of 1/2 (1-1/3+1/5+1/7+)
It can be observed that the middle part of the formula completely cancels out, and finally only1/2 (1-113) = 6/13 is left.
Namely1/3+115+1/35+1/63+1/99+1/.
Conceptual problem type
2. Eight tenths of A, ten tenths of B and fifteen tenths of C are the three simplest fractions, and it is known that the product of the three fractions is half. What is a three-pointer?
a/8×b/ 10×c/ 15 = ABC/ 1200
Because their product is 1/2, abc=600.
The prime factor of 600 is 600=2×2×5×3×2×5.
And because their denominators are 8, 10 and 15 respectively, and they are the simplest fractions, their molecules cannot have 2, 2 and 5, 3 and 5 in turn.
So it can only be 5×5=25, 3, 2×2×2=8,
So these three scores are: 25/8, 3/ 10, 8/ 15.
Discussion questions by category:
3. Two ropes with the same length, the first one is cut off by three fifths and the second one by three fifths. Which one has more left?
When the rope is more than one meter, there will be more than one left.
When the rope equals one meter, there are as many as two left.
The rope is less than one meter, and there are many second ones left.
Agreed multiples and congruences
1. Today is Saturday. /kloc-What day is 0/000 day?
2. Two natural numbers A and B (A > B) are known, and the remainder of a and B divided by 13 is 5 and 9 respectively. Find the remainder of a+b, a-b, A× b(a>b a2-b2 divided by 13 respectively.
3.2 100 is divided by a two-digit number, and the remainder is 56. Find this two-digit number.
4. The sum of dividend, divisor, quotient and remainder is 903, the known divisor is 35 and the remainder is 2. Ask for a dividend.
5.345 and 543 are divided by an integer to get the same remainder, and the quotient differs by 9. Find this number.
6. There is an integer, and the sum of the three remainders obtained by dividing 3 12, 23 1 and 123 is 4 1. Find this number.
1. A: According to the meaning of the question, it is not difficult to see that the number of children in this large class is the greatest common divisor of 1 15-7 = 108,148-4 =144,74. Therefore,
2. Answer: Similar to the above question, according to the meaning of the question, the side length of the cube should be the least common multiple of 9, 6 and 7, and the least common multiple of 9, 6 and 7 is 126. So at least this rectangular block is needed,126×126×126.
3. A: This number is 28. The method is the same as the example.
Answer: These two numbers are 4 and 120, or 8 and 60, or 12 and 40, or 20 and 24. The method is the same as the example.
Answer 5: The two numbers are 15 and 150, or 30 and 135, or 45 and 120, or 60 and 105, or 75 and 90. The method is the same as the example.
6. Answer: Because 1+2+…+9=5×9, the sum of these nine digits can always be divisible by 9, so 9 is the common divisor of these nine digits. At present, we take two of these nine places, such as 4 13798256 and 4 138.
7. Answer:1925 = 5× 5× 7×11. The two quotients are 5 and 1 1,1925 ÷ 5 = 385; 1 925 ÷11=175a: press1. It is not difficult to see that the number of children in this big class is the greatest common divisor of 1 15-7 = 108, 148-4= 144, 74-2=72. So this big class has at most 36 children.
2. Answer: Similar to the above question, according to the meaning of the question, the side length of the cube should be the least common multiple of 9, 6 and 7, and the least common multiple of 9, 6 and 7 is 126. So at least this rectangular block is needed,126×126×126.
3. A: This number is 28. The method is the same as the example.
A: These two numbers are 4 and 120, or 8 and 60, or 12 and 40, or 20 and 24. The method is the same as the example.