1. Mathematical Intelligence of Primary School Students in Olympic Games
1. A commodity is priced at a profit of 25% and then sold at a 10% discount. As a result, the number of pieces sold every day increased by 1.5 times. So, what percentage of the total daily profit of this commodity has increased compared with that before the price reduction? Answer: If the total cost of the number of pieces sold per day before the price reduction is regarded as "1", then the total profit per day before the price reduction is 25%, and the total profit per day after the price reduction is (1+1.5) × [(1+25% )× 90%]-.
2. The distance between the two cities is 930 kilometers, and buses and trucks leave the two cities at the same time. Six hours later, two cars met. The average speed of passenger cars is 80 kilometers per hour, and the average speed of trucks is how many kilometers per hour?
Solution: Let's assume that the truck travels an average of X kilometers per hour.
(80+x)×6=930
x=75
A: The average speed of trucks is 75 kilometers per hour.
2. Math puzzles for Olympic pupils
1, Party A, Party B and Party C plant trees in plots A and B, with 900 trees in plot A and 250 trees in plot B/kloc-0 ... It is known that Party A, Party B and Party C can plant 24, 30 and 32 trees each day. Party A plants trees in Site A, Party C plants trees in Site B, Party B plants trees in Site A first, and then goes to Site B ... The two plots start and end at the same time. On what day should B be transferred from A to B? The total number of plants is 900+ 1250=2 150, and 24+30+32=86 plants can be planted every day.
The planting days are 2 150÷86=25 days.
24×25=600 trees will be completed in 25 days.
Then B will finish 900-600=300 trees before helping C.
That is, after 300÷30= 10 days, I transferred from A to B on 1 1 day.
2. A project is contracted by Party A and Party B, which can be completed in 2.4 days, and it needs to be paid 1800 yuan; Contracted by Team B and Team C, it can be completed in 3+3/4 days, and it needs to be paid 1500 yuan; 2+6/7 days, cost 1600 yuan. On the premise of ensuring the completion within one week, which team should be selected for the lowest cost?
Answer: The one-day cooperation between Party A and Party B is 1÷2.4=5/ 12, and the payment is 1800÷2.4=750 yuan.
The cooperation between ethylene, propylene and Fang Yitian is 1÷(3+3/4)=4/ 15, and the payment is 1500×4/ 15=400 yuan.
The cooperation between Party A, Party C and Fang Yitian is 1÷(2+6/7)=7/20, and the payment is 1600×7/20=560 yuan.
Three people cooperate in one day (5/12+4/15+7/20) ÷ 2 = 31/60,
Three people cooperate to pay (750+400+560)÷2=855 yuan a day.
Party A alone completes 31/60-4/15 =1/4 every day, and pays 855-400=455 yuan.
Party B alone completes 3 1/60-7/20= 1/6 every day, and pays 855-560=295 yuan.
Party C alone completes 31/60-5/12 =110 every day and pays 855-750= 105 yuan.
Therefore, through comparison, Party B is selected to complete the project within 1÷ 1/6=6 days, and it only costs 295×6= 1770 yuan.
3. Math puzzles for Olympic pupils
1, a and b are the two endpoints of the diameter of the circular road. At present, two people, A and B, weave in opposite directions at the same time and run at a constant speed (the speed of A and B is not necessarily the same). Suppose that when B runs 100 meters, the two meet for the first time. When A runs 60 meters, A and B will run at the same time. Answer:
Analysis of the first time A and B met and ran laps, and B ran 100 meters; When we met for the second time, A and B ran away 1. Five laps, and then B ran100× 3 = 300m. At this time, A missed 60 meters and ran a lap, and got 0. Five laps is 300-60=240 meters, so one lap is 480 meters. At the first meeting, A ran 240-100 =140m, and after every meeting, A ran140× 2 = 280m, so at the twelfth meeting, A * * * ran140+280.
2. Two people, A and B, start from both ends of the diameter of a circular field and move around this circular route in opposite directions at the same time at a uniform speed. When B walked 65,438+000 meters, they met for the first time and met again 60 meters before A walked a week. Find the circumference of this circular area.
[Analysis] I met for the first time and walked half a circle together; When we met for the second time, we walked a circle again, so the distance from the first meeting to the second meeting was twice that of the first meeting, so when we met for the second time, Otsuichi left * * *100× (2+1) = 300m, and the total distance between two people was one and a half weeks, which is the distance A walked.
4. Math puzzles for Olympic pupils
1, Class A and Class B had a cross-country marching competition. Class A runs half the distance at a speed of 4.5 km/h and the other half at a speed of 5.5 km/h; During the competition, Class B travels at a speed of 4.5 km/h half the time and at a speed of 5.5 km/h the other half. Q: Who will win Class A or Class B? Solution: The longer you walk, the shorter it takes. The fast walking distance of Class A is the same as the slow walking distance, and the fast walking distance of Class B is longer than the slow walking distance, so Class B wins.
2. It takes 3 days for the boat to travel from City A to City B and 4 days from City B to City A ... How many days does it take to put an unpowered raft from City A to City B?
Solution: It takes 3 days for a boat to go downstream and 4 days for a boat to go upstream, that is to say, the boat travels in still water for 4-3 = 1 (days), which is equal to 3+4 = 7 (days) of the current, that is, the speed of the boat is 7 times of the current. Therefore, the three-day trip of the ship is equal to the 3+3× 7 = 24 (days) trip of the current, that is, it takes 24 days for the raft to drift from city A to city B.
Xiaohong and Xiao Qiang started from home at the same time and walked in opposite directions. Xiaohong walks 52 meters per minute and Xiao Qiang walks 70 meters per minute. They meet on the way. If Xiaohong leaves four minutes early and the speed remains the same, and Xiao Qiang walks 90 meters every minute, then the two will still meet at point A. How many meters away is Xiaohong from Xiao Qiang's home?
Solution: Because Xiaohong's speed and meeting place remain the same, Xiaohong's time from departure to meeting is the same twice. In other words, Xiao Qiang walked four points less than the first time. pass by
(70× 4) ÷ (90-70) = 14 (minutes)
It can be seen that Xiao Qiang left for the second time 14, and it is inferred that he left for the first time 18, and their homes were separated.
(52+70) × 18 = 2 196 (m)。
5. Math puzzles for Olympic pupils
1, 8 little boys are better than anyone together, and everyone says they are better. At this moment, an old gentleman came up and said, "Don't make any noise. We adopt the elimination system, two people wrestle, one person is eliminated in each game, and finally the champion is decided, that is, the person with strength. " Everyone is unanimously in favor. The old man added, "How many more fights will there be like this? You do the math and I'll be the referee. " Son, can you work it out? Answer: A * * * will play 7 games.
2. The school holds a sports meeting, and the first-year students stand in a row, counting from the left, and there are 10 people on his left; Counting to the right, there are eight people on your right. The teacher asked Hao Hao how many people are there in this row? Smart boy, can you count?
Answer: According to the meaning of the question, there are 10+8= 18 people in this row, so a * * has 18+ 1= 19 people.
There are 25 books in 6 volumes. If there is at least one copy per copy, and the number of copies per copy is different, how many ways are there?
A: There are five ways to divide * * *
4. After Xiao Ming gave Xiaoli 10 yuan, there was still 15 yuan. At this time, two people have the same amount of money. How much does Xiaoli have?
Answer: 15- 10=5 (yuan). Xiaoli originally had 5 yuan money.
Xiao Liang is 7 years old, and his father is 30 years older than him. How old was his father three years ago?
Answer: 30+7=37 (years old) and 37-3=34 (years old), so my father was 34 years old three years ago.