Analysis: When there are 12 trees left, it is not enough for everyone to take one. If we bring eight more trees, then each student can plant 10 trees. From this sentence, we can know that there are 12+8=20 students participating in tree planting. Together with the eight trees brought in, there are 20 * * 10 = 200 trees. So the original sapling =200-8= 192.
Answer: There are 12+8=20 students and 20* 10-8= 192 original saplings.
2. Young Pioneers go to plant trees. If each person digs five tree pits, there are still three tree pits that no one digs. If two of them dig four tree pits each and the others dig six tree pits each, they will have just dug all the tree pits. How many young pioneers are there in * *? * * * How many tree pits have been dug?
Analysis: This is a typical profit and loss problem, and the key is to unify the second sentence: "If two of them dig four tree pits each, the others dig six tree pits each, and all the tree pits are just dug". That is, six tree pits should be dug for each person to form a unified standard. That's equivalent to each person digging six tree pits, which means the difference is (6-4)*2=4 tree pits. So the total profit and loss is 3+4=7, so there are 7/(6-5)=7 young pioneers, and * * * has dug 5*7+3=38 pits.
Answer: The total profit and loss is equal to 3+(6-4)*2=7, there are 7/(6-5)=7 young pioneers, and * * * has dug 5*7+3=38 tree pits.
The school arranges students to listen to the report in the meeting room. If every three people sit on a bench, then the remaining 48 people will not sit; If every five people sit on a bench, only two benches are available. How many students are listening to the report?
Analysis: Typical profit and loss problem. The total profit and loss is 48+5*2=58, so the number of benches is equal to 58/(5-3)=29. Then, the number of people listening to the report is equal to 29*3+48= 135.
Answer: There are (48+5*2)/(5-3)=29 benches, and there are 29*3+48= 135 students listening to the report.
4. The difference between pens and ballpoint pens is 1 Yuan 2, the difference between five pens bought by Xiaoming and 0 yuan 5 is 65438+5, and eight ballpoint pens are 6. Ask Xiao Ming how much money he brought?
Analysis: In profit and loss problem, the formula we get refers to the same object. Now it's ballpoint pens and pens. Therefore, if we want to use the formula of profit and loss, we must turn it into the same object-a pen or a ballpoint pen.
The money for Xiao Ming to buy five pens is 1 50 yuan. We can convert it into buying five ballpoint pens, because we know that the difference between pens and ballpoint pens is 1 yuan and 20 cents. If we buy five ballpoint pens instead of five, we will save 6 yuan's money, which is 1 RMB 50, but we can buy more 6 yuan-1 RMB 50 =4 yuan 50. In this way, we turn the original problem into: Xiaoming bought five ballpoint pens with an extra 50 cents from 4 yuan and eight ballpoint pens with an extra 60 cents. Ask Xiao Ming how much money he brought? Then, the total profit and loss =4 yuan 5 -6 =3 yuan 9, and the price of each ballpoint pen =3 yuan 9 /(8-5)= 1 Yuan 3. So Xiao Ming * * has 8* 1 yuan 3 +6 = 1 1 yuan.
Answer: The difference between buying five pens is 1 RMB 50, which is equivalent to buying five ballpoint pens and 4 yuan 50. Price of each ballpoint pen =(4 yuan 50-60) /8-5)= 1 RMB 30. Xiao Ming brought 8* 1 Yuan 3 jiao +6 jiao = 1 1 Yuan.
The kindergarten distributed a basket of apples to the children. If each large class has five children, there will be10; Small classes give eight children, but there are two missing. As we all know, there are three more children in the big class than in the small class. How many apples are there in this basket?
Analysis: Similar to the previous question, it needs to be converted into two pairs of the same object.
Answer: If you give five children a large class, there will be 10 children, and the large class has three more children than the small class, which is equivalent to giving five children a small class, so there will be 10+3*5=25, the total profit and loss =25+2=27, and the number of small classes = 27/(8-5).
6. There are a group of freshmen in a school. If there are 8 people in each dormitory, use 33 dormitories. If there are two fewer people in each dormitory, the number of dormitories will increase 10. How many students are there?
Analysis: If there are 8 people in each dormitory and 33 dormitories are used, the number of people must be greater than 32*8=256, but not greater than 33 * 8 = 264; If there are two fewer people in each dormitory, the number of dormitories will increase by 10. That is to say, if there are 6 people in each dormitory and 43 dormitories are used, the number of people will definitely be more than 42*6=252, but not more than 43 * 6 = 258. After two comparisons, the number of people should be above 256 and not more than 258. So there may be 257 or 258 students in this group.
Answer: 8*32=256, 6 * 42 = 252,256 > more than 252,256 people; 8*33=264，6*43=258，258 & lt； 264, the number does not exceed 258. There may be 257 or 258 students in this group.
7. The kindergarten teacher distributed candy to the children. If each person is divided into 8 pieces, there are still 10 pieces left; If each person is divided into 9 pieces, the last person will get less than 9 pieces, but at least 1 piece will be given. So how many pieces of candy are there at most?
Analysis: If the last person gets less than 9 pieces, he can get 8 pieces at most, that is to say, if everyone gets 9 pieces, there is still a gap of 1 piece. According to the profit and loss calculation formula, the number of people is (1+10)/(9-8) =11,and the maximum number of sweets is 9 *1= 98; The last person got less than 9 pieces, but at least one piece was available, that is, the last person was at least 8 pieces short. According to the profit and loss calculation formula, the number of people is (8+ 10)/(9-8)= 18, and the maximum number of sweets is 9 *18 =154. So this batch of candy is at most 154.
Answer: 9- 1=8, the maximum number of people is (10+8)/(9-8)= 18, and the maximum number of candy people is 18*9-8= 154.
8. There are 48 books distributed to two groups of children. It is known that the second group has five more people than the first group. If all the books are distributed to the first group, then everyone has four books and there is a surplus; Five books per person, not enough books. If all the books are distributed to the second group, then each person has three books and there is a surplus; There are four books per person, and there are not enough books. How many people are in the second group?
Analysis: If all the books are distributed to the first group, then everyone has four books and there is a surplus; Five books per person, not enough books. Explain that the number of people in the first group is less than 48/4= 12 and more than 48/5 = 9...3, that is, 9 people; If all the books are distributed to the second group, then each person has three books and there is a surplus; There are four books per person, and there are not enough books. It shows that the number of people in the second group is less than 48/3= 16 and more than 48/4= 12. Because it is known that the second group has five more people than the first group, the first group can only have 10, and the second group has 15.
Answer: 48/4= 12, 48/5 = 9...5, 48/3= 16. In the first group, there were as few as 12 people and as many as 9 people. In the second group, there were less than 16 people and more than 12 people. Because it is known that the second group has 5 more people than the first group, the second group has 15 people.
9. In several boxes of cards, there are as many cards in each box. Give these cards to some children. If only one box is divided, everyone will get at least seven cards, but if all eight cards are divided, there are still five cards missing. Now the cards are all divided. Everyone has 60 cards, and there are still 4 cards left. How many children does * * * have?
Analysis: 60/7 = 8...4, 60/8 = 7 ...4, which means that the number of card boxes is 8, "If we divide all 8 cards, there are still 5 cards missing", that is, if we add 5 cards to each box (8 boxes * * * plus 40 cards), everyone will get 8*8=64 cards. Now, there are still 40 cards we borrowed, that is, 44 cards to be returned, 4/4== 1 1, that is to say, there are 1 1 individuals.
Answer: 60/7 = 8...4, 60/8 = 7 ...4, there are 8 boxes of cards, and the subnumber is (4+5 * 8)/4 =1.
10. Record the depth with a rope. The rope is folded three times, leaving 2 meters outside the well, and the rope is folded four times. Drop 1 m, less than wellhead. So how many meters is the depth of the well? How long is the rope?
Analysis: Typical profit and loss problem. Total profit and loss = 3 * 2+4 *1=10m.
Answer: Well depth = (3 * 2+4 *1)/(4-3) =10m, rope length = (10+2) * 3 = 36m.
1 1. There are two ropes with the same length. The first rope is cut into five sections on average, and the second rope is cut into seven sections on average. Each section cut by the first rope is 2 meters longer than each section cut by the second rope. How long is each rope?
Analysis: Each section cut by the first root is 2 meters longer than each section cut by the second root. Then if it is also five segments, the second segment is 5*2= 10 meter less than the first segment. Now the seven segments of the second one are as long as the five segments of the first one, which means that the length of the two segments of the second one is 10m, which means that each segment is10/2 = 5m. Therefore, the length of the rope is 5*7=35 meters.
Answer: The original length of each rope is 7*(2*5/2)=35 meters.
12, a class of students went boating. They calculated that if you add 1 boat, each boat will just take 6 people; If we reduce 1 boat, each boat will just take 9 people. Q: How many students are there in this class?
Analysis: there is a difference of two before and after adding one and subtracting one, that is to say, each boat takes exactly six people, and each boat takes nine people, leaving two boats. This is the standard form of profit and loss problem.
Answer: After adding a boat, the number of boats =9*2/(9-6)=6, and there are 6 * * 6 = 36 students in this class.
13, Zhang Yu left home for school at 7: 20 in the morning. If you walk 50 steps per minute, there are still 7 minutes before class; If you walk 35 steps per minute, you will be five minutes late. Asking about class time.
Analysis: This is another kind of common profit and loss problem. Mainly when calculating the total profit and loss, we must pay attention to the unity of the unit of quantity. The total profit and loss here is not 7+5= 12, but 7*50+5*35=525 steps. So it takes 525/(50-35)=35 minutes to get to school on time. So, the class time is 7: 55.
Answer: The time to get to school on time =(7*50+5*35)/(50-35)=35 minutes, and the time to get to school is 7: 55.
On Children's Day, 14, Xiaoming went to the store and bought a box of flowers and a box of white balls. The number of balls in the two boxes is equal. The original price of the flower ball is 65438+2 0 yuan dollars, and the original price of the white ball is 65438+3 0 yuan dollars. Due to the preferential sales of holiday shops, the prices of both kinds of balls are from 2 yuan to 5 yuan. As a result, Xiao Ming spent less money from 4 yuan. So how many balls did Xiaoming buy?
Analysis: The original price of the flower ball is 65438+2 0 yuan dollars, and the original price of the white ball is 65438+3 0 yuan dollars. That is, the original price of flowers120 in 0 yuan and the original price of white balls130 in 0 yuan. Then, also buy 30 flower balls and 30 white balls. Flower ball is more expensive than white ball 10/2 = 5 yuan, * * * needs 30/2+30/3=25 yuan. At present, the price of two kinds of balls is US$ 5 2 yuan, and it costs (30/5)*2*2=24 yuan to buy 30 flower balls and white balls respectively, which means that it can save 25-24= 1 yuan. Now * * * is deposited in 4 yuan, indicating that there are 30*4= 120 flower balls and white balls, and * * * bought 120*2=240.
Answer: If you buy 30 flower balls and 30 white balls, you can save = (30/2+30/3)-(30/5) * 2 * 2 =1yuan, and save 4 yuan, and buy 30*4= 120 flower balls and white balls respectively. So Xiaoming bought 240 balls.
15 There are some apples and pears. If five apples and three pears are packed in a bag and there are four apples, the pears are just finished; If 7 apples and 3 pears are packed in a bag, and the apples have just been eaten, there are 12 pears. So how many apples and pears are there?
Analysis: A bag of 7 apples and 3 pears has 2 more apples than a bag of 5 apples and 3 pears, and the number of pears has increased from just right to 12, which is equivalent to taking out 12/3=4 bags, taking out apples (4*5=20) and leaving 4 apples (* * 20+4). 2 per bag, plus 24/2= 12 bags just finished. So, the original 12+4= 16 bags, 16*5+4=84 apples, 16*3=48 pears, a total of 84+48= 132.
Answer: (12/3)*5+4=24, 5 apples and 3 pears in a bag, * * 24/2+4= 16 in a bag, so apples and pears * * have = 16 * (3+5).
Please refer to the link below for a detailed explanation.
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