Primary school profit and loss application problem 1 Don't forget to review after class. The following is the application problem of primary school profit and loss I collected for you. Let's practice together!
1. A number divided by 4 is greater than 3, divided by 5 is less than 2, and divided by 7 is less than 4. What is the smallest number?
2. What is the smallest number when a number is divided by 5 and greater than 2, divided by 6 and less than 2, and divided by 7 and less than 3?
3. On average, 5 cases are packed in 150 to 200 parts. If there are more 1, it will be changed to 6 cases and 4 more. If it is changed to 7 cases, there will be 5 more at last. How many parts are there in this batch?
4. There are less than 60 apples in a basket, and they are distributed to 5 children on average, which is more1; Give an average of six children and three more. If you give it to seven people on average, there will be two more in the end. A * * * How many?
5. There is a pile of balls, count to three, and finally there are two left; Five numbers of five, and finally there are three left; Seven numbers of seven, and finally there are two left. How many balls are there?
6. What is the smallest number that a number is divisible by 5+2, 6+3 and 7+4?
7. A string of colored lights, seven numbers of seven, and finally 1 more; Count to nine, the last night; Five numbers of five are just enough. How many colored lights are there at least on this rope?
8. What is the smallest number when a number is divided by 7 plus 2, by 10 minus 2 and by 165438 plus 0 plus 3?
9. Odd numbers are divided by 288 and 2 14 respectively, and the remainder is 29. What's this number?
10. An integer, divided by 300,262,205 respectively, with the same remainder. What should this number be?
When goods are distributed in different ways, it often happens that they cannot be divided equally. The surplus of commodities is called surplus, and the shortage of commodities is called deficit, which is the meaning of profit and loss problem.
Generally speaking, when a batch of goods is distributed to a certain number of people, the first distribution method has surplus goods (surplus) and the second distribution method has insufficient goods (deficit). When the difference between the two distribution methods is n items, there are:
Abundance+deficit = number of people ×n,
This is a very important question about the relationship between profit and loss.
The trick to solve profit and loss problem can be summarized by the following formula:
(profit+loss) ÷ two differences = number of people or units,
(Income-Income) ÷ Difference between two shares = number of people or units,
(deficit-deficit) ÷ Difference between two shares = number of people or units.
example
1, Young Pioneers from Class 1, Grade 3 take part in the school brick moving work. If each person moves 4 bricks, there are still 17 bricks left. If each person moves 7 bricks, there will be 10 bricks less. How many young pioneers are there in this class? How many bricks are there to move?
2. The school allocates dormitories to new students. If there are three people in each room, there will be 22 more people. If there are more than 5 people in each room, there are 1 room. How many rooms are there in the dormitory? How many freshmen are there
Mother bought a basket of oranges and distributed them to the whole family. If two of them are divided into four and the rest are divided into two, there will be four more. If one of them is divided into six parts and the others are divided into four parts, 12 is missing. How many oranges did mom buy? How many people are there in the family?
answer
1, Young Pioneers from Class 1, Grade 3 take part in the school brick moving work. If each person moves 4 bricks, there are still 17 bricks left. If each person moves 7 bricks, there will be 10 bricks less. How many young pioneers are there in this class? How many bricks are there to move?
Solution: The total difference is 17+ 10=27 (block);
The difference of distribution is 7-4=3 (block);
So there are young pioneers 27÷3=9 (people)
* * * Brick: 4×9+ 17=53 (block).
A: There are 9 Young Pioneers in this class, and there are 53 bricks to be moved.
Test center: profit and loss problem, with one profit and one loss.
2. The school allocates dormitories to new students. If there are three people in each room, there will be 22 more people. If there are more than 5 people in each room, there are 1 room. How many rooms are there in the dormitory? How many freshmen are there
Solution: the first profit is 22 people, and the second room is added, and the loss is 3+5=8 (people);
The total difference is 22+8=30 (person);
There is a difference of five people between the two assignments.
So the dormitory has 30÷5=6 (rooms).
Freshman * * * has 3×6+22=40 (person).
A: There are 6 dormitories with 40 freshmen.
Test center: profit and loss problem.
Note: If you vacate a room, you will lose eight people, and you will lose eight people.
Mother bought a basket of oranges and distributed them to the whole family. If two of them are divided into four and the rest are divided into two, there will be four more. If one of them is divided into six parts and the others are divided into four parts, 12 is missing. How many oranges did mom buy? How many people are there in the family?
Solution: two of them are divided into four, the rest are divided into two, and the extra four are "converted" into two for each family.
Excess 4+2× (4-2) = 8;
One person is divided into six and the others into four, so there is a lack of 12 ",which translates as" everyone in the family is divided into four,
Missing12-(6-4) =10;
According to profit and loss problem's basic formula, the number of family members is (8+ 10)÷(4-2)=9 (persons).
Buy oranges 2×9+8=26 (pieces)
Analysis on three knowledge points of profit and loss application problems in primary schools;
In daily life, such problems often occur: a certain number of items are distributed to a certain number of people, and there are more people, and the items are not enough; There are fewer people, so there are more things. Profit and loss problem determines the total number of items and the number of people participating in the distribution when the profit and loss are known.
The key to profit and loss problem's solution is to find out the relationship between profit and loss.
The quantitative relationship of profit and loss problem is:
(1) (profit+loss) ÷ twice distribution difference = number of copies.
(big profit-small profit) ÷ twice distribution difference = number of copies
(big loss-small loss) ÷ twice distribution difference = number of copies
(2) Number of shares per time × number of shares+surplus = total number of shares
Number of shares per time × number of shares-loss = total number
Example 1
A tree planting team planted trees. If each person plants 5 trees, there will be 14 trees left; If there are seven trees for each race, there will be four fewer trees. How many people are there in this tree planting group? How many trees are there?
analyse
As can be seen from the meaning of the question, the number of people planting trees is the same as that of trees. Comparing the two distribution schemes, the difference is 14+4 = 18, that is, the result of scheme 1 is more than that of scheme 2 18. This is because the difference between the two distribution schemes is 7-5 = 2. Therefore, the tree planting group has 18÷2=9 people, and one * * has 5× 9+ 14 = 59 trees.
Example 2:
The school awarded a batch of pencils to three outstanding students. If everyone wins 9, they will lose 45; If everyone wins 7, there will be 7 less. How many students are there in Sanhao? How many pencils are there?
analyse
Analysis and answer: This is a lose-lose problem. From the meaning of the question, we can know that the number of students and pencils in Sande is unchanged. Comparing the two distribution schemes, the difference is 45-7 = 38. This is because the difference between the two distribution schemes is 9-7 = 2 pencils. So there are 38÷2= 19 students and 9× 19-45 = 126 pencils.
Example 3:
Some young pioneers went to the mountain to plant a batch of trees. If everyone plants 16 trees, there are still 24 trees that are not planted; If each race 19 trees, there are still 6 trees without seeds. How many young pioneers are there? How many trees are there?
analyse
Analysis and answer: This is a mutually beneficial question. According to the meaning of the question, the number of young pioneers and the number of trees are unchanged. Comparing the two distribution schemes, the difference is 24-6 = 18 trees, which is because the difference between the two distribution schemes is 19- 16 = 3 trees. So there are 18÷3=6 young pioneers, 16× 6+24 = 120 trees.
Example 4:
The school allocated dormitories to a group of freshmen. If there are 12 people in each room, there is no room for 34 people; If each room is occupied by 14 people, four rooms will be vacant. How many dormitories are there? How many boarding students are there?
analyse
Analysis and solution: if each room has 14 people, then four rooms are vacant; if each room has 14 people, then there will be less 14×4 = 56 people. Comparing the two distribution schemes, the difference is 34+56 = 90 people, while the difference in each room is 14- 12 = 2 people. The number of rooms is 90÷2=45 and the number of students is 12× 45+34 = 574.
Example 5:
Young pioneers went to plant trees. If everyone digs five tree pits, there are still three pits that no one digs. If two of them each dig four holes and the rest each dig six tree pits, they can dig all the tree pits. How many tree pits did the Young Pioneers dig?
analyse
Analysis and solution: If everyone digs six tree pits, there will be (6-4) × 2 = 4 tree pits less, and the difference between the two times is 4+3 = 7 tree pits. This is because the difference between the two distribution schemes is 6-5 = 1 tree pit. So there are 7 young pioneers1= 7 people, and one * * * digs 5× 7+3 = 38 tree pits.
The application of profit and loss in primary schools is 4 1. There are a number of saplings in the school, which are given to a number of young pioneers for planting once and for all, one at a time, and finally 12 trees are not enough; If we bring eight more seedlings, then each young pioneer can plant 10 trees. How many young pioneers went to plant trees? How many primitive saplings are there?
Xiaoming bought five pencils and eight erasers for one yuan. If he bought/kloc-0 pencils, he got less than 2 points. If he buys an eraser, he will get an extra 1 point. How much is each pencil? How much is each eraser?
3. Class 4 (1) students planted trees, each planted 1 tree, and there were 20 trees left, each planted 2 trees, with a difference of 30 trees. How many students are there? How many seedlings are there?
4. Learn from Lei Feng's group to move bricks for the school. If everyone moves 18, there are 2 pieces left; If everyone moves 20 yuan, a classmate will have no bricks to move. Q * * * How many bricks are there?
The teacher distributed some apples to the children. If everyone gets one, there are eight apples left; If everyone gets two, there are still two apples missing. How many children are there in a * *?
Primary school profit and loss application problem 5 Young Pioneers in Class 1, Grade 3 participate in the school brick moving work. If each person moves 4 bricks, there are 7 bricks left; If everyone moves five bricks, two bricks are missing. How many young pioneers are there in this class? How many bricks are there to move?
Analyze and compare the relationship between the quantities in the two brick moving methods;
Each person moved four bricks, leaving seven; If everyone moves 5 yuan, there will be 2 yuan less. The difference between these two moves is 5-4= 1 (block).
The first one has more than 7 bricks and the second one has less than 2 bricks, so the total difference between the second one and the first one is 7+2=9 (bricks).
Everyone's difference is 1, and the total number of results is 9, so there are 9 young pioneers1= 9 (people).
* * * Brick: 4×9+7=43 (block).
Solution: (7+2)÷(5-4)=9 (person), 4×9+7=43 (block) or 5×9-2=43 (block) A:* * * * There are 9 young pioneers, and the total number of bricks is 43.
If "two bricks less" in the example 1 is changed to "many 1 brick", can you figure out how many young pioneers there are and how many bricks there are? As can be seen from this problem, the solution to this kind of problem is to regard the sum of surplus and deficiency as the total difference produced by two different ways of moving bricks, divide it by the difference of each person moving bricks, that is, the unit difference, and then you can get the number of units, which is the number of people moving bricks in this problem.
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