Profit and loss issues: Who can help me? Thank you!

The problem of profit and loss has been recorded in the sixth chapter of the ancient mathematical masterpiece "Nine Chapters of Arithmetic" in China, ---Insufficient Profit Chapter", surplus, that is, surplus; Deficit means insufficient.

A typical P&L problem is generally expressed in the following form:

Divide a number of apples (unknown) among several people (unknown), 20 more if each person divides 2, and 5 less if each person divides 3. Q: How many people are there in total? How many apples are there?

The invariant in the question is the number of people and the number of apples, and comparing the two different distribution methods, we can see that the apples are different:

20 + 5 = 25 (pcs); There is no doubt that the difference of 25 apples is due to the difference of 3 - 2 = 1 apples per person, in fact, there is only one situation that can lead to this, and that is when there are 25 apples!

After finding the number of apples, you can find the number of apples in two ways according to the topic:

2 25 20 70 (pcs) or 3 25 5 70 (pcs).

The formula for solving the profit and loss problem:

Number x = (deficit + gain) difference between the two distributions (n) (a b).

and Number of objects (x) Number of allocations (b) Number of people (y) Surplus (n).

Some application problems may not seem to be a profit and loss problem on the surface, but after careful analysis and appropriate transformation of the conditions, they can be turned into a profit and loss problem to be solved.

It can be seen from the formula for solving the profit and loss problem that the key to solving such problems is to carefully determine the difference between the two distributions and the total amount of profit and loss. If both distributions are surplus, the formula becomes the difference in surplus divided by the difference between the two distributions; If both allocations are insufficient, the formula becomes the difference in deficit divided by the difference between the two allocations, if ......

Sometimes, it is necessary to transform the conditions in the problem in order to find the solution from the complex quantitative relationship; Sometimes, it's more difficult to start with "contains", but it's easier to think indirectly from the opposite of "non-containment".

1.If the price of an antiviral drug operated by a store is increased by 100% in the case of market shortage, and the price department investigates and punishes it, the price increase is limited to only 10% of the original price, so what is the current price reduction of the drug?

Set the original price to A, and after the price increase is 100%, it is: 2A

The price department is limited to a 10% price increase, which is (1+10%)a=

The price reduction is x,2a (1-x)=

i.e. 2(1-x)=

Solution: x=2Wang Ming's father bought a batch of Haier air conditioners, in addition to paying taxes and fees at 17% of the purchase price, in order to ensure that there is a 20% profit, the price is set at 3014 yuan, please help his father calculate, when he buys this batch of air conditioners, how much should the purchase price be?

Set the purchase price of x yuan.

3014-17%x=x(1+20%)

x=2200

If the depth of the well is x meters (to the surface of the water), then the rope length is 2 (x + 9) m and 3 (x + 2) = 2 (x + 9).

x = 12 well depth (to the surface) 12 meters, rope length 42 meters.

Arithmetic: well depth: 2*9-3*2=12

Rope length: 2 (12 + 9) = 42

Solution: Set the rope length a meter, the depth of the well b meters, and the system of equations:

1) a/2-b=9

2) a/3-b=2

1)-(2) gets: a 6 = 7, a = 42 meters, substituting (1) formula to get b = 12 meters.

A: The rope is 42 meters long and the well is 12 meters deep.

Set the length of the rope x and the depth of the well y

1/2x-y=9

1/3x-y=2

x=42y=12

Rope length 42 and well depth 12.

1.From A to B 60 meters per minute 7 minutes late, 80 meters per minute to 5 minutes early, ask how far from A to B?

2.There was a class of students who went rowing, and they calculated that if one boat was added, there would be exactly 6 people in each boat, and if one boat was reduced, there would be 9 people in each boat. Q: How many students are in this class?

3.A store shipped a batch of fruits from Shenzhen, and the freight cost was 1,000 yuan, and the fruit was reported to be lost by 100 kilograms. If you sell it at 2 yuan 1 kilogram, you will lose 300 yuan; If it is sold at 3 yuan and 1 kilogram, it can make a profit of 500 yuan.

Q: How many kilograms were originally purchased? What is the amount of fruit purchased?

If the distance from Xiaoming's home to school is x, then:

x/50-8=(x-100)/60+2+5

x＝4000m

Assuming 50 meters per minute, it takes x minutes to reach the school, the column equation is as follows, and on both sides of the equation is the distance from the school to home:

50x=50×2+（50+10）×（x-2-8-5）50x=100+60(x-15)

50x=100+60x-900

10x=800

x = 80 (minutes).

50 80 = 4000 (meters).

Wang Xiaoming's home is 4,000 meters away from the school.

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After walking for 2 minutes, walk at the original speed for x minutes to be just late.

I walked for 2 minutes before accelerating, and I had to walk x+5 minutes to get there. The distance from home to school is 50*(2+x+5)meters.

If you accelerate, go 50 + 10 = 60 meters per minute, and you will have to walk for x-5 minutes. The distance from home to school is 50*2+60*(x-5) meters.

The column equation 50*(2+x+5)=50*2+60*(x-5) is solved to x=55 minutes.

So the distance is 50*(2+55+5)=3100 meters.

On the first floor, there is a wrong solution, so the wrong answer is reached.

The correct answer also adds 100 meters (the distance already traveled at the beginning).

So the correct answer is 490 meters.

Solution: (1) From the meaning of the question, if each person is divided into 5 pieces, there are 8 more pieces; If each person divides 6 pieces, it is 3 pieces less.

Therefore, the child has (8+3) (6-5)=11 (pieces), so that the biscuits have 11*5+8=63 (pieces).

A: There are 11 children, and there are 63 biscuits in this box.

2) If the apple is treated as a pear, then each person will divide 9 more than 6 pears; 10 per person, 4 less.

Therefore, the student has (6+4) (10-9)=10 (pieces), so that the apple has 10*7-6=64 (pieces).

Pears have 10*3+2=32 (pcs).

A: There are 10 students, 64 apples and 32 pears.

This is not a question of profit and loss, but a question of reconciliation.

If the sister gives the younger sister 7 yuan, it will be 3 less than the younger sister", that is, the sister will reduce 7 yuan, and 3 yuan less than the sister after adding 7 yuan. It turns out that there are more sisters than younger sisters.

7 2-3 = 11 blocks.

According to the formula of the sum and difference problem, it is obtained.

Sister = (39 + 11) 2 = 25 pieces.

Sister = (39-11) 2 = 14 pieces.

Suppose the sister turns out to have sugar x blocks and the sister y blocks.

My sister and sister had a total of 39 pieces of sugar.

So x+y=39

The sister gives the younger sister 7 pieces, so the sister has 7 pieces less, that is, the sister's existing candy x-7 sister has 7 more pieces, that is, the sister's existing candy y+7

Now my sister has 3 pieces less than my sister, so my sister's candy plus 3 is the number of my sister's candy.

i.e. x-7+3=y+7

The equations x+y=39 and x-7+3=y+7 can be obtained.

x=25，y=14

So my sister had 25 pieces of candy, and my sister had 14 pieces of candy.

28 people, three boats! 8 people * 3 boats + 4 people = 28

9 people * 3 boats + 1 person = 28