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Analysis It is known that the volume ratios of alcohol to water in the two bottles are: 3:1 and 4:1, respectively, and the ratio of alcohol to water after mixing is obtained.

On the face of it, it is known that the two ratios are different in the volume of alcohol represented by the former term and the volume represented by the latter term.

The volume of water is also different, and there is no connection between the two ratios.

However, we look at known conditions"Two identical bottles", know the volume of alcohol and water.

Yes, in this way, we convert the known ratio of alcohol to water into the ratio of alcohol to alcohol + water.

Thus: the ratio of alcohol in the first bottle to alcohol + water is 3:4, and the alcohol in the second bottle.

and the ratio of alcohol + water is 4:5

Rewrite these two ratios to 15:20 and 16:20

If the volume of 1 bottle is considered to be 20 parts, then the volume of 2 bottles is 40 parts, two.

The alcohol in the bottle accounted for a total of 15 + 16 = 31 parts. The water in the two bottles together accounts for 40-31=9

Portion. Therefore, the volume ratio of alcohol to water in the mixture is 31:9

This is a question that we need to grasp what is known"Two identical bottles", thus comparing two singles to one.

connections.

The ratio of alcohol to water by volume is (:(9

There are 26 books on the upper floor and 22 copies on the lower floor.

Let the upper layer x1 and the lower layer x2 according to the prompts: (x1-10) x 2 = x2 + 10 and (x2 - 10) x 3 = x1 + 10 to solve the equation.

Question 2: 21 people 47-11-30=6 There are 6 people who get 5 points in two subjects 30 divided by 2 plus 6 to get 21 is the number of languages.

Question 3: 9 grams Let x be the number of grams of the original wine, and the amount of alcohol before and after does not become the equation: x x 45% = (x + 16) x 25%.

Question 4: 2500 grams Let x be 45% grams of sugar water to get the equation: x x 45% + 4000 - x) x 5% = 4000 x 30%.

Question 5: Cup 24%.

26 22

21 set the original liquor x grams.

x*45%=（x+16）*25%

x*20%=16*25%

x = 20 grams.

20*45%=9 grams.

There are 9 grams of edible alcohol in the wine.

4000 * ((45%-30%) (45%-5%)) = 1200 grams of wine with x glasses of wine at a concentration of c

x*c/（x+1）=25%

x*c+1）/（x+1）=40%

x=17/3

c=5/17

17 3 * 5 17 = 5 3 cups.

The original 5 3 cups of alcohol with a concentration of 5 17

Question 1: There are several books on the upper and lower shelves. If you take ten copies from the upper layer and put them on the lower layer, the number of copies in the lower layer is twice as large as the number in the upper layer; If you take ten copies from the lower layer and put them on the upper layer, the number of copies in the upper layer is 3 times that of the lower layer.

The original books ( ) on the upper floor, and the original books ( ) on the lower floor.

Equation: There are x books on the upper shelf and y on the lower shelf.

Equation: x-10=2(y+10).

3（x+10)=y-10

There is no point in such a hurry, and the system of columns and equations has come out.

Is there a diagram or to make it clear.

In order to ensure that the conductor can always find change, it is necessary to ensure that among the several people in front of each child who takes 100 yuan, there are more or equal people who take 50 yuan than 100 yuan. First of all, the person who takes 50 yuan is regarded as the same, and the person who takes 100 yuan is regarded as the same, you can use the oblique right-angle triangle model model to think, each small horizontal line segment represents the person who is 50 yuan, and each small vertical line segment represents the person who is 100 yuan, because from point A to point B, no matter which point on the way, the small horizontal line segment is not less than the small vertical line segment, so this problem is equivalent to finding how many different ways to walk from A to B in the following figure. Using the marking method, it can be found that there are 42 ways to move from A to B.

But in fact, 10 people are different from each other, they must be lined up, which can be divided into two steps, the first step is to line up for 100 yuan, 5 people have a total of 5! = 120 types of arrangement; For those who get 50 yuan in the second step, there are a total of 120 ways to arrange them, so there are 5 in total! ×5！

14,400 queuing methods.

In this way, there are a total of 42 14400 = 604800 (types) of queuing methods that enable the conductor to find change

The 42 ticket purchase sequences do not require additional change at the ticket office.

I understand the ticket purchase sequence to be the arrangement of 10 people holding 50,100 yuan banknotes, so that the ticket office can sell out 10 tickets without change.

It should be 42 kinds.

Also, I thought of the same method as the first floor, but the A and B inversions seem to be better understood.

Let the sum of x and y be yes, and x, y are positive integers. and 0 x,y 20110x+111y=1993

x=(1993-111y) 110=18-y+(13-y) 110 If x is an integer, then (13-y) 110 is an integer, y can only be 13, and x is 5

Remove 15 and 7 from them to make the sum of the remainders of them is.

Or this is how it works:

Only if the second decimal place is included, and the second decimal place after the decimal point is 3, the number left is 3 or 13. , not divisible. Satisfy.

The remaining 13 and 5 meet the topic. Then cross out 15 and 7 from them, so that the sum of the remainder of them is.

Scratch out 15, 7.

The details are as follows: let the sum of x and y is, and x and y are positive integers. and 0 x,y 20110x+111y=1993

x=(1993-111y) 110=18-y+(13-y) 110 If x is an integer, then (13-y) 110 is an integer, y can only be 13, and x is 5

Remove 15 and 7 from them to make the sum of the remainders of them is.

Or this is how it works:

Only if the second decimal place is included, and the second decimal place after the decimal point is 3, the number left is 3 or 13. , not divisible. Satisfy.

The remaining 13 and 5 meet the topic. Then cross out 15 and 7 from them, so that the sum of the remainder of them is.

Do you want steps? Question 1 Because it is a four-digit number and the sum is 2000, the thousand digits can only be 1 Let the number be 1abc

then 1000+100a+10b+c+1+a+b+c=2000

Simplification to 101a+11b+2c=999

Assuming a=8, then it is 808+11b+2c=999, no matter what value b and c take, 808+11b+2c is less than 999, so a>8, so a can only take 9, then 101a+11b+2c=101*9+11b+2c=909+11b+2c=999

11b+2c=90 Suppose b takes 9, then 11*b=99>90 rounded off b takes 8, then 88+2c=90 c=1

b takes 7, then 77 + 2c = 90 c = obviously wrong b = 6 66 + 2c = 90 c = 12 is greater than 10 c is greater than 10 so it is not right so a = 9 b = 8 c = 1 this number is 1981

Question 2(4-2) (1 3000 - 1 4000) = 24000

Question 3 Let the elder brother be x 3 years ago, and the younger sister be y

x=3yx+5)=2(y+5) The solution gives x=15 y=5

So my sister is 5+2=7 years old this year.

Question 4 Let the cost of A be x and B be y

x+y=220

x*(1+30%)+y*(1+20%)]90%=220+23

The solution is x=60 y=160

1.The two places are located at a distance of x km. Let the speed of the armor ride be y.

The time for the first encounter is (x-7) y

The time for the second encounter is (x-4+7) y (draw a picture for yourself and see it at a glance).

It should be the first time that A and B have completed a full course, and the second encounter A and B have completed two full courses, so the second time is twice as long as the first one.

So (x-7) y 2=(x-4+7 ) yx=17

2.To know that the minute hand travels 360° every hour, 6° per minute, and the hour hand moves 1 block 30° per minute.

So it's the process of the minute hand chasing the clock.

From 8 o'clock, the hour and minute hands are exactly in a straight line, and the hour and minute hands catch up with 60° and it takes 60 (minutes).

Also from 8 o'clock, the minute hand and the hour hand coincide exactly and the minute hand has to chase 60 + 180 = 240 ° and the time is 240 (minutes.

The difference between the two times is the time for Xiaohua to do his homework 360 11 minutes (about 33 minutes).

3.It should be If the passenger car travels for 3 hours and the train travels for 2 hours, the two cars will be 11 30 away from each other, which is 19 30 after the whole journey

So, if you run for 6 hours for a passenger car and 4 hours for a train (doubling the travel time), you would have traveled 38 30 for the whole journey

The first condition is to move in the same direction at the same time, and meet 4 hours later.

Subtract twice, get 2 hours with more passenger cars traveling 38 30-1=8 30 then 2 15 for the whole journey per hour of passenger cars

Therefore, the bus journey takes 1 2 15=hours.

Amsterdam is located in Zone 1 East and Beijing is located in Zone 8 East, there is a time difference of 7 hours (Amsterdam local time is -7 hours Beijing time), and the actual flight time needs to be converted to the time of the same time zone.

The departure time from Beijing is 11:55 Beijing time, and the arrival time in Amsterdam is 15:15 local time, that is, 22:15 Beijing time, so the actual flight time is 22:15-11:55 = 10 hours and 20 minutes;

The departure from Amsterdam is 21:25 local time, that is, 4:25 Beijing time the next day, and the arrival time in Beijing is 14:10 Beijing time, and the actual flight time is 14:10-4:25 = 9 hours and 45 minutes.

Therefore, there is not much difference in the actual flight time between the two.

Because there is a rotation of the earth.

The earth rotates from west to east, you fly from east to west, and the earth turns from west to east, which is equivalent to the plane and the destination running in opposite directions, so if the speed is the same, it takes less time than the destination not moving.

Conversely, when you fly from west to east, the plane moves in the same direction as the destination, which takes longer than the destination not moving.

Is this an Olympiad math problem......

We have crossed the International Date Line.

Amsterdam, Netherlands is in the +1 time zone.

Beijing is in the +8 time zone.

Therefore, the standard time difference between Amsterdam and Beijing in the Netherlands is 7 hours, and the Netherlands is 7 hours slower than Beijing.

The flight time from Beijing to Amsterdam is 7 hours + 3 hours and 20 minutes, and the return time from Amsterdam to Beijing is 16 hours 45 minutes - 7 hours.