The increase is the original: 3/5+ 10%.
So it was supposed to be done: 280/(3/5+ 10%)=400 yuan.
(2) The books produced by a school-run factory this month increased by 30,000 yuan. If VAT is paid at 17% of the value-added amount, how much VAT should be paid this month? (Please write down the calculation process)
Payable: 30,000 *17% = 5100 yuan.
(3) Dad's salary this month is 2 100 yuan. According to the regulations, the income tax shall be paid on the salary1.above 600 yuan. If you pay the personal income adjustment tax at the rate of 5%, how much should Dad pay this month? How much does he actually earn? (Please write down the calculation process)
Maturity: (2 100- 1600)*5%=25 yuan.
Actual income: 2 100-25=2075 yuan.
1. Application of area calculation of parallelogram, triangle and trapezoid.
1 and * * * soldiers cultivated a parallelogram vegetable field. Its bottom is 24 meters and its height is 16 meters. What is the area of this field?
s=ah 24* 16=384
2. Trapezoidal wheat experimental field with an upper bottom of 86m, a lower bottom134m and a height of 60m. How many square meters is its area?
s =(a+b)* h/2(86+ 134)* 60/2 = 6600
3. Triangular land with a bottom height of 358m and a height of 160m. What is the area of this land?
s=ah/2 358* 160/2=28640
Second, summarize the application questions
1, * * * The transportation company transports a batch of coal. If each truck is loaded with 4.5 tons, it will take 16 cars to transport it at one time. If each truck is loaded with 6 tons, how many cars do you need to transport it all at once?
4.5* 16/6= 12
2. Students put flowers, each with 9 pots, which requires 36 people; If 18 people want to put it, how many pots should each person put?
36*9/ 18= 18
Third, the application of three-step calculation method
Taiyanggou Primary School held a math knowledge contest. There are 60 participants in the third grade and 45 in the fourth grade. The number of participants in the fifth grade is twice that of the fourth grade. How many people took part in the competition in grade three?
45*2+45+60= 195
Fourth, meet the application problems
1, Zhang Ming and Li Hong set out from two places at the same time, facing each other. Zhang Ming walks 50 meters per minute and Li Hong walks 40 meters per minute. 12 minutes later, they met. How many meters are they apart?
(50+40)* 12= 1080
2. The distance between Party A and Party B is 255km, and two cars leave both places at the same time. Car A runs 48 kilometers per hour and car B runs 37 kilometers per hour. Two cars meet in a few hours.
255/(48+37)=3
5. List simple equations to solve practical problems
1. Xiangqun Stationery Factory can produce 250 pencil cases per hour. How many hours can it produce 10000?
Suppose: X hours can produce 10000 pieces.
250x= 10000
x=40
Answer: 40 hours 10000.
Six, about the application of cuboids and cubes, the calculation of surface area and volume.
1. A rectangular iron box, length 18cm, width 15cm and height 12cm. What is the volume of this iron box?
18* 15* 12=3240
2. The side length of the cube is15cm. What is its volume?
15* 15* 15=3375
1, fill in.
(1) There are () simplest true fractions whose denominator is 12, and their sum is ().
(2) One conductor is 45 meters long, which is 14 meters shorter than the other, and the two conductors are * * * () meters.
(3) One conductor is 45 meters long, the other conductor is shorter than it by 17 meters, and the other conductor is () meters long.
(4) Addition and subtraction of fractions with different denominators, first (), then (), and then addition and subtraction.
(5) A batch of fertilizer was shipped 13 on the first day and 25 on the second day, and the remaining batch of fertilizer () was not shipped.
(6) Make the following fractions and decimals reciprocal.
0.75=( ) 25 =( ) 3.42=( )
58 =( ) 2. 12=( ) 4 14 =( )
2. Calculation problems
5 12 +34 + 1 12 7 10 -38 - 18 4 15 +56
12 -(34 -38 ) 56 -( 13 +3 10 ) 23 +56
3. Solve the equation
17+x = 23 45-x = 14 x- 16 = 38
Step 5 solve the problem
(1) There is a piece of cloth. It takes 78 meters to make a coat and 34 meters to make a pair of trousers, leaving 1 12 meters. How many meters is this cloth?
(2) An engineering team built roads, the first week was 49 kilometers, the second week was 29 kilometers, and the third week was less than the sum of the previous two weeks 16 kilometers. How much was repaired in the third week?
(3) In class, students spend 15 hours doing experiments, teachers spend 3 10 hours explaining, and students finish their homework independently in the rest of the time. Assuming that each class lasts for 23 hours, how much time do students spend doing their homework?
fill (up) a vacancy
1.0 m is to divide 1 m into () parts and take () parts.
2. The decimal unit of is (), and it has () such decimal units.
3. Yes, there is one in the room.
4. Fill in the appropriate scores in the brackets.
24 kg = () tons 4 meters 20 cm = () meters.
360m = () km 1 hour = () days.
5.= = = =( )÷9=44÷( )
6. The maximum true score is (), the minimum false score is () and the minimum simplest fraction is ().
7. Divide the 2m-long wood into 7 sections on average, each section is 1 m long, and each section accounts for the whole length.
8.+ means () plus (), and the total is ().
9. Among these fractions,,, and, what can be reduced to a finite fraction is ().
10. Arrange the scores of the following groups in descending order.
,No. () > ()> ()
、4.5()>； ()& gt( )
Second, multiple-choice questions:
1. Among the following figures, not less than ().
a、 1 B、C、
2. Put 5 kg of salt into 20 kg of water, and the weight of salt accounts for () of salt water.
A, B, C,
3. There are () simplest real scores less than.
A, 3 B, 4 C, countless
4. And these two scores ().
A means the same; B, the size is equal; C, the decimal units are the same.
5. If A equals B, then A () B.
A, greater than B, equals C, less than.
Third, the question of judgment.
1.3kg water is as heavy as 1kg water. ()
2. Tons of cotton = tons of iron. ()
3. 1 is the simplest score. ()
4. Because the ratio is very small, the decimal unit of is smaller than that of. ()
5. The true score is always less than the false score. ()
6. The food ratio is large. ()
7. The numerator and denominator of the simplest fraction have no common factor. ()
Fourth, oral calculation.
+0.5 + 3.6+ +
2.4- 1 +3.6 6.43- -0.375
5. Calculate the following questions. (If you can simplify it, try to simplify it. )
1+ - + - - -
2. 15-( - ) 2.85+ +2. 15+ 3.4-(0.25+ )
Sixth, solve the equation.
+x = 5.6 x-= x-( 1.4+)= 1.8
Seven, column calculation.
1.A number is 0.75 more than b number. What is the sum of the two numbers?
2. Subtract the difference of 3.25 from a number, and the result is 2.5. What's this number?
Eight, application questions.
1 class. There are 48 students in 53 classes, including 2 boys1. What percentage of girls are in the class? What is the ratio of boys to girls?
2. To produce the same parts, from 27 pieces in 12 hours to 13 pieces in 6 hours and 19 pieces in 8 hours. Who can do it fastest? Who is the slowest?
3. Build a road with a length of 1500m. If the whole project is completed in the first week and the whole project is completed in the second week, what is the score for completing the whole project?
Wang Lin read a book. On the first day, he finished reading the whole book. The next day and the third day, he read a whole book more than the first day. After three days, how many parts are left in the whole book?
5. There is a rectangle with a circumference of 68 cm, which is known to be 2 cm long and how many centimeters wide.
Responder: Folding Angel ylq- Scholar Level 3 1- 18 10:07.
What are you doing?
Respondent: Xiao's probation period is Grade 1 1-20 13: 12.
Formulas for solving the application problems of fractions and percentages
The unit "1" is known: unit "1"× corresponding fraction = corresponding quantity.
Unit 1 or unit 1 is unknown: corresponding quantity ÷ corresponding score = unit 1.
Formula for finding the fraction (or percentage) of one number and another:
One number ÷ another number = A number is a fraction (or percentage) of another number?
Find out how much one number is more than another:
Excess ÷ unit "1" = how many fractions (or percentages) one number is more than another.
Find out how much one number is less than another:
Small quantity ÷ unit "1"= how many fractions (or percentages) one number is less than another.
(Note: The words "more" and "less" here can also be replaced by words such as "increasing production" and "saving". )
(Note: Example: (1) There are 120 peach trees in the orchard, and the number of pear trees is 20% more than that of peach trees. How many pear trees are there in the orchard?
(2) There are 120 peach trees in the orchard, which is 20% less than that of pear trees. How many pear trees are there in the orchard?
Analysis idea: first find out the unit "1" and determine whether it is known or unknown. If the unit "1" is known, use multiplication; if the unit "1" is unknown, use division. What is the formula of "how much more (less) than who"? "1+(-)"
Formula: (1)120× (1+20%)
(2) 120÷( 1-20%)
Formulas to solve the application problems of discount, profit, interest and tax.
Meaning: "20% off" means: the current price is 20% off the original price; "15% discount" means that the current price is 85% of the original price.
Formula:
Current price = original price × discount (usually written in percentage form)
Profit = selling price-cost
Interest = principal × interest rate× time
After-tax interest = principal × interest rate× time× 80% (note: national debt and education savings are not taxed)
Tax payable = tax payable × tax rate
Formulas and key sentences about the circumference and area of a circle
The ratio of the circumference to the diameter of a circle is called pi. π = c÷d。
Find the perimeter of a known diameter: C = πd Find the diameter of a known perimeter: d = C ÷π.
Find the perimeter of a known radius: C = 2πr Find the radius of a known perimeter: r = C÷π÷2.
Find the area of known radius: S =πr
Find the area of known diameter: r = d÷2.
S = πr
Find the area of the known perimeter: r = C÷π÷2.
S = πr
Semi-circle circumference = C ÷ 2+d (note: semi-circle circumference = 5. 14r, suitable for filling in the blanks)
Semicircular area = S ÷ 2
Divide a circle into several parts evenly and make an approximate rectangle. (See this book)
(1) Area of rectangle = area of circle.
(2) The length of the spliced rectangle = half the circumference (length =)
(3) The width of the spliced rectangle = the radius of the circle (width = r)
Fill in the blanks. (65438 +0 points for each space, ***20 points)
(1) A number consists of three 100, two 10 and five 0.0 1. This number is written as ().
2. 7 tons and 560 kilograms = () tons, 1 hour = () minutes.
(3) decompose BaZi 80 into prime factors, (180 =)
(4), the scoring unit is (), plus a scoring table like ().
Bit gets the smallest prime number.
[5], the ratio of 2.7∶ 1 to the simplest integer is (), and the ratio is ().
A triangle has at least () acute angles.
At one time, a steel cylinder could be cast into () cones with equal bottoms and equal heights.
(8) Remove the rice with a 5-meter cloth. How many meters are left? The formula is ().
Levies, circle is axisymmetric circle, its axis of symmetry is ().
⑽. The number of winners in the primary school mathematics competition is ***30, and the ratio of the number of first, second and third prizes is.
1∶2∶3, and the number of people who won the third prize is ().
⑾ The circumference of a circle is 18.84 cm, and the area of this circle is ().
On the map with the scale of 1: 3000000, the distance from Beijing to Guangzhou is 6.
Cm, the actual distance from Beijing to Guangzhou is about () kilometers.
Two. True or false. (Mark "√" correctly in brackets and "×" incorrectly) (* * 8 points)
The greatest common divisor of (1) 16 and 24 is their least common multiple. ()
(2) The circulating decimal number is 0.5, and the rounding to two decimal places is about 0.55. ()
(3) Fifty trees were planted in the orchard, but three trees did not survive, with a survival rate of 97%.
(4) The number of A is 20% less than that of B, and the number of B is 25% more than that of A.. ()
All six faces of a cube are squares. ()
[6], 3 kg weighs like 1 kg. ()
Once, the distance was fixed, and the speed was inversely proportional to the time. ()
Being, the sum of three consecutive natural numbers is m, then the largest number is (+1). ()
Third, multiple choice questions. (Fill in the serial number of the correct answer in brackets) (65438+ 0 point for each question, ***8 points)
(1) The product of two prime numbers must not be ().
A, prime number b, composite number c, odd number d, even number
(2) If it is a false score and a true score, then ().
a、X5 C、X=5 D、X=6
(3) Xiaohong got on the bus at 9: 40 pm and got off at 8: 0012 the next morning. Her time on the train is ().
A, 10 hour 32 minutes b, 1 hour 28 minutes c, 10 minute 32 minutes.
(4), the triangle area is certain, and the bottom and height ().
A, proportional to B, inversely proportional to C, out of proportion
5. Two cubes with a side length of 4cm are combined into a cuboid, and the surface area of this cuboid is () cm2.
a、 168 B、 192 C、 160
[6] The number of base angles of an isosceles triangle is the degree of vertex angle, and the vertex angle is ().
A、 1200 B、 1350 A、300
(7) It's best to draw a statistical chart, which clearly shows the number of students in each class of grade six in our school.
A, horizontal bar b, dotted line c, fan-shaped
Being, the number of a is 135, (), what is the number of b? This question lacks a condition. If you calculate the number b,
The formula is: 135× (1+). Please fill in the following conditions in brackets.
A, B is B of A, A is more C than B, and B is more than A..
Four. Calculation problem. (***34 points)
1, a number written directly. (6 points)
0. 125+ = 0.6-0.06= 4-3 =
× = 6 ÷3= 1÷ =
2. Find the value of x below. (6 points)
x-0.3×2.4 = 1.54 1∶3.5 =
3. Off-mold calculation. (12)
72.56― 18.74―2 1.26 3.7× +63×
1375- 1702÷23 24÷ 1.6-0.8×0.9
4. Column calculation. (6 points)
(1)24 minus 3 minus 25% of 4, what is the quotient?
2. The number 2.4 is less than a number 7.6. Find this number.
5. The side length of the square in the picture below is 3 minutes. Find the area of the shaded part. (4 points)
Verb (abbreviation of verb) application problem. (5 points for each question, ***30 points)
1, Zhangjiajie department store reduced the price by 20% to sell a sweater, and only sold 96 yuan money. What is the original price of this sweater?
2. Erjiahe Township plans to plant 1346 trees on a barren beach. It has been planted for 7 days, with an average of 103 trees per day. The rest will be planted for 5 days. How many trees will be planted on average every day?
The distance between the two cities is 624 kilometers. A bus and a truck leave from two places at the same time. The average speed of buses is 65 kilometers per hour, and the average speed of trucks is the average speed of buses. How many hours after the two cars left?
4. Xiaohua reads books. I originally planned to read 85 pages a day, and I can read them in 12 days. If he reads 102 pages a day, how many days can he finish it? (Use proportional solution)
5. Cast an iron block with a volume of 3 14 cubic centimeter into a cylinder. The diameter of the cylinder bottom is 10 cm, and the height is how many cm?
6. A grain store sold 720 kilograms of raw rice this month. At this time, the stored rice is exactly 80% of the original rice. How many Jin of raw grain does this grain shop have?
Question 1. The clerk changed a 5 yuan RMB and a 50-cent RMB into 28 yuan RMB with face values of 1 yuan and 1 respectively. How much RMB do you want?
Question 2: There are 50 RMB * * with total face value 1 16 yuan. As we all know, one yuan is more than two yuan. How many RMB are there in three denominations?
Question 3: There are 400 movie tickets from 3 yuan, 5 yuan and 7 yuan, with a value of 1920 yuan, among which 7 yuan and 5 yuan have equal tickets. How many movie tickets are there for each of the three prices?
Question 4: Two kinds of cars are used to transport goods. Each car contains 18 boxes, and each car contains 12 boxes. Now there is a 18 car, worth 3024 yuan. If each case is cheap in 2 yuan, the goods are worth 2520 yuan. Q: How many cars are there?
Question 5. A truck can transport ore 20 times a day in sunny days and 12 times a day in rainy days. Transportation 1 12 times a day, with an average of 14 times a day. How many days are it rainy these days?
Question 6. A batch of watermelons has been delivered and will be sold in two categories, the large one in 0.4 yuan and the small one in 0.3 yuan. In this way, these watermelons are worth 290 yuan. If the price per kilogram of watermelons is reduced by 0.05 yuan, this batch of watermelons can only be sold in 250 yuan. Q: How many kilograms is the watermelon?
Question 7. In the darts competition, it is stipulated that each player gets 65,438+00 points, and each player misses the target and gets 6 points. Each player throws 10 times and scores * * * 152 points, in which player A scores more than player B 16 points. Q: How many times did each player win?
Question 8. There are 20 questions in the math contest. Every time he answers a question correctly, he gets 5 points. If he answers a wrong question, he will not only get no points, but also deduct 2 points backwards. Xiaoming got 86 points in this competition. Q: How many questions did he answer correctly?
X pieces of 1 yuan and (28-x) pieces of 1 angle.
x+0. 1(28-x)=5.5
0.9x=2.7
x=3
28-x=25
A: There are three tickets for Zhang Yiyuan and 25 dimes.
2. Let 1 yuan have x, 2 yuan (x-2) and 5 yuan (52-2x).
x+2(x-2)+5(52-2x)= 1 16
x+2x-4+260- 10x = 1 16
7x= 140
x=20
x-2= 18
52-2x= 12
A: 0 yuan has 20, 2 yuan has 18 and 5 yuan has 12.
3.7 yuan and 5 yuan have X pieces, and 3 yuan has (400-2x) pieces.
7x+5x+3(400-2x)= 1920
12x+ 1200-6x = 1920
6x=720
x= 120
400-2x= 160
A: 3 yuan has 160 and 7 yuan and 5 yuan have 120.
4. Total cargo: (3024-2520)÷2=252 (boxes)
There are x buses and (18-x) cars.
18x+ 12( 18-x)= 252
18x+2 16- 12x = 252
6x=36
x=6
18-x= 12
Answer: Bus No.6, 12.
5. Days = 1 12÷ 14=8 days.
It rained on day X.
20(8-x)+ 12x = 1 12
160-20x+ 12x = 1 12
8x=48
x=6
It rained for six days.
6. Watermelon quantity: (290-250) ÷ 0.05 = 800kg.
There is a big watermelon x kg.
0.4x+0.3(800-x)=290
0.4x+240-0.3x=290
0. 1x=50
x=500
There are 500 kilograms of big watermelons.
7.a score: (152+ 16)÷2=84.
B: 152-84=68 points.
Set armor x times
10x-6( 10-x)=84
10x-60+6x=84
16x= 144
x=9
Set b to y times.
10y-6( 10-y)=68
16y= 128
y=8
A: A has nine times and B has eight times.
8. Suppose he answered question X correctly.
5x-2(20-x)=86
5x-40+2x=86
7x= 126
x= 18
A: He got it right 18.
Example: 1: Unload several cases from the freighter with a total weight of 10 ton, and the weight of each case shall not exceed 1 ton. In order to ensure that these boxes can be transported at one time, how many cars with a load of 3 tons are needed at least?
[Resolution] Because the weight of each box is not more than 1 ton, the weight of each box that one car can transport is not less than 2 tons, otherwise only one box can be put. So five cars are enough, but four cars may not be able to carry all the boxes. For example, if there are 13 cases, then each car can only carry three cases, 13.
Therefore, in order to ensure that all the boxes can be shipped at one time, at least five cars are needed.
Example 2: Intercept 100 short bamboo poles with a length of10 foot respectively. How many raw materials should be used at least? What is the most cost-effective cut?
[Analysis] A bamboo pole with a length of 10 feet should be cut in three ways:
(1) 3 feet 2 and 4 feet 1, the most economical;
(2) three feet three, more than one foot;
(3) four feet and two, the other two feet.
In order to save materials, try to use the method of (1). With 50 raw materials, you can cut 100 3-foot bamboo poles and 50 4-foot bamboo poles. If 50 4-foot bamboo poles are short, it is best to choose method (3), which requires the least raw materials, only 25, and at least 75 raw materials.
Example 3: The lengths of the three sides of an acute triangle are two digits respectively, and they are three consecutive even numbers. The sum of their numbers is a multiple of 7. What is the longest circumference of this triangle?
[Resolution] Because the three sides of a triangle are three consecutive even numbers, their unit digits can only be 0, 2, 4, 6, 8, and their sum is even, and because the sum of their unit digits is a multiple of 7, it can only be 14, and the maximum value of the three sides of a triangle can be 86, 88, 90, so the longest circumference is 86+80.
Exodus 4: Divide 25 into the sum of several positive integers to maximize their products.
[Analysis] Start with a small number shape and find out its rules:
6 divided by 3+3, its product is 3×3=9.
Divide 7 by 3+2+2, and the product is 3×2×2= 12.
Divide 8 by 3+3+2, and the product is 3×3×2= 18.
9 divided by 3+3+3, its product is 3×3×3=27. ……
That is to say, in order to maximize the product of decomposition numbers, 3 should appear as much as possible. When a natural number can be expressed as the sum of several 3' s and 1, one 3' s and 1 should be taken out and then decomposed into two 2' s, so that 25 can be decomposed into 3+3+3+3+2+2.
Example 5: A and B are going to explore the desert. They go deep into the desert for 20 kilometers every day. It is known that each person can carry one person's food and water for up to 24 days. If some food is not allowed to be stored halfway, how many kilometers can one of them go deep into the desert (the last two need to return to the starting point)? What if some food can be stored on the way back?
[Analysis] Suppose A goes back after X days. When A goes back, he leaves the food he needs, and the rest is transferred to B. At this time, B*** has (48-3X) days of food, so X=8. With the remaining 24 days of food, B can only move forward for another 8 days, leaving 16 days of food for him to return, so that B can go to the desert.
If the conditions are changed, the crux of the problem is the food left over in B24 days when A returns. Because 24 days of food can make B go deep into the desert alone 12 days, and the other 24 days of food will provide A and B with a walk back and forth, that is, 24÷4=6 days, so B can go deep into the desert 18 days, that is, one day.
Ex. 6: Every worker and every piece of equipment in two garment factories, A and B, can completely produce suits of the same specifications. Factory A produces tops, pants and only 900 suits a month. Factory B spends a lot of time producing tops and trousers, and just produces 65,438+0,200 suits a month. Now the two factories are jointly producing, trying to produce more suits. So how many more suits are produced each month than in the past?
[Analysis] According to the known conditions, the time ratio of producing a pair of trousers and a coat in a factory is 2: 3; Therefore, the ratio of the number of shirts and trousers produced by a factory in a unit time is 2: 3; It can also be seen that the ratio of the number of shirts and trousers produced by factory B in unit time is 3: 4; A factory is good at producing pants, and B factory is good at producing jackets. The two factories jointly produce, give full play to their respective advantages, and arrange factory B to fully produce jackets. As factory B produces 1 0,200 jackets a month, factory B can produce 1 0,200 ÷ = 210,000 jackets a month, and at the same time, factory A is arranged to fully produce pants.
In order to support production, a factory first fully produced 2 100 pairs of trousers, which required 2 100÷2250 = pieces a month, and then a factory independently produced 900×=60 suits a month, so now the joint production produces more suits every month than in the past.
(2100+60)-(900+1200) = 60 sets.
There are 65,438+0,400 Weiqi pieces today. Party A and Party B play the game of taking Go. Party A takes it first, and Party B takes it later. They take turns eating once. It is stipulated that only 7P(P is 1 or any prime number not exceeding 20) can be taken at a time. Who will win the game in the end? Ask both parties who has a winning strategy.
[Analysis] Because 1400=7×200, the original question can be translated as: There are 200 chess pieces, and both parties take p pieces in turn, and whoever takes the last one wins.
[Solution] B has a winning strategy.
Since 200=4×50, P is either 2 or can be expressed in the form of 4k+ 1 or 4k+3 (k is zero or a positive integer), the strategy adopted by B is as follows: If A takes 2,4k+1 and 4k+3, B takes 2,3,1.
[Description] (1) In this question, B is the "late Mover", so the first Mover does not necessarily have a winning strategy. The key is to look at the "situation" they face;
(2) We can analyze the solution of this problem in this way, and divide all cases-the number of remaining pieces into two categories. The first category is a multiple of 4, and the second category is others. If someone meets the second category when playing chess, then he can go 1 or 2 or 3, and the rest is the first category. If he is faced with the first category when playing chess, he will give the rest to another person.
There is a tour group of 80 people, including 50 men and 30 women. Their hotel has three room types: 1 1, 7 and 5 people. Men and women live in different rooms. How many rooms should they live in at least?
[Analysis] In order to minimize the number of rooms, first arrange 1 1 rooms, so that 50 men arrange 3 1 1 rooms, 2 5 rooms, 1 7 rooms. 30 women should arrange11/room 2 7, 1 5 with * * 10 room.
[practice]
1, the sum of ten natural numbers is equal to 100 1, so what is the maximum possible value of the greatest common divisor of these ten natural numbers? (excluding 0)
2. When the sum of two right-angled sides is constant, which right-angled triangle has the largest area? If the sum of two right-angled sides is 8, what is the maximum area of a triangle?
Five people are each holding a bucket in front of the tap, waiting for water. The time they need to fetch water is 1 minute, 2 minutes, 3 minutes, 4 minutes and 5 minutes respectively. If only one faucet arranges their water intake order reasonably, then the sum of everyone's queuing and water intake time can be minimized. How many minutes is this at least?
4. A pool can be filled with water from two pipes, A and B. Single pipe A needs to be filled for 12 hours and single pipe B needs to be filled for 24 hours. If the pool needs to be filled within 10 hour, and the less time it takes for A and B pipes to be put together, the better. How many hours will it take for A and B pipes to be put together?
5. A highway is littered with 1995 young pioneers to publicize traffic regulations. Ask them where they should be on the expressway after completing the task, so that the total distance from their respective propaganda posts along the expressway to the place of * * * is the smallest.
6. Party A and Party B take turns to write down the natural number not exceeding 10 on the blackboard. The rule is that it is forbidden to write the divisor of the number that has been written on the blackboard. Those who cannot complete the next step are losers. Q: Will the first writer or the last writer win? How to win?
[Question reference answer and train of thought analysis]
1, ∫1001= 7×113, ∴ 7× 13 can be common divisors, so these ten positive integers can be common divisors.
2. For right triangle, the area of isosceles right triangle is the largest under certain conditions. If the sum of two right angles is 8, the maximum area of a triangle is ×4×4=8.
3. There are two ways to minimize the sum of people queuing for water:
(1) The number of people waiting in line should be as small as possible; (2) The queuing time should be as little as possible. Therefore, people who draw water quickly should draw water first, so as to ensure that when there are many people in the queue, everyone will wait less, so * * * needs 5× 1+4×2+3×3+2×4+5=35 (minutes).
4. Since Party A and Party B can't fill the pool within 10 hour when they are separated, it is necessary to have time to put them all together. In order to keep them together for the least time, try to open the pipe A (fast), so that if Party A 10 fills the pool, the rest can only be filled by Party B, which will take at least 4 hours.
5, this problem we can start with the simplest problem, find the law, so as to solve complex problems, and finally * * * position should be in the middle.
6. The first author has a winning strategy. A writes 6 in the first step, and B can only write one of 4, 5, 7, 8, 9, 10, which is divided into several pairs (4, 5), (8, 10) and (7, 9). If b writes one of them,
Do these first, 5. Calculation problem: 3a-2a+4a27a = 7a2+9a0.5st+4+3st-4 = 7% 2st.
2(2ab+3a)-3(2a-ab) = 7ab，3， wenku.baidu/search？ C4 % EA % BC % B6 % C9 % CF & amp； lm = 0 & ampod=0
Children, look in the library. There will be something you need. 2. Go out by yourself
Different version! ! ! ! ! 2. Help me solve 30 calculation problems, 30 equation problems, 15 application problems.
The textbook is Beijing Normal University Edition. ..
I just want to ask for help, because I can't get it out. = _ = ||||| |