Elementary school math problems ~ answers and analysis

Fill in the blanks:

A 2-meter-long straight cylindrical wood was cut horizontally by 2 decimeters. Compared with the original, the surface area of the remaining cylindrical wood is reduced by 12.56 square decimeter. The original bottom area of cylindrical wood is (3. 14) square decimeter and its volume is (62.8) cubic decimeter. Solution: 2 meters =20 decimeters Let the radius of the bottom of the cylinder fabric be x decimeters. For the solution of 2*2*3. 14x= 12.56, X= 1, so the bottom area is 3.14 *1= 3.14 square decimeter volume: 3.

Add 3 grams of salt and 7 grams of water to the salt water with a salt content of 30%, and the ratio of salt to water in the salt water is (3:7). Solution: Let the salt in raw salt water be 3kg and the water be 7kg. Salt: water = 3k+3: 7k+7 = 3 (k+1): 7 (k+1) = 3: 7.

If the length of a rectangle decreases by 1.5m, or the width decreases by 1.2m, its area will decrease by 6 m2, and the area of this rectangle is (20 m2). Solution: Let the original rectangle be x meters long and y meters wide. Get xy-(x-1.5) y = 6xy-(y-1.5) x = 6, get x=5 y=4, so the rectangular area is: 5*4=20 square meters (expand the equation into a binary linear equation).

For trapezoid, the ratio of upper bottom edge to lower bottom edge is 4: 9. If the bottom surface is reduced by 15cm, it becomes a square, and the area ratio of this square to the original trapezoid is (8: 13). Solution: Let the trapezoid have an upper bottom of 4 cm and a lower bottom of 9 cm. We get 9k- 15=4k, and we get k=3, so the upper bottom of trapezoid = 4K = 12cm, the lower bottom of trapezoid = 9K = 27cm, the height of trapezoid = the side length of square = 9K- 15 = 12cm.

Cut out four largest and equal circles on a square cardboard with a side length of 4 decimeters, and the area of the remaining part is (16-4π or 3.44 square decimeters). According to the actual operation, the radius of the cutting circle is 1. Remaining area = square area-area of four circles = 4 * 4-4 π *1*16-4 π (or =16-4 * 3.14 =/kloc-

The section of a dam is trapezoidal, with an upper bottom of 3m, which is smaller than the lower bottom by 18m, and the height is half that of the lower bottom. The cross-sectional area of the dam is (126 m2). Solution: From the bottom of the topic: 3+ 18 = 2 1m height:1/2 * 21=10.5m, so the dam cross-sectional area is: (3+21).

The subtraction formula is (0.5-(- 1) = 1). Solution: Let the minuend be x, the minuend be y, the difference be Y-X, X+y+y-x= 1 y-x=3y, x=- 1, y=0.5.

Twenty is 20% less than (25). Solution: Let this number be X and get x*( 1-20%)=20, and get x=25.

A number divided by 160+4 and 240+6, the maximum number is (78). Solution: let this number be x, Ax+4= 160 bx+6=240, that is, ax= 156 bx=234 156 and 234, and the greatest common factor is 78. So x=78.

A ship sails from place A to place B at a speed of 30 kilometers per hour, and then returns the same way. If the average speed back and forth is 40 kilometers, should you sail (60) kilometers per hour when you return? Solution: We sail at x km/h, and the distance from A to B is "1". (2/40- 1/30)x= 1，x=60。

Application questions:

To produce a batch of parts, Party A can make 18 pieces per hour, and Party B needs to do it alone 12 hours. Now Party A and Party B cooperate to complete the task. The proportion of parts produced by Party A is 3: 5. How many parts does Party A produce?

Solution: Let Party A and Party B cooperate for x hours.

Judging from the meaning of the question.

Because the proportion of parts produced by both parties is 3: 5, and the working hours are the same.

Therefore, the efficiency ratio of parts produced by Party A and Party B is 3: 5.

So B produces 30 parts per hour.

18x*8/3= 12*30

The solution is x=7.5.

So 18x= 135.

A: A * * * produces 135 parts.

Car A and car B set out from Party A and Party B at the same time and met five hours later. Then, they continued to drive in the same direction for three hours. At this time, there is still135km between A and B, and165km between A and B ... How many kilometers is there between A and B?

Solution: Let car A be X km/h and car B be Y km/h..

(2 * 5-8)(x+y)= 135+ 165

Solution (x+y)= 150.

So 5(x+y)=750.

A: The distance between A and B is 750 kilometers.

Two trains leave from Party A and Party B at the same time, and meet at a distance of 48 kilometers from the midpoint four hours later. It is known that the speed of the local train is 5/7 of that of the express train. What's the speed of the express train and the local train? How many kilometers is it between A and B?

Solution: the express train is set to x km/h, and the local train is set to y km/h. ..

Get 4(x-y)=48*2.

y=5/7x

X=84，y=60。

4(x+y)=576

Attendant: The express train is 84 kilometers per hour, and the local train is 60 kilometers per hour ... The distance between A and B is 576 kilometers.

/kloc-a batch of parts can be completed in 0/2 days. After several days of cooperation, Party B has something to ask for leave. At this time, Party B only completed 3/ 10 of the total task. Party A continued to do it, and it took 14 days from the beginning to the completion of the task. How many days will Party B take leave?

Solution: Let Party A complete part X/day and Party B complete part Y/day.

12(x+y)= 1

14x/ 1 = 1-3/ 10

X= 1/20，y= 1/30。

Therefore, the working days of Party B are: 3/ 10/ 1/30=9 (days), that is, Party B asks for leave 12-9=3 days.

A: B takes three days off.

Wang flew to the library in the mountains to borrow books. He climbed the mountain at a speed of 3 kilometers per hour and returned from the original road at a speed of 6 kilometers per hour. Ask him for the average speed of going up and down the mountain.

Solution: Let the average speed of Wang Fei going up and down the mountain be x km/h.

( 1/3+ 1/6)x = 1 * 2

The solution is x=4.

A: The average speed of going up and down the mountain in Wang Fei is 4 kilometers per hour.

The bus and the van run in opposite directions from the midpoint of the two places at the same time. Five hours later, the bus arrived at A, and the van was 60 kilometers away from B. It is known that the speed ratio of the van to the bus is 5: 7. What is the distance between the two places?

Solution: Set X km/h for passenger cars and Y km/h for freight cars. ..

5(x-y)=60

y=5/7x

X=42，y=30。

So 5(x+y)+60=420.

A: The distance between A and B is 420 kilometers.

There is a batch of goods in the warehouse, and the weight ratio of the transported goods to the remaining goods is 2: 7. If 64 tons are transported, the remaining goods are only 3/5 of the original goods in the warehouse. How many tons of original goods are there in the warehouse?

Solution: Set up a warehouse with X tons of goods.

2/9x+64=( 1-3/5)x

The solution is x=360.

A: The original goods in the warehouse are 360 tons.

Party A and Party B jointly completed 242 machine parts. A it takes 6 minutes to make a part, and B it takes 5 minutes to make a part. When they finished this batch of parts, how many parts did each of them make?

Solution: It takes x minutes to complete the part.

x/6+x/5=242

The solution is x=660.

So a finished part: 660/6 =110bfinished part 660/5= 132.

A: A made 1 10 parts, and B made 132 parts.

In the division formula, both quotient and remainder are 5, and the sum of dividend, divisor, quotient and remainder is 8 1. What are dividend and divisor?

Solution: let the dividend be x and the divisor be y.

Y/x = 5...5, that is, (y-5)/x=5.

x+y+5+5=8 1

X= 1 1，y=60。

A: The dividend is 1 1 and the divisor is 60.

It is known that the speed of the local train is 5/6 of that of the express train. The two trains are heading for each other from Station A and bilibili, and meet at a distance of 4 kilometers from the midpoint. What's the distance between Station A and bilibili?

The conditions are insufficient, but the question type is the same as "two trains leave from two places at the same time and meet at 48 kilometers after 4 hours." It is known that the speed of the local train is 5/7 of that of the express train. What's the speed of the express train and the local train? How many kilometers is it between A and B? "

Solution: the express train is set to x km/h, and the local train is set to y km/h ... The two cars will meet in an hour.

y=5/6x

a(x-y)=4*2

X=…，y=…

So a (x+y) = …

A: What's the distance between Station A and bilibili? ...

Simple calculation:

1000+999-998-997+996+995-994-993+…+ 104+ 103- 102- 10 1

Original formula = (1000+999-998-997)+(996+995-994-993)+…+(104+103-102-)

=4*( 1000/4)

=4*500

=2000