There are 50 Olympiad math problems for the 6th grade of elementary school, and there are only the o

Solution: Add together twice, 8 15 safflower + 1 2 yellow flower + 8 15 white flower = 40 + 44 = 84 flowers 1 formula;

If you take 1 2 each, that is, 1 2 safflower + 1 2 yellow flower + 1 2 white flower = 80 flowers 2 formula.

1 - 2 1 30 safflower + 1 30 white flowers = 4 --- safflower + white flower = 120 3 flowers.

Then yellow flowers = 160-120 = 40 flowers.

According to the title: 1 3 safflower + 1 4 yellow flower + 1 5 white flower = 44 --4 formula.

1 5 safflower + 1 4 yellow flower + 1 3 white flower = 40 --5 formula.

4-5 gives 2 15 safflower-2 15 white flower = 4--- safflower - white flower = 30 6 formula.

From formulas 3 and 6: red flowers = 75 flowers, white flowers = 45 flowers.

Set red, white, and yellow flowers each x, y, and z flowers.

Set red flowers x flowers, white flowers y flowers, yellow flowers z flowers

The columnar formula is x+y+z=160

x*1/5+y*1/4+z*1/3=40 ②

x*1/3+y*1/4+z*1/5=160-116 ③

Solution: y=160-x-z

x*1/5+(160-x-z)*1/4+z*1/3=40 ④

x*1/3+(160-x-z)*1/4+z*1/5=44 ⑤

x/5+40-x/4-z/4+z/3=40

x/20)+(z/12)=0

z/12=x/20

z=(x/20)*12

z=3x/5

Substitute z=3x 5 into x*1 3+(160-x-z)*1 4+z*1 5=44

then is equal to x 3+40-x 4-z 4+z 5=44

x/12-z/20=4

x/12=4+z/20

x/12=4+(3x/5)/20

Find the result of x, and then substitute to find y and z

Set safflower x, white flower y, yellow flower z, then.

x+y+z=160 x 5+y4+z=160-120 x 3+y4+z5=160-116.

Set safflower, hundred flowers, and yellow flowers as a, b, and c flowers, and a total of 160 red flowers, white flowers, and yellow flowers, then a+b+c=160

If you take away 1 5 of the red flower, 1 4 of the yellow flower, and 1 3 of the white flower, a total of 120 flowers, then a 5 + b 4 + c 3 = 160-120 = 40;

If you take away 1 3 of the red flower, 1 4 of the yellow flower, and 1 5 of the white flower, a total of 116 flowers, then a 3 + b 4 + c 5 = 160-116 = 44;

The solution yields a=75, b=45, c=40

Set red, white, and yellow flowers each x, y, and z flowers, which are derived from the title.

x+y+z=160

1.The ratio of the bottom area of the two cuboid containers A and B is 4:3. The water surface of container A is 4 cm higher than the water surface of container B, and the same amount of water is poured into both containers, which happens to be 25 cm deep. How deep is the water in the original container A?

Solution: Special value method.

The bottom area of the two containers is 4x and 3x respectively.

From the inscription: A container water volume: 4 x 25

Container B water volume: 3x 25

Volume of water 25x cubic centimeters.

That is, "A is 4 cm higher than the water surface of B", that is, the volume is 25 x cubic centimeters higher.

If the surface of water A is originally y centimeters high, then the surface of water B is (y 4) centimeters.

4xy－3x（y－1）＝25

Solution: y 13 or 16

Answer: It turns out that the depth of water in container A is 13 or 16 cm.

2.A steel mill directly presses the steel plate with molten steel, if the mass of the molten steel per square meter is kilograms, and the loss is 5% when pressing, Q: How many meters is the length of the steel plate when pressing the steel plate with a width of 1 meter and a thickness of 10 cm with tons of molten steel?

The mass of a steel plate with a length of 1 meter, a width of 1 meter, and a thickness of 10 cm is 1*1*kg.

The ton of molten steel is kilogram after removing the loss.

Therefore, the length of the steel plate = 44460 780 = 57 meters.

3.A ship travels 60 kilometers downstream, 32 kilometers against the water for 5 hours, and the current speed is known to be 2 kilometers per hour.

Let the hydrostatic velocity be x, then there is the equation: [60 (x+2)]+32 (x-2)]=5, and finally we get x1=18, x2=, because x2 is less than the velocity against the water, so x=18

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7. There are 1,100 male and female employees, of which all male and female workers can complete the same work in the same number of days; If the number of male workers and the number of female workers are reversed, then all men will need 36 days to complete the work in 25 days.

8 There are two clocks A and B, A is 5 minutes slower than standard time every day, and B is 5 minutes faster than standard time every day, and the two minutes are exactly aligned at 0:00 on March 15 If it is known that at a certain time, the hour and minute hands of B and A coincide separately, and from March 15 to this time, the hour and minute hands of B coincide 10 times more than that of A clock, then what is the standard time at this time?

9 The ratio of the number of the first team and the second team is 3:4, and the ratio of work efficiency per person is 5:4, and the two teams accept two projects with exactly the same workload and conditions at the same time, and the second team completes the project 9 days earlier than the first team Later, a new team is formed by the first team of workers and the second team of workers, and the rest of the workers form a new second team The two new teams accept two projects with exactly the same workload and conditions at the same time, and the new second team completes 6 days earlier than the new first team Try to find the ratio of the workload of the two projects before and after?

1. There are two baskets of apples, there are 80 in basket A and 32 in basket B, take out 14 of them from basket A and put them in basket B each time, how many times can you make the number of apples in the two baskets the same?

2. There are four classes in the fifth grade of Chengnan Primary School, with an average of 44 students in each class, including 85 in the 51st class and 52nd class, 88 in the 52nd and 53rd classes, and 87 in the 51st and 53rd classes.

3. It takes 10 hours for the master to do a batch of parts, and 15 hours for the apprentice to do it alone, and it is known that the master processes 20 more per hour than the apprentice. Q: How many hours does it take for the master and apprentice to work together on this batch of parts?

4. Red Star Garment Factory wants to process 1500 pieces of tops, and plans to process 150 pieces per day, and after 3 days, the work efficiency has been improved, and 175 pieces are processed per day. In this way, it was done a few days earlier than originally planned?

5. On Children's Day, the students made paper flowers, Xiaohua bought 7 pieces of red paper, Xiaoying bought 5 pieces of yellow paper with the same red paper, and the teacher divided the papers equally among Xiaohua, Xiaoying and two other students, and the other two students paid the teacher a total of 9 yuan. Question: How does the teacher give the 9 yuan to Xiaohua and Xiaoying?