There is a pasture, and if there are 24 cows, the grass can be eaten in 6 days.

1) The grass eaten by 24 cows for 6 days is: 24 6 144 These 144 include the original grass of the pasture and the new grass of 6 days. 2) The grass eaten by 21 cows for 8 days is:

21 8 168 These 168 include the grass that was originally in the pasture and the grass that grew new in the pasture. 3) The grass that grows new at 1 day is: (168 144) (8 6) 124) The original grass on the pasture is:

24 6 12 6 725) The new grass grows enough to feed 12 cows every day, and 12 cows minus 12 cows, leaving 4 to eat the grass of the original pasture:

72 (16 12) 72 4 18 (days) So raise 16 cows, and it takes 18 days to eat up all the grass on the pasture.

Equation. Solution: Suppose the amount of grass eaten by each cow per day is x, the amount of grass growth per day is y, and 16 cows eat pasture grass on day z, and the original amount of grass in the pasture is a.

From the question, it can be seen that a+6y = 24*6x(1).

a+8y = 21*8x（2）

a+yz = 16xz （3）

2)-(1), obtain: y= 12x(4), that is: 12 cows eat grass in a day is exactly equal to the daily growth, so to make the grass never finish, grazing up to 12 cows.

3)-(2), obtain: (z-8)y = 8x(2z-21)(5) from (4) and (5) obtain: z=18

A: If you graze 16 cows, you can eat the grass in 18 days.

To keep the grass from running out, graze up to 12 cows.

Suppose the grass that a cow eats in a day is the unit "1".

Then the grass that grows every day is [21*8-24*6] [8-6]=12 units, and it turns out that there is grass is 24*6-6*12=72 units.

To never finish eating, that is, the amount of grass eaten every day is equal to the amount of growth, that is, to:

12 1 = 12 cows.

Equation solution: Let the pasture have a grass amount x, the grass grows y per day, and each cow eats a certain amount of grass per day x+6y) (24*6)=(x+8y) (21*8)x+6y) 6=(x+8y) 7

x=6y, set a maximum of m cattle pasture, and never finish the grass.

x+6y)/(24*6)=y/m

12y/(24*6)=y/m

m=12 (only).

You can write about the plan.

Original: +6 days, new 24*6, 144

Original: +8 days, new 21*8, 168

Let's say a cow eats 1 of grass per day.

Grass growth per day (168-144) (8-6) 12 So the grass that grows every day is just right for 12 cows to eat.

16 cows, 12 days can be eaten, the latter I don't know, obviously impossible.

20 days. The calculation process is as follows:

Let this grassland have grass x, and grass grows every day.

x+25*y=12*25 (1)

x+10y=24*10 (2)

Subtract the two formulas.

15y=60

y=4 is substituted into (2) to get x=200

then (200+20*4) 20=14(head).

It can feed 14 cows for 20 days.

Add 12 heads to eat less for 15 days, and for each additional head to eat less, 14 heads are 2 more than 12 heads, which is less than 25 days.

days, so 14 heads can be eaten for days.

Let this grassland have grass x, and grass grows every day.

x+25*y=12*25(1)

x+10y=24*10(2)

Subtract the two formulas.

15y=60

y=4 is substituted into (2) to get x=200

then (200+20*4) 20=14(head).

It can feed 14 cows for 20 days.

A system of binary linear equations is not used, but a one-dimensional linear equation is used. I've taught the one-dimensional equation in elementary school, so there should be no problem.

Set up a cow to eat one serving of grass a day;

24 cows eat for 6 days" can be eaten in total: 24 6 = 144 (parts), "21 cows eat 8 days" can be eaten in total: 21 8 = 168 (parts), the number of servings of grass growing per day is: (168-144) (8-6) = 24 2 = 12 (parts), the number of parts of the original grass in the pasture: 144-12 6 = 144-72 = 72 (parts), the number of days that the grass in this pasture can be eaten by 16 cows is: 72 (16-12) = 72 4 = 18 (days);

A: The grass on this ranch can feed 16 cows for 18 days

Let's say a cow eats 1 unit of the amount a day.

After eating in 6 days, a total of 6*24 is equal to 144 units, and after eating in 8 days, a total of 21*8 is equal to 168 units, so a day long (168--144) (8-2) is equal to 12 units, so there is originally 144--6*12 is equal to 72 units. Put 12 cows, eat 12 units a day, and 12 units will grow, so you can't finish eating.

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Make each cow graze 1 serving per day.

Then 24 6 1 = 144 parts.

21 8 1 = 168 servings.

168-144) (8-6) = 12 portions 12 portions per day 144-6 12 = 72 portions of grass 72 parts (16-12) = 18 days in pasture.

A: 18 days to eat.

When the number of cattle is not more than 12 and the grass is not exhausted, a maximum of 12 cattle can be raised.

1) Let the amount of grass eaten by each cow per day be a, the amount of grass on the grassland is b, and the amount of grass growing per day is c.

6*24a=6b+c

8*21a=8b+c

Get: b=12a, c=72a, so let's take x days when 16 cows finish grazing x*16a=x*b+c=x*(12a)+72a x=18

2) If you can't eat enough grass, the cow can't eat more grass per day than the grass grows every day. i.e. 12a

So up to 12 cows can be placed.

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The amount of grass that each cow eats per day is 1

So 24 cows ate 6 days and ate 24 6 = 144

21 cows ate 8 days and ate 21 8 = 168

So the pasture grows grass 168-144=24 in two days, and 24 2=12 per day, so the pasture has grass 144-6 12=72

16 cows eat 16 a day and grow 12, 16-12 = 4 less per day, so enough to eat 72 4 = 18 (days).

The comprehensive column formula is (21 8-24 6) (8-6) = 1224 6-12 6 = 72

72 (16-12) = 18 (days).

This problem can be solved quickly by using the method of cow eating grass.

Grass growth rate: (17x30--19x24) 6=9 original grass = (17-9)x30=240

A number of cows eat for 6 days, and let's say x cows eat for 6 days.

x-9)x6+(x-4-9)x2=240 gets x=40, so there were 40 cows.

Analysis and Solution Assuming that the amount of grass eaten by each cow per day is 1, then the sum of the original grass in the pasture and the new grass growing in 30 days is 1 17 30 = 510The sum of the original grass in the pasture and the new grass growing in 24 days is 1 19 24 = 456The new grass growing in a day in pasture is (510-456) (30-24)=9

The original grass in the pasture is 510-9 30 = 240This is the famous Newtonian problem, also known as the cow grazing problem.

Let's say 1 cow eats 1 unit of grass in 1 day

First seek the grass every day: (17 30 19 24) (30 24) 9 Then find the original grass in the grassland: 17 30 9 30 240 If you don't kill 4 cows, then eat grass for 8 days: 240 + 9 (6 + 2) + 2 4 320

There were cattle: 320 (6+2) 40 (only).

A: There were 40 cows

Set each cow to eat 1 serving of grass per day, and the growth rate of the grass:

17 30-19 24) (30-24), = 54 6,9 (portions);

The number of original grasses in the pasture:

17 30-9 30, 510-270,240 (servings);

There were oxen: 240-6 4) (6 + 2) + 4 + 9, 216 8 + 13, 27 + 13, 40 (head);

A: There were 40 cows

So the answer is: 40

Grass for 24 cows in one pasture for 6 daysAmount of grass: 24 6 144 for 21 cows for 8 daysAmount of grass: 21 8 168

Two more days of grass: 168 144 24

The amount of grass grown every 1 day is 24 2 12

The amount of grass that is eaten in the pasture (excluding the cattle that grow grass every day), (21 12) 8 (24-12) 6=72

Then the grass in this pasture can feed 16 cows for 18 days: 72 (16-12) 18 (days).

It takes 12 days to raise 21 cows to eat all the grass on the pasture.

1. General solution:

If you think of the grass that a cow eats in a day as 1, then there is:

The grass that the cow ate for 6 days was: 27 6 162 (These 162 include the grass that was old in the pasture and the grass that grew new in 6 days.) )

The grass that the cow eats for 9 days is: 23 9 207 (These 207 include the grass that was originally in the pasture and the grass that grew new in 9 days.) )

The grass that grows in the sky is: (207 162) (9 6) 15

4) The original grass on the pasture is: 27 6 15 6 72

5) The new grass grows every day is enough for 15 cows, 21 cows minus 15, and the remaining 6 cows eat the grass of the original pasture: 72 (21 15).

72 6 12 (days).

So it takes 21 cows to eat up the grass on the pasture in 12 days.

2. Column equation:

Set the amount of grass eaten by each cow per week, the amount of grass in the pasture, the amount of grass in the pasture, the grass growth rate v, and 21 cows can eat for x days.

6a*27=c+6v

9*23a=c+9v

x*21a=c+xv

Solving the system of equations yields x=12

1) The grass eaten by 27 cows for 6 days is: 27 6 = 162 (these 162 include the original grass in the pasture and the new grass in 6 days. (2) The grass eaten by 23 cows for 9 days is:

23 9 = 207 (This 207 includes the grass that was originally in the pasture and the grass that grew new in 9 days.) (3) The new grass on 1 day is: (207 162) (9 6) = 15 (4) The original grass on the pasture is:

27 6 15 6 = 72 (5) The new grass grows enough for 15 cows every day, and 21 cattle minus 15, leaving 6 to eat the grass of the original pasture:

72 (21 15) = 72 6 = 12 (days).