A typical cow grazing problem... Urgently needed to be solved in one day!!!! It is best to explain

According to your question, it seems that there is no solution. Because days are integer units, but the result is a decimal place with no zero digits after the decimal point. Solution: Set:

Every 1 cow eats x grass per day, the pasture reduces the amount of grass per day to y, and 10 cows eat 100% of the grass for z days.

Then, there is a system of ternary linear equations: {

33x*5+5y＝1

24x+6+6y＝1

10x*z+y*z＝1

As the weather gets colder, the grass on the pastures is decreasing at a constant rate. The grass on the pasture is known to feed 33 cattle for 5 days or 24 for 6 days. How many cows can be fed for 10 days on this pasture?

How many cows eat for 10 days?

How many cows eat for 10 days?

Due to the gradual colder weather, the grass on the pasture decreases at an even rate every day. It was calculated that the grass on the pasture would feed 20 cows for 5 days, or 16 cattle for 6 days. So, how many days is enough for 11 cows?

Landlord, you copied the wrong question, there is wood! There is wood! There is wood!

Let's say each cow eats x per day and minus a per day

165x+5a=144x+6a

a=21x, so total grass 270x

10 cows plus 21 cows per day minus the grass eaten by 21 cows equals 31 cows.

270x 31x is a few days.

Well, not necessarily...

Suppose the grass that grows every day is eaten by x cows, and 10 cows can be eaten in a day.

33-x)*5=(24-x)*6 yields: x=-21

33-x)*5=(10-x)*y gets:y=

Let's say each cow eats x per day and minus a per day

33*5x+5a=24*6x+6a

a=21x, so the total amount of grass is 270x

minus a = 21x per day

270x (10x+21x) is approximately equal to 8

Send you the formula. Two 1(Number of cows, days of grazing more - number of cows, number of days of grazing) (number of days of eating more - days of eating less) = the amount of new grass growing in the grass per day.

2.Number of cattle days of grazing - new growth per day Number of days of grazing = amount of original grass in the grass.

The grass decreases by 33*5-24*6=11 in one day10 cows can eat x days, 10x+11x=33*5; x = 55 for 7 days.

The problem of cattle grazing, also known as the problem of growth and decline or Newton's pasture, was proposed by the great British scientist Newton in the 17th century. The condition of a typical cow grazing problem is to find how many cows can eat the same grass by assuming that the growth rate of grass is fixed, and the number of days it takes for different numbers of cattle to eat the same grass is different. Because the number of days eaten is different, and the grass grows every day, the stock of grass constantly changes with the number of days the cow eats.

There are four basic formulas commonly used to solve the problem of cattle grazing, which are:

1) Set the amount of grass a cow eats in a day to "1".

The growth rate of the grass (the corresponding number of cows eat more days the corresponding number of cows eat less days) (the number of days eaten more and the number of days eaten less);

2) The amount of original grass, the number of cattle heads, the number of days eaten, the growth rate of grass, the number of days eaten; `

3) the number of days eaten, the amount of original grass (the number of cows, the growth rate of grass);

4) The number of cattle heads, the amount of grass, the number of days eaten, and the growth rate of grass.

These four formulas are the basis for solving the problem of growth and decline.

Since the grass is constantly growing in the process of grazing in the process of cattle grazing, the key to solving the problem of growth and decline is to find ways to find invariants from change. The original grass on the pasture is unchanged, and although the new grass is changing, the amount of new grass growing every day should be the same because it grows at a uniform rate. It is because of this invariant that the above four basic formulas can be derived.

The problem of cattle grazing is often given that different numbers of cattle eat the same grass, and the field has both the original grass and the new grass that grows every day. Due to the different number of cows that eat grass, find out how many days the grass in the field can be eaten by several cows.

The key to solving the problem is to figure out the known conditions, conduct comparative analysis, and then find the number of new grass growing every day, and then find the amount of original grass in the grassland, and then solve the problem that the question is always asked.

The basic quantitative relationship for this type of problem is:

1.(Number of cows, days of grazing more - number of cows, number of days of grazing) (number of days of eating more - days of eating less) = the amount of new grass growing in the grass per day.

2.Number of cows Grass days - new growth per day Number of grass days = original grass in the meadow.

How to solve multiple meadows.

For the problem of "cattle eating grass" in multiple grasslands, in general, find the least common multiple of multiple grasslands, which can reduce the difficulty of calculation, but if the data is large, it is relatively simple to unify the area as "1".

Newton's problem, commonly known as the "cow grazing problem", is that the cow eats grass every day, and the grass grows evenly every day. There are four main steps in the problem-solving process:

1. Find the amount of grass grown every day;

2. Find out the original amount of grass in the pasture;

3. Find the actual amount of grass consumed every day (the amount of grass eaten by cattle -- the amount of grass grown = the amount of grass consumed);

4. Finally, find the number of days that can be eaten.

The amount of grass was originally A, the grass grew B every day, and each cow ate C every day. Let the cattle cart be x and the number of days be y, then.

a+by=x*bc

You can find the relationship between a, b, and c by bringing them in separately, and then you can find the quantity.

Number of days eaten = amount of original grass (number of cattle head - growth rate of grass);

Seeking new grass first = total time difference.

Seek old grass again = total amount - new grass.

Number of days eaten Original amount of grass (number of cow heads, growth rate of grass), number of cattle heads, original amount of grass, number of days eaten Grass growth rate.

There are four basic formulas commonly used to solve the problem of cattle eating grass, which are (1) the growth rate of grass, the corresponding number of cow heads, the number of days eaten more, the corresponding number of cow heads, and the number of days eaten less (more days eaten and fewer days eaten);

2) The amount of original grass, the number of cattle heads, the number of days eaten, the growth rate of grass, the number of days eaten; 3) the number of days eaten, the amount of original grass (the number of cows, the growth rate of grass);

4) The number of cattle heads, the amount of grass, the number of days eaten, and the growth rate of grass.

1) Set the amount of grass a cow eats in a day to "1".

1) the growth rate of the grass (the corresponding number of cows, the number of days eaten more, the corresponding number of cows, the number of days eaten less) (the number of days eaten more, the number of days eaten less);

2) The amount of original grass, the number of cattle heads, the number of days eaten, the growth rate of grass, the number of days eaten; 3) the number of days eaten, the amount of original grass (the number of cows, the growth rate of grass);

4) The number of cattle heads, the amount of grass, the number of days eaten, and the growth rate of grass.

Growth = (long time number of cattle heads for a long time - short time number of cattle heads for a short period of time) (long time - short time);

Total grass = long time number of cattle heads for a long time - growth over a long period of time.

The growth rate of the grass (the corresponding number of cows eat more days the corresponding number of cows eat less days) (the number of days eaten more and the number of days eaten less);

The amount of original grass The number of cattle heads The number of days eaten The growth rate of the grass The number of days eaten; Number of days eaten = amount of original grass (number of cattle head - growth rate of grass);

The number of cattle heads, the amount of grass, the number of days eaten, and the growth rate of grass.

"Cattle eat grass problem", cattle eat grass every day, and the grass is growing evenly every day. There are three main steps in the problem-solving process:

1 Find the growth rate of the grass.

2. Find out the original amount of grass in the pasture;

3 Finally, find the number of days to eat or the number of heads of the ox.

Related formulas. The growth rate of the grass (the corresponding number of cows eat more days the corresponding number of cows eat less days) (the number of days eaten more and the number of days eaten less);

The amount of original grass The number of cattle heads The number of days eaten The growth rate of the grass The number of days eaten;

Number of days eaten = amount of original grass (number of cattle head - growth rate of grass);

The number of cattle heads, the amount of grass, the number of days eaten, and the growth rate of grass.

I hope you can use this example to understand how to solve the cow grazing problem with binary linear equations!

A uniformly grown meadow that can feed 27 cows for 6 weeks, or 23 cows for 9 weeks, how many weeks will 21 cows eat?

Solution: The original grass amount of the grassland is x, and the amount of new grass per week is y, which can be used for 21 cattle to eat a week.

According to the equation of the equiquantity relationship (the total amount of grass eaten by the cow: the number of heads of the cow = the amount of original grass + the amount of new grass per unit time), I hope you can understand this equivalence relationship thoroughly.

27×6=x+6y ①

23×9=x+9y ②

Solve the equation to get:

x=72y=15

Again, using the sub-column equation of the total amount of grazing cows grazing:

21a=72+15a, which gives a=12

A: Enough for 21 cows for 12 weeks.

1.(The number of cows destroying the town, the number of days that eat more grass - the number of cows, the number of days that eat less grass) (the number of days that eat more - the number of days that eat less) = the amount of new grass growing every day.

2.Number of cattle days of grazing - new growth per day Number of days of grazing = amount of original grass in the grass.

There is a pasture that is overgrown with pasture grass that grows at a uniform rate every day. This pasture can feed 17 cows for 30 days or 19 cows for 24 days. After 6 days, 4 cows died, and the remaining cattle ate the grass for 2 days, and the number of cattle was found.

1) the growth rate of the grass (the corresponding number of cows, the number of days eaten more, the corresponding number of cows, the number of days eaten less) (the number of days eaten more, the number of days eaten less);

2) The amount of original grass, the number of cattle heads, the number of days eaten, the growth rate of grass, the number of days eaten; 3) the number of days the cow eats the amount of grass (the number of cows, the growth rate of the grass);

4) The number of cattle heads, the amount of grass, the number of days eaten, and the growth rate of grass.

Digital Law:

1) the growth rate of the grass (the corresponding number of cows, the number of days eaten more, the corresponding number of cows, the number of days eaten less) (the number of days eaten more, the number of days eaten less);

2) The amount of original grass, the number of cattle heads, the number of days eaten, the growth rate of grass, the number of days eaten; 3) the number of days eaten, the amount of original grass (the number of cows, the growth rate of grass);

4) The number of cattle heads, the amount of grass, the number of days eaten, and the growth rate of grass.

Equation method: A cow can eat the grass in day B, cow C can eat the grass in day D, and N cow can eat the grass in day W? (N or W is only one unknown, as the case depends, while ABCD is known).

Suppose a cow eats m grass in a day, n cows can eat all the grass in w days; The original amount of grass is y, and the daily growth of grass is x, and the following equation is obtained:

y=(a x)b y=(c x)d y=(n x)w or.

abm=y+bx cdm=y+dx nwm=y+wx

The solution is (n= or w= ) y= x=

1) the growth rate of grass (the corresponding number of cow heads, the number of days to eat more, the corresponding number of cow heads, the number of days to eat less) (more days to eat old celery, less days to eat);

2) the amount of original grass, the number of cattle waiters, the number of days eaten, the growth rate of grass, the number of days eaten; 3) the number of days eaten, the amount of original grass (the number of cows, the growth rate of grass);

4) The number of cattle heads, the amount of grass, the number of days eaten, and the growth rate of grass.

Increase = (bull head time bull head time) time difference.

Original amount = (bull head increase) time.

Bull head = original amount of time + addition of brightness.

Time = original amount (bull head increase).

At the same time, it should be noted that the problem of cattle grazing is a special form of engineering problems, and the key to grasping the amount of raw grass and the growth rate of grass is not to sell and resist change, and the key is to determine two constant amounts.

And set the speed of the cow grazing to "1".

Cows eat grass"The key to asking the question:

1.The amount of grass on the pasture is a

2.The amount of grass grown in the pasture per day b

3.Cattle eat the amount of grass that is changed every day

A + B * number of days = number of cattle * number of days eaten * c

Each cow eats x per day, and the growth rate per mu per day is y, 10*30*x = 5 + 30*5*y = > 60*x = 1 + 30*y

28*45*x = 15 + 45*15*y => 84*x = 1 + 45*y

x = 1/12, y = 2/15

The third plot of land is eaten by Z cows for 80 days.

z*80*x = 24 + 80*24*y => z = 42

This is a binary equation ... Maybe I didn't learn the Olympiad in elementary school).

If the amount of grass eaten by each cow per day is 1, the total amount of grass per mu for 30 days is: 10*30 5=60;The total amount of grass per mu for 45 days is: 28 * 45 15 = 84 then the amount of new grass per mu per day is (84-60) (45-30) = the amount of original grass per mu is, then the amount of original grass per mu is 12 * 24 = 288, the amount of new grass for 80 days of 24 mu is 24*, the total amount of grass for 24 mu and 80 days is 3072 + 288 = 3360, and all 3360 80 = 42 (head).

10 cows can eat 5 mu in 30 days can launch 30 cows to eat 15 mu in 30 days, according to 28 cows eat 15 mu in 45 days, you can launch 15 mu of new grass per day (28 45-30 30) (45-30)=24;15 acres of original grass: 1260-24 45=180;15 acres of 80 days need cattle 180 80 + 24 (head) 24 acres need cattle: (180 80 + 24) * (24 15) = 42 heads.