The first Noel

Let's take the number of shepherds as $x$ and the number of sheeps as $y$ . We know that shepherd's and sheep's have $1$ head each. So, we can get an equation, $x+y=100----(1)$ But, a shepherd has $2$ legs whereas a sheep has $4$ legs. Hence, we get another equation, $2x+4y=300----(2)$ Multiplying equation $(1)$ with $2$ and subtracting it from equation $(2)$ , we get $2y=100$ $\Rightarrow y=50$ As the number of sheep is $y$ , the answer is $\boxed{50}$ .

x=no. of shepherds y=no. of sheep,

x+y=100( for heads) 2x+4y=300(for legs)

solving ,we get x=50,y=50

Let there be X sheep & Y shepherds. Each sheep has 4 legs & each shepherd has 2 legs. According to the given data: X + Y = 100..........................(i) 4X + 2Y = 300...........................(ii) Solving (i) & (ii) we get X = Y = 50

This problem can be solved easily using algebra to construct the simultaneous equations:

$x + y = 100$

$4x + 2y = 300$

However, I won't solve those. I want to share another approach for this type of problem, which I learnt when I was in primary school, roughly translated as "Temporary Assumption".

Assume for a moment that all 100 heads belong to the sheep. With this assumption, the number of legs must be 400. This exceeds the number of legs given, which is 300.

Now, if we replace 1 sheep by 1 shepherd, the number of legs decreases by: $4 - 2 = 2$ . If we replace 2 sheep by 2 shepherds, the number of legs decreases by 4 and so on. We must continue to replace sheep by shepherds until the total legs reach the given number.

The number of sheep must be replaced by shepherds, a.k.a. the number of shepherds is:

$\frac{400-300}{4-2} = 50$

Hence the number of sheep is:

$100 - 50 = 50$

Let x be the number of sheep and y be the number of shepherds.....then total heads=heads of x sheeps + heads of y shepherds....derfor x+y=100...x sheeps will have 4x legs and y shepherd will have 2y legs derfore total legs=300=4x+2y slving equations we get x=50

Let the number of sheep be denoted by S and the number of shepherds be denoted by H.

Since there are total 100 heads in the field, we have S + H = 100 ....... (1)

Since there are total 300 legs in the field, and since each shepherd has 2 legs and each sheep has 4 legs, we have 4S + 2H = 300 ...... (2)

Solve equations (1) and (2), we get S = 50.

That's the answer!

Let us assume that all $100$ heads belong to shepherds. Then there are $100\times2=200$ legs, which is $300-200=100$ less than the actual amount. For each shepherd that we switch to sheep, there is a gain of $4-2=2$ legs. We need a gain $100$ legs so we need to switch $100\div2=\boxed{50}$ shepherds to sheep.

The number of total legs is 300, while the heads are only 100. Assume the number of shepherds to be x. This makes the number of sheep (100-x). Hence, 2x+4(100-x)=300. Solve the equation to get the correct answer of 50. This is the number of shepherds, subtracted from 100, we get the number of sheeps, which in this case, are also 50.

Lets say the number of sheep is represented by "X" and shepherds by "Y".

Each shepherd and sheep has 1 head each, therefore:

X + Y = 100

If one sheep has 4 legs, and 1 shepherd has 2 legs,then

4X + 2Y = 300

This is because the NUMBER of shepherds and sheep are represented by "X" and "Y" respectively.

Substitute: X + Y = 100 into 4X + 2Y =300 X = 100 - Y

4(100 - Y) + 2Y =300 400 - 4Y + 2Y = 300 -2Y = - 100 Y = 50 Remember that each shepherd and sheep has 1 head each. So if Y = 50, therefore X = 50

Let x be a part of a sheep's body and y be a part of a shepard's body. Taking x and y's heads, x + y = 100. Taking x and y's legs, 4x + 2y = 300. By using elimination method, multiply the first equation by 4. So, 4X + 4Y = 400 subtract,4x + 2y =300 So, 2y = 100 Therefore, y= 50. x=100-50 = 50. Therefore the shepards have 50 sheep.

count legs of shepherds = \frac{2}{6} \times 300 = 100 count head of shepherds = \frac{100}{2} = 50

So the answer is 50

no. of sheeps (let) =x , no.of shepherds(let)=y
now, 4x+3y=300 and x+y=100 solving, x=50

let x the number of shepherds and let y the number of sheep . There are 300 legs in the field. Equate the first equation . 2x+4y=300 There are 100 heads in the field. Equate the 2nd equation. x+y=100. We have 2 equation and two unknown.Solve the equation by elimination . therefore x=50 shepherds and y=50 sheep

Let us take the no. of sheeps as x. Since there are a total of 100 heads, so shepherds are (100-x).

Total no. of legs of the sheep = 4x and Total no. of legs of shepherds = 2(100-x)

According to the problem,

$4x+2(100-x)=300 \implies 4x+200-2x=300 \implies 2x=100 \implies x=50$

So, no. of sheeps = x = $\boxed{50}$

There are 300 legs in the field. Sheep have four legs and shepherds have two legs, so we must split these 300 legs in the ratio 2:4 - $2 + 4 = 6$ $300/6 = 50$ 50 times 2 = 100 and there are 300 legs in the field so we can split the legs into the ratio 100:200.

This means that there are 200 sheep legs in the field. As the ratio of sheep to legs is 1:4 (in other words, for every sheep there are four legs) we must divide 200 by 4 to get the number of sheep.

$200 / 4 = \boxed{50}$

X=Sheep Y=Shepherd First Equation X+Y=100 -Total no. of heads Since Sheep have 4 legs and shepherds have 2 legs Second Equation 4X+2Y=300 -Total no. of legs

By substitution, X=50 and Y=50

Number of the heads: x + y = 100; Number of the legs: 2x + 4y = 100; <=> x = 50, y = 50

let there be x shepherds. Number of sheep=100-x A/Q => 2x + 4(100-x)=300 => 2x + 400 - 4x =300 => 2x = 100 => x=50

I think i have to fulfill 100 heads condition. so, for 200 hundred legs i got 50 sheep and for left 100 legs i got 50 shepherds. so there is total 50 sheep

Its simple

• no.of sheperds = X

  no.of sheeps = Y

• we get 2 eqns.

  X + Y = 100

  2X + 4Y = 300

• Solving we get 50 sheeps and 50 sheperds.

let, x be the number of ships,

and, y be the number of shepherds

we get two equations, x+y= 100 .........(1)

and 4x+2y= 300........................(2)

solving these equations we get, x= 50 , y = 50

therefore, number of ships is, 50

300 legs and 100 heads so assume there are 50 shephards each having 2 legs so, 300 legs - 100 legs = 200 legs. Now we are left with 50 heads and each sheep have 4 legs so, 50*4 legs=200 legs. So the shephards have 50 sheep.