Question

A farmer owns sheep and chickens. All the sheep have 4 legs and the chickens have 2 legs. He has a total of 8 animals, and there is a total of 20 legs. 1) If x is the number of sheep and y is the number of chickens, write a system of equations that models this problem and graph it. 2) Determine the number of sheep and chickens.

Answer 1

2 sheep and 6 chickens

Explanation:

Let the variable S represent the number of sheep and the variable C represent the number of chickens

Since each sheep has 4 legs, S sheep will total 4S legs

Since each chicken has 2 legs, C chickens will total 2C legs

Total legs = 20

4S + 2C = 20 [1]

S + C = 8 [2] (total animals)

Eliminate C term as follows

[1] - 2 x [2]

4S + 2C = 20
-
2S + 2C = 16
--------------------
2S = 4

S = 4/2 = 2

C = 8 - 2 = 6

So there are 2 sheep (for a total of 8 legs) and 6 chickens (for a total of 12 legs)

Answer 2

The system of equations to model the number of sheep (x) and chickens (y) is x + y = 8 and 4x + 2y = 20. Solving this system, the farmer has 2 sheep and 6 chickens.

The farmer's problem of determining the number of sheep and chickens can be modeled with a system of linear equations. Let x represent the number of sheep and y represent the number of chickens. The first equation represents the total number of animals, which is 8:

x + y = 8

The second equation accounts for the total number of legs, which is 20. Since each sheep has 4 legs and each chicken has 2 legs, we can write:

4x + 2y = 20

To solve this system of equations, we can use the method of substitution or elimination. Let's use substitution in this case. First, solve the first equation for y:

y = 8 - x

Now, substitute the expression for y into the second equation:

4x + 2(8 - x) = 20

Simplify and solve for x:

4x + 16 - 2x = 20

2x = 4

x = 2

Now, we find y by substituting x into the first equation:

y = 8 - 2 = 6

Therefore, the farmer has 2 sheep and 6 chickens.