Mrs jones has ducks and sheep on her farm. the animals have a total of 6 heads and 16 legs. how many ducks does mrs jones have? how many sheep does mrs jones have?

Mrs. Jones has 2 sheep and 4 ducks in her farm.

Given that there are:

6 heads and 16 legs belonging to both sheep and ducks own by Mrs. Jones.

Note:

A duck has only 2 legs and 1 head.

A sheep has 4 legs and 1 head.

To solve this word problem, express the given case as algebraic equations as follows:

Let,

Therefore:

 (total number of heads of animals in Mrs. Jones farm)

(total number of  legs of the animals in Mrs. Jones Farm).

Solve the systems of equations to find the values of x and y respectively, using the elimination method.

(eqn. 1)

(eqn. 2)

Multiply eqn. 1 by 2.

Next, eliminate y by subtracting eqn. 3 from eqn. 2.

Thus:

Thus, the number of sheep in Mrs. Jones farm is 2.

Find y by substituting x = 2 in eqn. 1

Number of ducks = 4

Therefore, there are 2 sheep and 4 ducks in Mrs. Jones farm.

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There are 4 ducks and 2 sheep.

Step-by-step explanation:

Let x be the number of ducks and y be the number of sheep.

We know that each duck has 2 legs and each sheep has 4 legs.

Now, According to the given information , we have

Multiply 2 on both sides of equation (1), we get

Eliminate equation (3)  from (2), we get

Substitute y=2 in (1), we get

Hence, there are 4 ducks and 2 sheep.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x