Answer: 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
[tex]x+y=6------------(1)\\\\2x+4y=16--------(2)[/tex]
Multiply 2 on both sides of equation (1), we get
[tex]2x+2y=12----------(3)[/tex]
Eliminate equation (3) from (2), we get
[tex]2y=4\\\\\Rightarrrow\ y=2[/tex]
Substitute y=2 in (1), we get
[tex]x+2=6\\\\\Rightarrow\ x=6-2=4[/tex]
Hence, there are 4 ducks and 2 sheep.
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,
[tex]x = sheep\\y = duck[/tex]
Therefore:
[tex]x + y = 6[/tex] (total number of heads of animals in Mrs. Jones farm)
[tex]4x + 2y = 16[/tex] (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.
[tex]x + y = 6[/tex] (eqn. 1)
[tex]4x + 2y = 16[/tex] (eqn. 2)
Multiply eqn. 1 by 2.
[tex]2 \times (x + y = 6)\\2x + 2y = 12 $ (eqn. 3)[/tex]
Next, eliminate y by subtracting eqn. 3 from eqn. 2.
Thus:
[tex]2x = 4\\x = 2[/tex]
Thus, the number of sheep in Mrs. Jones farm is 2.
Find y by substituting x = 2 in eqn. 1
[tex]2 + y = 6\\y = 6 - 2\\y = 4[/tex]
Number of ducks = 4
Therefore, there are 2 sheep and 4 ducks in Mrs. Jones farm.
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