Respuesta :
There would be 9 ducks and 3 swans because square root of 9 is 3 and 9+3-12
Answer:
There are 9 ducks and 3 swans in the pond.
Step-by-step explanation:
According to the problem, the number of swans in the pond is equal to the square root of the number of ducks, this can be expressed as
[tex]s=\sqrt{x}[/tex]
Where [tex]x[/tex] represents the number of ducks in the pond.
If the total number of swans and ducks is 12, the expression would be
[tex]s+x=12[/tex]
Now, we replace the first equation in the second one
[tex]\sqrt{x} +x=12[/tex]
Then, we elevate each side to the square power
[tex]\sqrt{x} =12-x\\(\sqrt{x} )^{2} =(12-x)^{2} \\x=144-24x+x^{2} \\x^{2} -25x+144=0[/tex]
Using a calculator, the roots are 9 and 16.
Let's evaluate each value.
For [tex]x=9[/tex], [tex]s=\sqrt{9}=3[/tex], and [tex]9+3=12[/tex], which is true.
For [tex]x=16[/tex], [tex]s=\sqrt{16} =4[/tex], and [tex]16+4=20[/tex], which is false.
Therefore, there are 9 ducks and 3 swans in the pond.
