Question

There are x ducks in a pond. The number of swans in the pond is equal to the square root of the number of ducks. If the total number of swans and ducks in the pond is 12, find the number of ducks.

Answer 1

There would be 9 ducks and 3 swans because square root of 9 is 3 and 9+3-12

Answer 2

There are 9 ducks and 3 swans in the pond.

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

`s=√(x)`

Where
`x` represents the number of ducks in the pond.

If the total number of swans and ducks is 12, the expression would be

`s+x=12`

Now, we replace the first equation in the second one

`√(x) +x=12`

Then, we elevate each side to the square power

`√(x) =12-x\\(√(x) )^(2) =(12-x)^(2) \\x=144-24x+x^(2) \\x^(2) -25x+144=0`

Using a calculator, the roots are 9 and 16.

Let's evaluate each value.

For
`x=9`,
`s=√(9)=3`, and
`9+3=12`, which is true.

For
`x=16`,
`s=√(16) =4`, and
`16+4=20`, which is false.

Therefore, there are 9 ducks and 3 swans in the pond.