Question

Out of group of swans, 7/2 times the square root of the total number are playing on the shore of a pond. The remaining two are swimming in water. Find the total number of swans.

Answer 1

Let the total number of swans be x. Then,

Number of swans playing in the shore = $\frac{7}{2}\sqrt{x}$

Therefore,

$x=\frac{7}{2}\sqrt{x}+2$

$x-\frac{7}{2}\sqrt{x}-2=0$

$y^2-\frac{7}{2}y-2=0$, where $y^2=x$

$2y^2-7y-4=0$

$2y^2-8y+y-4=0$

$2y(y-4)+(y-4)=0$

$(y-4)(2y+1)=0$

$y=4$

$x=y^2=16$

Hence, the total number of swans is 16.