Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond.

Question

Out of a group of swans, \(\frac{7}{2}\) times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.

Answer 1

Let’s assume the number of swans in the pond be ‘a’.

Given that, out of a group of swans, \(\frac{7}{2}\) times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water.

So, expressing the total number of swans in a equation, we have

⇒ 7√a = 2a – 4

On squaring both sides,

⇒ 49a = 4a² + 16 – 16a

⇒ 4a² – 65a + 16 = 0

⇒ 4a² – 64a – a + 16 = 0 [By factorisation method]

⇒ 4a(a – 16) – (a – 16) = 0

⇒ (4a – 1)(a – 16) = 0

⇒ a =\(\frac{1}{4}\) or a = 16

Since, number of swans can only be a natural number we can neglect the solution of a = \(\frac{1}{4}\)

Hence, the total number of swans is 16.