# Out of a group of swans, 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.

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

Given, out of a group of swans, 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.

7√a = 2a – 4

Squaring both sides

49a = 4a2 + 16 – 16a

4a2 – 65a + 16 = 0

4a2 – 64a – a + 16 = 0

4a(a – 16) – (a – 16) = 0

(4a – 1)(a – 16) = 0

a can’t be 1/4, thus a = 16

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