Math Help Forum: A classic riddle

This little riddle is written by the Indian mathematician Bhaskara(1114-1185), in his book Lilivati.
Originally he wrote it to give his keep his daughter occupied with(rather than an unhealthy love-affair)

Out of a flock of geese, ten times the square-root [of the total] went to the Manasa lake when a cloud approached,
one-eighth went to a forest filled with hibiscus,
and three couples were seen playing in the water.
Tell me, maiden, the number of the flock.

It's not perhaps the hardest riddle, but it's a neat one. Also you can easily get stuck if you don't read it correctly, or if you try to think overly-complex!

PS: Don't spoil the fun for everyone else by blurting out the answer. If none has understood it in a week or so, I'll post an explanation

Tricky,

I keep getting fractions of geese

Hehe, as I said... It looks easy, but somehow you end up crunching at it for a while!

I suppose it's pretty safe to post the solution now, as it seems the (little interest that was) has died out

The correct representation of this word-puzzle in mathematics terms follows.
By making x be the number of total geese on the left side, and then putting in the word puzzle on the right we get this:

Lets do the maths then...






144 geese in total

There are two little tricks to this riddle.
Remember that on line 3 you have to use the correct expansion.
On line 5 you have to treat it like any other second degree polynominal.