Man bought some turkeys and later sold some of them. Find total number of turkeys

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A man bought a number of turkeys at a cost of $60.00, and after reserving
fifteen of the birds he sold the remainder for $54.00, thus gaining 1O¢ a head
by these. How many turkeys did he buy?

Answered question
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Let's assume, man bought x turkeys for $60, thus price per turkey is
 60
____
 x
  He kept 15 turkeys and sold the remainder for 54$ gaining 10 cents per turkey.
 Let's convert this into algebraic expressions
 Remaining number of turkeys = x - 15
 Selling price of x-15 is 54$, so selling price per turkey is
  54
 ____, but he made 10 cents (0.1$) profit per turkey so
  x-15
 54	   60
____  -   ____ = 0.1  ---------(1)
 x-15	   x
 54x-60x+900 = 0.1*x*(x-15)
 10*(-6x+900) = x*(x-15)
 -60x+9000 = x^2-15x
 x^2+45x-9000 = 0 => (x+120)(x-75) = 0
 => x = -120 or x = 75
   Discarding -ve value, the man bought 75 turkeys for 80 cents each
and sold, 60 turkeys (reserving 15 for himself) for 90 cents each making total
profit of 10 cents per turkey

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