a father was 25 years older than his son five years ago. if the product of the son and his father's ages then was 900 years. how old is the son now.

  25

Step-by-step explanation:

Let x represent the son's age now. 5 years ago, it was x-5, and the father's age was (x -5)+25 = (x+20).

The product of their ages at that time was 900, so we have ...

  (x -5)(x +20) = 900

  x^2 +15x -100 = 900

  x^2 +15x -1000 = 0 . . . . subtract 900

  (x +40)(x -25) = 0 . . . . factor

  x = -40 or +25 . . . . these values make the factors zero

The son's age now is 25.

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