Hard Problem - Question long so plz read desc

Question

In his will, a factory-owner leaves $80 000, to be shared equally by his sons but hours before his death, he disinherits several sons. The remaining boys then receive an extra $24 000 each. How many sons share the spoils?

Answer 1

Let us assume the remaining number of boys is x, and number of disinherited sons is y, and 24000 is 30% of 80000, so we have:

1/x - 1/(x+y) = .3

Perform fraction substraction:

(x+y)/(x*(x+y)) - x/(x*(x+y)) = .3

y/(x*(x+y))=.3

Multple both sides with the denominator:

y = 0.3 * x * (x+y)

y = 0.3 *x² + 0.3 * x* y

Solve for y, and we have:

y = - (3*x²) / (3*x - 10)

At this point you can do it by hand or by an integer solution equation solver from your favorite graphics calculator or packages like Mathematica or Maple. My solver gave me 5 solutions, but only 2 of them have all positive integer solutions for both x and y:

x = 2, y = 3

x = 3, y = 27

So, both of these solutions work mathematically. We started with 5 sons, and 3 got disinherited, or we started with 30 sons, and 27 got disinherited.

The first solution sounds more sensible, but the 2nd solution is also plausible.