[Easy]Divide my uncle's estate!!

[Arjun Shastry]

This was asked recently by one company during test:
When my Uncle in Bombay died recently ,he left a will, instructing his executors to divide his estate of Rs. 1,920,000 in this manner:
Every son should receive three times as a daughter,and that every daughter should get twice as much as their mother
What is my aunt's share?

[Timothy Chen Allen]

Originally posted by Capablanca Kepler:

When my Uncle in Bombay died recently ,he left a will, instructing his executors to divide his estate of Rs. 1,920,000 in this manner:
Every son should receive three times as a daughter,and that every daughter should get twice as much as their mother
What is my aunt's share?

Assuming that A is the number of sons and B is the number of daughters, and "s" is the son's share, "d" the daughter's, and "m" the mother's, the formula for the mother's share would derive as follows:
s = 3d // Son's share is 3 x daughter's
d = 2m // Mom's share is 2 x mother's
As + Bd + m = 1920000
A(6m) + B(2m) + m = 1920000
m = 1920000 / (6A + 2B + 1)
Here is a Java program to show all possible combinations between 0 and 9 sons and/or daughters (assuming only one mother!):

public class Estate {
  private static double ESTATE = 1920000;
  public static void main(String[] args) {
    for (int sons = 0; sons < 10; sons++) {
      for (int daughters = 0; daughters < 10; daughters++) {
        System.out.println("sons: " + sons +
            ", daughters: " + daughters +
            ", mom = " + motherShare(sons, daughters));
      }
    }
  }
  private static double motherShare(int sons, int daughters) {
    return ESTATE/(6 * sons + 2 * daughters + 1);
  }
}