Originally Posted by
DivideBy0 I assume you want the sons to have equal amounts of money, then the solution is easier than you might think.
Let x = the value of the father's will, then
The first son receives $\displaystyle 1+\frac{1}{7}(x-1)=\frac{x+6}{7}$ dollars.
The second son receives $\displaystyle 2+\frac{1}{7}\left(x-\left(\frac{x+6}{7}\right)-2\right)=\frac{6x+78}{49}$ dollars.
As these are equal, equate and solve for x:
$\displaystyle \frac{x+6}{7}=\frac{6x+78}{49}$
$\displaystyle x=36$
Now it's easy to find the number of sons. Since now we know the first son receives 6 dollars, and all the sons receive the same amount, the man has $\displaystyle \frac{36}{6}=6$ sons.
I can't believe how long I spend looking at functions of functions and trying to turn everything into massive overcomplicated expressions, all the while overlooking this easy solution.