We can use logic to simplify this into an easy algebraic problem

Lets say X is the starting amount each son receives. And T is the total amount left.

We know the first son and his wife get

X + (T-X)/9

and we know this is equal to T/7

So

X + (T-X)/9 = T/7

X + T/9 - X/9 = T/7

8X/9 = T/7 - T/9

8X/9 = 9T/63 -7T/63

multiply both sides by 9/8

9/8 * 8X/9 = 2T/63 * 9/8

X = 18T/504

504/18 *X = T

28X = T

So T is equal to 28 X.

A Little Logic will make the solution easy.

The Seventh Son gets

X + 6 + (T/7 - (X+6))/9

(The total goes down by 1/7th each time so the total when the sixth sons

turn comes is 1/7 or T/7)

But here is the catch. there cannot be a remainder SO......

(T/7 -(X+6)/9 = 0

Lets get rid of the fractions--if we multiply both sides by 9 we get

(T/7 -(X+6) = 0

T/7- X - 6 = 0

We know T = 28X

28X/7 -X - 6 = 0

4X - X - 6 = 0

3x - 6 = 0

Add 6 to both sides

3x = 6

And so X = 2 and

28X = T

So T = 56

1/7 * 56 means each son got $8.

I sure hope there wasn't a lawyer Eric.

And that this family lived in early 1800's.