A sum of money is shared among three brothers. The eldest receives 7/13 of it and the 13 next receives 2/3 of the remainder. If the youngest brother receives $6, find the sum of money shared.

Remainder = 13/13 - 7/13 = 6/13.

Next-to oldest share = 2/3 * 6/13 = 12/39.

Youngest bro. share = 13/13-7/13-12/39 = 39/39-21/39-12/39 = 6/39 = 2/13.

2/13 * x = 6.00, X = $39. = Sum of money shared.

Let's assume the sum of money shared among the three brothers is represented by X.

According to the given information:
The eldest brother receives 7/13 of the sum of money. So, the eldest brother receives (7/13) * X.
The remainder of the money after the eldest brother receives his share is (1 - 7/13) * X = (6/13) * X.

The next brother receives 2/3 of the remainder. Therefore, the next brother receives (2/3) * (6/13) * X.

The youngest brother receives $6, so we can set up the equation:
(2/3) * (6/13) * X = 6

To find the value of X, we can solve this equation for X.

Multiply both sides of the equation by (3/2)(13/6):
X = 6 * (3/2)(13/6)
X = 6 * (39/12)
X = 19.5

Therefore, the sum of money shared among the three brothers is $19.50.

To find the sum of money shared, we need to work backwards from the given information.

Let's assume the sum of money shared among the three brothers is represented by 'x'.

The eldest brother receives 7/13 of the shared amount:
Eldest brother's share = (7/13) * x

The remainder after the eldest brother receives his share is:
Remainder = x - (7/13) * x = (6/13) * x

The next brother receives 2/3 of the remainder:
Next brother's share = (2/3) * ((6/13) * x) = (4/13) * x

The remainder after the next brother receives his share is:
Remainder = ((6/13) * x) - ((4/13) * x) = (2/13) * x

Finally, the youngest brother receives $6, which is equal to:
Youngest brother's share = (2/13) * x = $6

Now we can solve for 'x' by setting up the equation:
(2/13) * x = $6

To solve for 'x', we multiply both sides of the equation by (13/2):
x = ($6) * (13/2) = $39

Therefore, the sum of money shared among the three brothers is $39.