How do you divide an amount by 4 with one amount getting an additional 15%

Question

I am dividing money for an estate and the trustee gets an additional 15% for looking after finances. There are four people including the trustee to divide the money between.

Answer 1

If each person gets $x dollars, and the trustee gets $1.15x, for a total of $y, the formula for y as a function of x is:

 

   y = x + x + x + 1.15x

   y = 4.15x

 

So, x = y / 4.15      [this gives x as a function of y]

 

Example:  If the estate evaluates to $100,000, then

   y = x + x + x + 1.15x

   y = 4.15x

  100000 = 4.15x

and

   x = 100000 / 4.15

   x = 24096.39         [rounded]

      and the trustee gets:

   1.15x = 1.15(24096.39)
   1.15x = 27720.83     [subtract:  $100000 - 3*24096.39]

 

Check:

     $24096.39 + $24096.39 + $24096.39 + $27710.83  =  $100,000

Answer 2

Each person would get x dollars

 

The trustee would get:

 

  x dollars plus 15% of x

 

= x + .15x

 

= 1.15x

 

You would divide it as:

 

$x, $x, $x, $1.15x