1. First give $1 to manager, and 1/7th of the remaining to the eldest child.
2. Now give $1 to the manager and 1/7th of the remaining to second oldest child and so on.....
3. After giving the money to the seventh (youngest) child, divide the remaining money among the seven stepchildren equally.

• The ages of each of the seven children are different, and:
• Each of the 15 individuals received a positive integer number of dollars

I don't know if this would help in the analysis, but the next few solutions for the current problem (that is, beyond the minimum amount) have the following for the initial amount and the amount left for each stepchild:

 init amt   each stepchild
  6588338    319926
 12353139    599862
 18117940    879798