Update Sum from Total from one list into line of new list

I am trying to find a way to group list items, take the total of a column and have that number updated in another list automatically. So here is the process.

Invoice-- Amount-- Tax

1654 ----22.50 -----5.00

1654---- 27.50----- 5.26

1654---- 20.50----- 4.23

1726 ----21.50 -----4.60

1726---- 27.50----- 5.26

So it then looks like this in the new list.

Invoice-- Amount-- Tax

1654----- 70.50----- 14.49

1726----- 49--------- 9.86

Here's the catch, they need to be able to update the column in List B as Items get deleted. So lets say line 2 from List A gets deleted, we need List B to then look like this

Invoice-- Amount-- Tax--

1654---- 43.00----- 9.23

1726---- 49 --------9.86

My thought process was to group and run the sum on the first list, which is something we can do, and then it is always updated in live time. However, how then do I get that updated SUM from the grouping into the new list.

I did look at http://ift.tt/1aPdcha , however I noticed once I changed a number to zero, or deleted an line item, it did not update list B. So that is why I thought to move to the grouping and totaling, and pulling the total of the grouped item into the new list, and have it updated through a workflow.

Please note I cannot use any third party products in order to achieve this based on the administrative limitations. Just Sharepoint, or Sharepoint Designer and Workflows through there.