Detect manually entered numbers and update other formulas accordingly

If I have cell with a value of 5 and a series of numbers that add up to 100 such as 10,15,15,15,15,15,15 where the 10 is manually entered and the 15's are formulas that automatically calculate based on the first manually entered number of 10 (100-10=90/6=15) but I manually change the first 15 to a 10, how do I get the other 15's to automatically update to 10,10,14,14,14,14,14,14?

What formula can determine that one of the numbers which originally had a formula was updated with a manually entered number and then update the other numbers with a formula?