How did the three fifths compromise represent the interests of both southern and northern states

The three fifths compromise was a plan that would benefit both the south who wanted all of their slaves to count towards representation (amount of representitives was determined by population) but they didn't want any of them to count when being taxed per person. Therefore, the three fifths compromise meant 3 out of 5 of the entire slave population would be counted towards representation and the same number would be counted towards being taxed. Both sides agreed because the North who had few slaves would retain their representation while the south would still retain their representation without paying a whole lot of extra money.