The Answer, thanks to Spider

Great piece  But at least solve the problem of how many slaves a family of four whites needs for the state to gain as much representation in the House of Reps. from each group on the plantation! X times 3/5 = 4, X = 20/3 or 6 and 2/3 slaves equals four whites. So you must have seven slaves, six is too low  (nice little lesson there on rounding up fractional units!).