How did the Constitution balance the interests of the states?

Answer 1

The main controversy was over slavery. Approximately one person in four living in Colonial America in 1787 was of African origin, and most of these were bound in slavery in the Southern states. The compromise reached, after much haggling, was to allow the slave trade to continue for 20 years and then cease. That would mean that slaves could be imported until the beginning of 1808. Also, for purposes of representation in Congress, slaves would count as three fifths of a person in the census. This strange calculation meant that slave states in the South would have over representation in Congress and the presidency for the next 73 years until the American Civil War.
The slavery issue never went away. It came up again and again as new states were added to the union - - the Missouri Compromise of 1820, the Compromise of 1850, the Kansas Nebraska Act in the mid fifties -- but these are beyond the scope of your interest.

Answer 2

read your history book for pity's sake under the parts about compromise and stuff.