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Historical question: What problem does the "three-fifths compromise" government want to solve?
The history blog website helps you answer this question: the existence or abolition of slavery.

The Three-fifth Compromise was an agreement reached between the South and the Northeast in 1787. Compromise multiplies the actual population of slaves by three fifths as a representative purpose of tax distribution and distribution of members of the US House of Representatives. This compromise was put forward by the members attending the meeting, james wilson and roger sherman.