What did the delegates do to solve the problem of how many representatives each state could have

This issue all goes back to the Constitutional Convention, when there was an issue of big states vs. small states. After a heated debate, the Great Compromise was proposed by Roger Sherman, which created a bicameral legislature. Each states would have equal representation in the Senate (satisfied the small states) and the size of the population of each state would determine the state's representation in the House of Representatives (satisfied the big states). There is also a similar case in the state of Alabama in which the state legislature were apportioned and assigned to districts, based on populations. This supreme court case is known as Reynolds v. Sims. (GOOGLE)