Explain the differences between the virginia plan and the new jersey plan. how were these differences resolved

Both plans involved how the new Constitution would define representation in Congress. The Virginia Plan proposed that the number of delegates be based upon population, thus favoring larger states with more people. The New Jersey Plan proposed that each state have an equal number of delegates, thus favoring smaller states with fewer people. 

Under the Virginia Plan, a state like Virginia would have had a much greater say in Congress than smaller New Jersey since Virginia had a larger population. Under the New Jersey Plan, New Jerseyans would have had a disproportionate say relative to Virginians. Consider this, if each state had two delegates (under the NJ Plan) let's say New Jersey had 500,000 people and Virginia had 1,000,000 (not the real numbers). With two delegates, New Jersey would have had 1 say in Congress per 250,000 voters while Virginia would have had 1 say in Congress per 500,000 voters. 

These differences were resolved by creating a bicameral legislature. Today, the House of Representatives is a remnant of the Virginia Plan. States with larger populations have more seats in the House than those with smaller populations. For example, California has far more Representatives than Wyoming meaning California has a much greater say in the House. The Senate, on the other hand, is a remnant of the New Jersey Plan. Each state has two Senators regardless of population, which means each state has an equal say. Again, California has two Senators and Wyoming has two Senators despite the fact that California is much larger than Wyoming - this gives Wyoming a much greater say per voters than California. No law can pass through Congress without approval from both chambers of Congress, which means that smaller states are not overpowered, while larger states still have the ability to set the agenda.