How many free states existed in 1850 ?

There were 30 states at the beginning of 1850 and 31 at the end. 
At the start: 
15 free states- Maine, Vermont, New Hampshire, Massachusetts, Rhode Island, Connecticut, New York, New Jersey, Pennsylvania, Ohio, Michigan, Indiana, Illinois, Iowa, and Wisconsin 

15 slave states- Delaware Maryland, Virginia, North Carolina, South Carolina, Georgia, Florida, Kentucky, Tennessee, Mississippi, Missouri, Arkansas, Texas, Louisiana, and Alabama 

Then, with the Compromise of 1850, California came into the Union as a free state.