Fiona and Greg were assigned a set of logic puzzles. They decided to split the work: each solved half of the puzzles on their own and then they collaborated to solve the remaining half together. Fiona achieved a $70\%$ correct rate on the puzzles she solved alone, and an overall correct rate of $76\%$ for the entire assignment. Greg achieved a $90\%$ correct rate on the puzzles he solved alone. What was Greg's overall percentage of correct answers?