Mr. and Mrs. Traver went bowling with Mr. and Mrs. Greene. They all bowled one game, and no two of them had the same score. The combined score of Mr. and Mrs. Traver was 187, the same as that of Mr. and Mrs. Greene. You will be provided statements below that you should take as true, and from them, you must determine which first name (one is Joe) matches with which last name. You must also determine each bowler's score.

Fred's score was lower than the average score, but he did not have the lowest score of the four bowlers.
Karen's score was three points lower than Nancy's.
Mr. and Mrs. Traver's final scores had only one point difference between them.
The average score of the two women was two points lower than the average score of the two men.
Based on the above information, you must complete the following chart correctly in order to earn your extra credit:
last name score
Karen:
Fred:
Joe:
Nancy: