Question: In a math test, there were 20 questions of three levels: easy questions (2 points), medium questions (3 points), and hard questions (5 points). The total score of all questions was 70 points.
The total score of all medium questions and the total score of all easy questions were in the ratio of 9 : 1.
Tai correctly answered all easy questions, half of the medium questions and two-third of the hard questions. How many points did he score in total? Show your work.