Theory:

Patrick couldn’t believe his luck to have the answer to all of his problems here. He said, “Only if you do all my homework till the end of the semester, that’s 35 days. If you do a good enough job, I could even get A’s.”
Explanation:

It was hard for Patrick to take on that he was so blessed to get a solution to all his difficulties through this tiny man. So Patrick asked elf if he could do his homework till the end of the semester, that is 35 days to support him score ‘A’ grade.
 
Meanings of difficult words:
 
Numbers
Word
Meaning
 1.
Lucky
Fortunate
2.
Problems
Difficulties
3.
Semester
A half or quarter term in school or university
Reference:
National Council of Educational Research and Training (2006). Honeysuckle. Who did Patrick's Homework - Carol Moore (pp. 7-10). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.