Matthias H. answered 06/04/19
Passionate Math, Science tutor who loves sharing his knowledge.
Instead of grade percentages, think about trophies. Imagine that the teacher has 100 trophies for you to earn at the beginning of the school year.
In your question there are now only 10 trophies left for attendance. Therefore you could have earned 90 trophies (100 - 10) so far. Your grade is 65%, meaning you earned 65% of the 90 trophies = 58.5 trophies (65% * 90). If you win all 10 trophies for attendance, you will have 68.5 trophies out of 100 total trophies for a final grade of 68.5%.
Now you may ask: "How many trophies were there for the research paper?"
You know that you earned 58.5 trophies from your "average and final", and your grade was 95%. These 58.5 trophies are 95% of the "average and final" trophies available. So 58.5 / 0.95 = 61.6 trophies for "average and final". Therefore Research paper was worth: 100 (total trophies) - 61.6 (trophies for average and final) - 10 (trophies for attendance) = 28.4 trophies for research paper.
Now replace trophies with % and you know that the research paper was worth 28.4% of the total grade.