So here is the class breakdown (an A is 90%):
5% Classwork
15% Homework
20% Mean Quiz Score
15% Test 1
15% Test 2
15% Test 3
15% Final Exam
And there is a catch, which is why I need help figuring this out: The grade you get on your final exam will replace your lowest test score (if it benefits you).
So here are my scores:
5% ---- Classwork: 250/250 points
15% ---- Homework: 2,350/2,350 points
20% ---- Mean Quiz Score: 80/80 points
13.2% ---- Test 1: 88/100 points
7.845% -- Test 2: 34/65 (lol I have a good excuse for this)
13.5% --- Test 3: 90/100
Final: Not yet taken (accounts for 15%)
So the grade I get on the final, assuming it is beneficial for me, will count for 15% of my grade AND it will replace the grade of my lowest test score (test 2). So for example: If I get 13% on the final, the grade for test two will increase to 13% as well.
So my question is, what is the minimum grade that I need to get on the final so that I can get an A in the class?
Would it be 11.7%?
If you get below a 34/65 on the final, then you can easily check that you'll end up with at most an 82.392% in the class.
If you get above a 34/65 on the final, then Test 2 will be worth 0% of your grade and the final will be worth 15%+15% = 30% of your grade.
So, in this case, your grade will be:
$5 \cdot \dfrac{250}{250} + 15 \cdot \dfrac{2350}{2350} + 20 \cdot \dfrac{80}{80} + 15 \cdot \dfrac{88}{100} + 0 \cdot \dfrac{34}{65} + 15 \cdot \dfrac{90}{100} + 30 \cdot x$
where $x$ is your grade on the final. Now, simply set this equal to $90$ and solve for $x$.