Suppose you are told that the grade breakdown for a certain college course is as follows: Homework: 15%
Quizzes: 20%
Project: 10%
Tests: 40%
Final Exam: 15%

Submit a discussion board post that answers the following questions.

Write a formula that will compute the final grade for the course, using G to represent the final grade, H to represent the homework average, Q to represent the quiz average, P to represent the project grade, T to represent the test average, and F to represent the final exam grade. Note: Keep in mind how you must write the percents that show the weighting of each category when doing computations!
Now suppose you have the following grades in each category: Homework average - 30, Quiz average - 75, Project grade - 90, Test average - 78, Final exam grade - 75. Use your formula from #1 to compute your final grade in the course. Show your calculation as well as the final answer.
How would your grade have changed in #2 if your homework average had been 90 instead of 30? Discuss this result. Does it surprise you? Why or why not?

Now suppose that you know all of your grades for all of the categories except the final exam. Use your formula and algebra (do not guess & check) to determine whether it is possible for you to make a B (80%) in the course. Your known grades are as follows: Homework average - 100, Quiz average - 60, Project grade - 95, Test average - 75. Explain whether or not it is possible for you to still earn a B, and calculate the grade on the final exam that would be needed, if it is possible. Show all calculations. Again, do not guess at the answer, but use your formula to solve for the answer. If it is not possible to make a B, use your formula to show why it is mathematically impossible.

Each question is worth 5 points, for a total of 20 points. Your answers will be graded for completeness and correctness. This discussion post counts as a quiz grade. (You will not be able to view posts from other classmates until you have created your post. Once you have posted your solution, you will not be able to edit/delete your post.)