Example 7.1.1. Course Grades.
The mechanics syllabus says that there are two exams worth 25% each, homework is 10%, and the final is worth 40%. You have a 40 on the first exam, a 80 on the second exam, and your homework grade is 90.
What do you have to earn on the final exam to get a 70 in the class?
Solution.
Your known grades and the weighting factors are
\begin{align*}
G_i \amp = \left [40, 80, 90, FE \right]\\
w_i \amp = \left [25\%, 25\%, 10\%, 40\% \right ]
\end{align*}
Find final exam score \(FE\) so that your average grade \(\bar{G}\) is 70%.
\begin{align*}
\bar{G} \amp= \frac{\sum G_i w_i}{\sum w_i}\\
70 \amp = \frac{(40 \times 0.25) + (80 \times 0.25) + (90 \times 0.1) + (FE \times 0.4)}{(0.25 + 0.25 + 0.1 + 0.4 )}\\
FE \amp = \frac{70 (1) - (10 +20 + 9)}{0.4} = 77.5
\end{align*}
.