There are $5$ questions: $4$ main questions and $1$ quiz question. $4$ main questions has score $20,\,30,\,30,\,20$ (The sum is $100$). $1$ quiz question equals $50$ points to help the main score. But, the sum of these $5$ questions must not exceed $100$.
The quiz question is optional to work with, but the $4$ questions must be done.
Example of cases:
- If the student answers $4$ main questions correctly they get $100$.
- If the student answers $4$ main questions and $1$ quiz question correctly they get $100$.
- If the student answers $4$ main questions $(20+20+20+20=80)$ they get $80$
- If the student answers $4$ main questions $(20+20+20+20=80)$ and $1$ quiz question $(50)$ they get $100$.
- If the student answers $4$ main questions $(5+10+5+5=25)$ and $1$ quiz question $(50)$ they get $75$.
Attempt:
$$\begin{align} \text{S}=\frac{A}{150}\times 100\\ S&=\text{Score}\\ A&=\text{All possible score} \end{align}$$
But that formula only applies if the student answer the quiz question. How to formulate the score, so with or without answering quiz question the formula holds?
I'm assuming you want a function that caps the score at 100. There's a perfect function for this: $S = \min(A, 100)$.
If $A \leq 100$, this will return the value of $A$, but if the score goes over 100 ($A>100$), then it will return 100.