### Home > PC3 > Chapter 7 > Lesson 7.1.1 > Problem7-6

7-6.

Mr. Nguyen scores his test in a unique way. A student’s score on the exam is directly proportional to the number of problems on the exam and inversely proportional to the square root of the number of problems a student misses. Let $S=\text{the student’s score}$, $p=\text{the number of problems on the exam}$ and $m=\text{the number of problems missed}$. Homework Help ✎

1. Write an equation that calculates a student’s score. Do not forget the constant of proportionality.

$S(q)=\frac{kp}{\sqrt{m}}$

2. On the last exam, there were $25$ questions and Saadia missed $4$. Her score for the exam was $90$. On the same exam, Alex missed $9$ questions. What was Alex’s score?

1. Substitute Saadia's information into the equation in part (a) and solve for $k$.
2. Rewrite the equation with the known $k\text{-value}$.
3. Determine Alex's score.

3. Mr. Nguyen’s exams are REALLY hard! No one has ever gotten all of the problems correct. Based on his scoring method, what will happen if a student gets every problem correct?

What happens when the denominator is $0$?