### Home > PC > Chapter 5 > Lesson 5.2.2 > Problem5-61

5-61.

Mr. Reader scores his test in a unique way. A student’s score on the exam is directly proportional to the number of questions and inversely proportional to the square root of the number of problems a student misses. Let $S=$ the student’s score, $p=$ the number of problems and $m=$ the number of problems missed.

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 Corina missed $4$. Her score for the exam was $90$. On the same exam, Alex missed $9$ questions. What was Alex’s score?

1. Substitute Corina’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. Reader’s exams are REALLY hard! No one has ever gotten all of the problems correct. Based on his scoring method, what would happen if a student got every problem correct?

What happens when the denominator is $0$?