Given:
The price per student for the admission, m=$5.
Extra amount spent by a student, c=$ 9.
Total amount spent, T=$34.
Let x be the number of students. Then, the expression for the total amount is,
[tex]T=mx+c[/tex]Substitute values and solve for x.
[tex]\begin{gathered} 34=5x+9 \\ 34-9=5x \\ 25=5x \\ x=\frac{25}{5} \\ x=5 \end{gathered}[/tex]Therefore, the number of students is 5.
Option (b) is correct.