Given Data:
The cost for joining the club is: c = $12
The cost for one activity is: a = $ 6
The total amount that she has in her hand is: T = $ 50
let 'n' be the total number of activity that Cassidy able to join.
[tex]\begin{gathered} T=c+n\times a \\ n=\frac{T-c}{a} \end{gathered}[/tex]Substitute values in the above expression.
[tex]\begin{gathered} n=\frac{50-12}{6} \\ n=\frac{38}{6} \\ n=6.33 \\ n\approx6 \end{gathered}[/tex]Thus, Cassidy will be only able to join at most six activities.