ANSWER
[tex]\begin{gathered} 30=\frac{20m+40}{m} \\ 4\text{ months} \end{gathered}[/tex]
EXPLANATION
It costs $40 upfront to join the club and $20 per month.
Let the number of months be m.
This means that the equation that represents the equation that represents the total cost is:
[tex]C=20m+40[/tex]
The average cost of joining the club is the total cost divided by the number of months.
That is the average cost will be $30 when:
[tex]30=\frac{20m+40}{m}[/tex]
To find the number of months it will take for the average cost per month of joining the swimming club to be $30, we have to solve for m:
[tex]\begin{gathered} 30=\frac{20m+40}{m} \\ 30m=20m+40\text{ (multiply both sides by m)} \\ \Rightarrow30m-20m=40 \\ 10m=40 \\ m=\frac{40}{10}\text{ (divide both sides by 10)} \\ m=4 \end{gathered}[/tex]
It will take 4 months.
