Answer
More than $41$ days
Work Step by Step
Let $x$ be the number of days swam to make the membership worth it.
If you have a membership, the cost for $x$ days will be $82+x$, while if you do not purchase a membership the cost will be $3x$. Let's determine teh value of $x$ for which the cost is the same:
$82 + x = 3x$
$2x = 82$
$x = 41$
Therefore, you need to swim more than $41$ days to make the membership worth it.
