Question

How do I set this up

Answer 1

To justify the yearly membership, you want to pay at least the same amount as a no-membership purchase, otherwise you would be losing money by purchasing a yearly membership.  So set the no-membership cost equal to the yearly membership cost and solve.

no-membership costs $2 per day for swimming and $5 per day for aerobic, in other words, $7 per day.  So if we let d = number of days, our cost can be calculated by "7d"

a yearly membership costs $200 plus $3 per day, or in other words, "200 + 3d"

Set them equal to each other and solve:

7d = 200 + 3d

4d = 200

d = 50

So you would need to attend the classes for at least 50 days to justify a yearly membership.  I hope that helps!