If you're a new member and begin golfing the first week of May and play until the first week of September (a 22-week span), you would need to play 1.8 rounds of 9-hole golf per week to, as you say, "break even".
If you're an 18-hole golfer, it is about 1.4 times per week.
Returning member: $720*
For a classified "returning" member, one would need to play two 9-hole rounds per week, or 1.6 rounds of 18-hole golf to fulfill your personal quota.
*Note: breakdown is based off of 2016 green fee rates (non-senior) and do not include the whole month of April or the last three weeks of September.