Assumptions:
There are 9 members in a club that share a pool of season tickets to football games at a local university. Membership in the club affords members the option to buy tickets from the pool and attend games during the current year. In addition, it also renews that privilege the following year. The university charges the club $27,000 (total) every year for the tickets, with that cost shared by members according to their level of participation. If any member fails to pay their portion of their financial obligation in any year, they are barred from the club forever.
Before the season starts and before ticket selections are made, each member is obligated to pay the identical amount (in this case $3,000 each). As members declare for and are awarded their favorite tickets, that obligation shifts accordingly. Some members are active and purchase tickets. Other members are passive and do not purchase tickets. All members wish to keep their membership in order to have the option to buy tickets for the next year.
In summary, the university charges the club a yearly fee of $27,000 for:
1. use of the tickets for the current year and
2. a guaranteed option to buy them again the following year
This year, only 4 of the 9 members exercise their option to buy tickets from the pool in the following amounts:
Member 1: $12,000
Member 2: $9,000
Member 3: $4,000
Member 4: $2,000
Total: $27,000
As active members make payments to the pool for their respective tickets, the obligation of the other passive members to the university is reduced accordingly. Both active and passive members acknowledge that the contribution of one member reduces the financial obligation of others, equitably and to the extent of the respective contributions.
Question: What is the monetary obligation of each of the 9 members?
A worksheet with formulas included would be greatly appreciated. Thanks in advance.
OldScout
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