Question

Tonya plans to join a fitness club. She researched the costs to join different clubs in her area and found that there is a linear relationship between the total cost of belonging to a club and the number of months that you are a member. Each club charges monthly dues, and some clubs require new members to also pay a one-time membership fee. The total costs of being a member for 6 months, 12 months, and 24 months at each of three clubs are shown in the table.

Total Cost of Fitness Club Membership
Length of membership
Club 1
Club 2
Club 3
6 months
$108
$120
$126
12 months
$216
$210
$252
24 months
$432
$390
$504

How many of the clubs require new members to pay a one-time membership fee?
0
1
2
3

Answer 1

1

Work: For each club total = monthly_rate * months + membership_fee.

- Club 1: (216−108)/(12−6)=18 per month. 18·6=108 so fee = 0.
- Club 2: (210−120)/(12−6)=15 per month (also (390−210)/(24−12)=15). 15·6=90, but cost is 120, so fee = 30.
- Club 3: (252−126)/(12−6)=21 per month. 21·6=126 so fee = 0.

Only Club 2 requires a one-time fee, so 1 club.