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To find the value of k for the cheaper membership, we need to compare the prices of the two memberships for a year.
For Gym A:
The cost of a membership for 5 months is $50.
The cost of a membership for 1 month is $50/5 = $10.
The cost of a membership for 12 months is $10 × 12 = $120.
For Gym B:
The cost of a membership for 3 months is $40.
The cost of a membership for 1 month is $40/3 ≈ $13.33.
The cost of a membership for 12 months is $13.33 × 12 ≈ $160.
Comparing the prices, we see that the membership at Gym A is cheaper for a year.
The equation for Gym A can be written as: y = 10x (where x represents the number of months)
The equation for Gym B can be written as: y = 13.33x
So, the value of k for the cheaper membership is 10.