Question

Healthy Gym charges members a fee for each visit, while Fitness Gym charges members a one-time yearly charge plus a fee for each visit. The equations below represent the amounts members pay at each gym, where t represents the total yearly cost and n represents the number of visits.

Healthy Gym: 6n = t
Fitness Gym: 50 + 5n = t

Which statement about the total yearly cost of the memberships is true?
The total yearly cost is $300 at each gym for 50 visits.
The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.
The total yearly cost is the same at both gyms when members make 10 visits to each one.
The total yearly cost at Healthy Gym is about $50 lower than the total yearly cost at Fitness Gym.

Answer 1

A. The first choice. Each would be $300 for 50 visits

Answer 2

The total yearly cost is $300 at each gym for 50 visits.

Explanation:

Given equations,

Healthy Gym: 6n = t

Fitness Gym: 50 + 5n = t

Where, n represents the number of visits and t represents the total cost for n visits,

First option :

If n = 50,

Yearly cost in Healthy gym, t = 6(50) = $ 300

And, yearly cost in Fitness gym, t = 50+5(50) = 50 + 250 = $ 300,

Second option :

If 6n < 50 + 5n

⇒ 6n - 5n < 50

⇒ n < 50

Hence, the total yearly cost will be higher at Fitness Gym than at Healthy Gym for less than 50 visits,

Third option :

If n = 10,

Yearly cost in Healthy gym, t = 6(10) = $ 60

And, yearly cost in Fitness gym, t = 50+5(10) = 50 + 50 = $ 100,

Fourth option :

Yearly cost in Fitness gym - yearly cost in Healthy gym = 50 + 5n - 6n = $(50 - n) < $ 50

Hence, only option FIRST OPTION is correct