Felix spends​ $150 each month for his gym membership plus​ $30 each week for a personal trainer. A new gym charges​ $255 a​ month, which includes a weekly session with a personal trainer. Would Felix save money by switching to the new​ gym? Explain. Assume there are 4 weeks in a month.

Question

Felix____ save money by switching to the new gym. The integer that represents the total monthly cost of the current gym membership is __. The integer that represents the total monthly cost of a membership at the new gym is__

Answer 1

To determine whether Felix would save money by switching to the new gym, we need to calculate his total monthly costs at both gyms.

Current Gym Costs:

• Monthly gym membership: $150
• Personal trainer: $30 per week

Since there are 4 weeks in a month, the total cost for the personal trainer per month is: \[ 30 \text{ (dollars/week)} \times 4 \text{ (weeks)} = 120 \text{ dollars} \]

Now, add the gym membership and the personal trainer costs: \[ 150 \text{ (gym)} + 120 \text{ (trainer)} = 270 \text{ dollars} \]

New Gym Costs:

• Monthly gym membership (which includes a weekly session with the personal trainer): $255

Comparison:

• Total monthly cost at the current gym: $270
• Total monthly cost at the new gym: $255

Conclusion: Felix would save money by switching to the new gym.

The integer that represents the total monthly cost of the current gym membership is 270. The integer that represents the total monthly cost of a membership at the new gym is 255.