Question

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.

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**.