nick wants to join a gym, and he is deciding between two options. infinity fitness charges $45 per month…

nick wants to join a gym, and he is deciding between two options. infinity fitness charges $45 per month, plus a one - time registration fee of $20. the power zone charges $37.50 per month, plus a one - time registration fee of $65. which equation can you use to find m, the number of months it would take for the total cost at either gym to be the same? 20m + 45 = 60m + 37.5 20 + 45m = 65 + 37.5m after how many months would the total cost at either gym be the same? months

nick wants to join a gym, and he is deciding between two options. infinity fitness charges $45 per month, plus a one - time registration fee of $20. the power zone charges $37.50 per month, plus a one - time registration fee of $65. which equation can you use to find m, the number of months it would take for the total cost at either gym to be the same? 20m + 45 = 60m + 37.5 20 + 45m = 65 + 37.5m after how many months would the total cost at either gym be the same? months

Answer

Explanation:

Step1: Set up cost equations

For Infinity Fitness, the total cost (C_{1}) is the sum of the one - time registration fee and the monthly fee times the number of months. So (C_{1}=20 + 45m). For The Power Zone, the total cost (C_{2}) is (C_{2}=65+37.5m).

Step2: Set (C_{1}=C_{2})

Set (20 + 45m=65 + 37.5m)

Step3: Solve for (m)

Subtract (37.5m) from both sides: (20+45m-37.5m=65 + 37.5m-37.5m) (20 + 7.5m=65) Subtract (20) from both sides: (7.5m=65 - 20) (7.5m=45) Divide both sides by (7.5): (m=\frac{45}{7.5}=6)

Answer:

The equation is (20 + 45m=65 + 37.5m) and the number of months (m = 6)