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? 20 + 45m = 65 + 37.5m 20m + 45 = 60m + 37.5 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? 20 + 45m = 65 + 37.5m 20m + 45 = 60m + 37.5 after how many months would the total cost at either gym be the same? months

Answer

Explanation:

Step1: Set up the cost - equations

The total cost for Infinity Fitness is the one - time registration fee plus the monthly cost times the number of months. So, the cost $C_1$ for Infinity Fitness is $C_1 = 20+45m$, where $m$ is the number of months. The total cost for The Power Zone is the one - time registration fee plus the monthly cost times the number of months. So, the cost $C_2$ for The Power Zone is $C_2=65 + 37.5m$. We want to find when $C_1 = C_2$, so the equation is $20 + 45m=65 + 37.5m$.

Step2: Solve the equation for $m$

First, subtract $37.5m$ from both sides of the equation: $20+45m-37.5m=65 + 37.5m-37.5m$ $20 + 7.5m=65$. Then, subtract 20 from both sides: $20-20 + 7.5m=65-20$ $7.5m=45$. Finally, divide both sides by 7.5: $m=\frac{45}{7.5}=6$.

Answer:

6