Michael is planning to join a local gym and is researching his options. His first option, Bodies In Motion, charges a one time enrollment fee of $\$ 60.00$ , plus an additional monthly fee of $\$ 18.00$ . His second option, Cardio World, does not have an enrollment fee, but charges $\$ 30.00$ per month. In how many months will the total cost for a gym membership at both gyms be equal?

Full solution

Q. Michael is planning to join a local gym and is researching his options. His first option, Bodies In Motion, charges a one time enrollment fee of

\$ 60.00

, plus an additional monthly fee of

\$ 18.00

. His second option, Cardio World, does not have an enrollment fee, but charges

\$ 30.00

per month. In how many months will the total cost for a gym membership at both gyms be equal?

Set up equation for total cost: Set up an equation to represent the total cost for each gym membership over time. $\newline$ Let $x$ represent the number of months. $\newline$ For Bodies In Motion, the total cost after $x$ months is the enrollment fee plus the monthly fee times the number of months: $\newline$ $60 + 18x$ $\newline$ For Cardio World, the total cost after $x$ months is just the monthly fee times the number of months: $\newline$ $30x$ $\newline$ We want to find out when these two costs will be equal, so we set up the equation: $\newline$ $60 + 18x = 30x$
Solve equation for x: Solve the equation for x to find out after how many months the costs will be equal. $\newline$ Subtract $18x$ from both sides of the equation: $\newline$ $60 + 18x - 18x = 30x - 18x$ $\newline$ This simplifies to $60 = 12x.$ $\newline$ Now, divide both sides by $12$ to solve for x: $\newline$ $\frac{60}{12} = \frac{12x}{12}$ $\newline$ $x = 5$
Final Answer: We found that the value of $x$ is $5$ . $\newline$ This means that after $5$ months, the total cost for a gym membership at both Bodies In Motion and Cardio World will be equal.