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?

Question

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?

Bytelearn · Accepted Answer

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

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