Question

Colin plans to join a fitness facility. The Wellness Center charges a one-time registration fee of $400 and monthly dues of $5. Family Fitness does not have a registration fee but charges monthly dues of $30. After how many months will the cost of both fitness facilities be the same?

A) 10 months
B) 15 months
C) 20 months
D) 25 months

Answer 1

After 16 months, the cost of both fitness facilities will be the same.

Step-by-step explanation:

To determine the number of months in which the cost of both fitness facilities will be the same, we need to set up an equation and solve for the unknown variable, 'x'.

Let 'x' represent the number of months.

The cost at the Wellness Center is the one-time registration fee of $400 plus the monthly dues of $5x.

The cost at Family Fitness is the monthly dues of $30x.

To find the number of months when the costs are equal, we can set up the equation:

400 + 5x = 30x

Now, we can solve for 'x' by subtracting 5x from both sides:

400 = 25x

Finally, divide both sides by 25 to isolate 'x':

16 = x

Therefore, after 16 months, the cost of both fitness facilities will be the same.