Question

At one gym, there is a $12 start-up fee, and after that each month at the gym costs $20. At another gym, it costs $4 to startup, but after that, each month at the gym costs $22. After how many months will the cost of both gyms be the same?

Answer 1

To determine after how many months the cost of gym memberships at two gyms will be equal, we set up equations for both gyms and solved for the number of months. After setting up the equations, we found that the costs are the same after 4 months.

Step-by-step explanation:

The question asks after how many months the cost of memberships at two different gyms will be the same. To solve this problem, we can set up two equations representing the total cost for each gym after x months. For the first gym with a $12 start-up fee and $20 monthly cost, the equation is T1 = 12 + 20x. For the second gym with a $4 start-up fee and a $22 monthly cost, the equation is T2 = 4 + 22x. To find when the costs will be the same, we need to set T1 equal to T2 and solve for x.

So we have 12 + 20x = 4 + 22x. Solving for x, we subtract 20x from both sides, getting 12 = 4 + 2x, and then subtract 4 from both sides, yielding 8 = 2x. Dividing both sides by 2, we find x = 4. Therefore, after 4 months, the total cost for both gyms will be the same.

Answer 2

4 months

Step-by-step explanation:

At the first gym, $12 is the start-up fee and after that each month at the gym costs $20.

At the second gym, $4 is the start-up fee and after that each month at the gym costs $22.

Let us assume that after x months the cost of both the gym will be the same.

Therefore,

12 + 20x = 4 + 22x

⇒ 2x = 8

⇒ x = 4 months. (Answer)