At Silver Gym, membership is $40 per month, and personal training sessions are $25 each. At Fit Factor, membership is $70 per month, and personal training sessions are $15 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?

3 training sessions

Step-by-Step Explanation:

What we are going to have are two equations set equal to each other. Our variable is going to be the letter x. X represents the number of personal training sessions we would have to have at their current costs for the two equations to equal each other. Because we are only doing one month, the membership costs will stay constant.

For Silver Gym, membership is $40 and training sessions are 25$ per session. That "per session" tells you that this is where the variable goes. Your equation for a month at Silver Gym is 25x + 40.

Do the same for Fit Factor; $70 membership, $15 per session: 15x + 70.

Now let's set them equal to each other:

25x + 40 = 15x + 70

Next, we want to get variables on one side and constants on the other. I like to do variables on the left and constants on the right but, this is just personal preference - - we'll end up with the same answer regardless. To do this, we are going to subtract 15x from both sides, subtract 40 from both sides, and then simplify. So the above equation becomes:

25x - 15x + 40 - 40 = 15x - 15x + 70 - 40

Simplify by combining like terms. The 15x and - 15x cancel each other out, same with the 40 and - 40. Leaving us with:

10x = 30

Divide both sides to isolate your variable x and satisfy the division property of equality.

x = 30/10

x = 3

You would have to do 3 training sessions for the two gyms to be equal in cost.