At silver gym, membership is $45 per month, and personal training sessions are $25 each. at fit factor, membership is $75 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?

Let S represent the cost of use of Silver Gym for a month.
Let F represent the cost of use of Fit Factor for a month.
Let T represent the number of training sessions used in the month.

S = 45 +25T
F = 75 +15T

We want to find T so the costs are equal.
.. S = F
.. 45 +25T = 75 +15T
.. 10T = 30 . . . . . . . . . subtract 45+15T
.. T = 3 . . . . . . . . . . . . divide by 10

Sarah would have to buy 3 training sessions to make the cost at the two gyms equal.