Diana is comparing the membership costs at two fitness centers. the community fitness center costs $60 per month. the fitness center located where she works has a $100 registration fee and costs $40 per month. after how many months of membership will the costs be the same?
2

It would be five months

Since you're trying to find when they'd cost the same amount, we set it up as an equation. Key word in finding that is "same". Each side of the equation will be a membership cost, and x will represent time, in this case, months:
60x ($60/month) = 100 + 40x ($100 one-time fee, plus $40/month)
60x = 100 + 40x (subtract 40x from both sides) -> 20x = 100 (divide both sides by 20) -> x = 5. So your answer is 5 months.