Green's Gym charges a one time fee of $50 plus $30 per session for a personal trainer. A new fitness center charges a
yearly fee of $250 plus $10 for each session with a trainer. For
how many sessions is the cost of the two plans the same?

After 10 session with personal trainer the cost of both gym plans would be same. Step-by-step explanation: Let number of session with the trainer be 's'. Given: Get fit gym Plan: Yearly fee = $250 Each session with personal trainer = $10 So we can say that; Total Cost after 's' session will be equal to Yearly fee plus Each session with personal trainer multiplied by number of session with the trainer framing in equation form we get; Total Cost =  250+10s Tight N' Toned gym Plan: One time fee = $50 Each session with personal trainer = $30 So we can say that; Total Cost after 's' session will be equal to One time fee plus Each session with personal trainer multiplied by number of session with the trainer framing in equation form we get; Total Cost =  50+30s We need to find the number sessions after which cost of the two plans will be the same. To find the number sessions after which cost of the two plans will be the same we will make both the equations equal we get; 250+10s =  50+30s Combining like terms we get; 30s-10s = 250-50 20s = 200 Now dividing both side by 20 we get; 20s/20 = 200/20 s = 10Hence after 10 session with personal trainer the cost of both gym plans would be same.