Question

Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

Nicole's 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?

Answer 1

Answer: For 10 sessions, the cost of the two plans the same.

Explanation:

Let x= Number of sessions.

Given: Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

Total charge for x sessions = 50+30x

Nicole's fitness center charges a yearly fee of $250 plus $10 for each session with a trainer.

Total charge for x sessions = 250+10x

When both plan charges the same, then

`50+30x=250+10x\\\\\Rightarrow\ 30x-10x=250-50\\\\\Rightarrow\ 20x=200\\\\\Rightarrow\ x=10`

i.e. For 10 sessions, the cost of the two plans the same.