Get fit gym charges a yearly fee of $250 plus $10 for each session with a personal trainer. Tight N' Toned gym charges a one time fee of $50 plus $30 per session

Get fit gym charges a yearly fee of $250 plus $10 for each session with a personal trainer. Tight N' Toned gym charges a one time fee of $50 plus $30 per session for a personal trainer. For how many sessions is the cost of the two plans the same?

Answer:

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 = [tex]250+10s[/tex]

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 = [tex]50+30s[/tex]

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;

[tex]250+10s=50+30s[/tex]

Combining like terms we get;

[tex]30s-10s=250-50\\\\20s = 200[/tex]

Now dividing both side by 20 we get;

[tex]\frac{20s}{20}=\frac{200}{20}\\\\s=10[/tex]

Hence after 10 session with personal trainer the cost of both gym plans would be same.