Question

You are trying to choose between two gym options. For a monthly plan, planet fitness has a fee of $16 plus also cost 2.50 every time you go. Bay State Gym’s fee is 30$ but is only 1$ every time that you go. At what point do the 2 gyms cost the same amount of money?

Answer 1

At
`9(1)/(3)` the 2 gyms cost the same.

For number of visits that is 9 or less, more cheper is Planet Fitness;

for number of visits that is more than 9, the Bay State Gym is cheaper.

Explanation:

Let x be the number of times you visit the gym.

Planet fitness:

Monthly fee = $16

Each time cost =$2.50

x times cost =$2.50x

Total cost =$(16+2.50x)

Bay State Gym:

Monthly fee = $30

Each time cost =$1

x times cost =$x

Total cost =$(30+x)

If two gyms cost the same, then total costs are equal, thus

`16+2.50x=30+x\\ \\2.5x-x=30-16\\ \\1.5x=14\\ \\15x=140\\ \\x=(140)/(15)=(28)/(3)=9(1)/(3)`

So, for number of visits that is 9 or less more cheper is Planet Fitness, for number of visits that is more than 9, the Bay State Gym is cheaper.