Submit the two equations that represent the cost of going to the gym based on if we join or do not join. Identify the number of times a person would go and have the costs of the 2 plans be the same.

To determine the equations representing the cost of going to the gym based on whether we join or do not join, we need some information:

Let's assume:
- The cost of joining the gym per month is represented by J (in dollars).
- The cost of going to the gym per visit (without joining) is represented by V (in dollars).
- The number of times a person would go to the gym in a month is represented by N.

Equation 1: Cost of joining the gym per month
The cost of joining the gym per month is simply the membership fee, which remains the same regardless of the number of visits. Therefore, Equation 1 is:
Cost of Joining = J

Equation 2: Cost of going to the gym without joining
The cost of going to the gym without joining is the cost per visit multiplied by the number of times a person goes in a month. Thus, Equation 2 is:
Cost without Joining = V * N

Now, we want to find the number of times a person would go where the costs of the two plans (joining and not joining) are the same. Mathematically, we want to find the value of N where the equations are equal:

J = V * N

By rearranging the equation, we can solve for N:

N = J / V

So, to find the number of times a person would go and have the costs of the two plans be the same, divide the cost of joining the gym (J) by the cost per visit without joining (V).