Given:
For gym A, initiation fee = $12 and cost = $10 per month.
For gym B, initiation fee = $20 and cost = $6 per month.
To find:
The equation that aims to find when these two gyms will cost the same amount of money,
Solution:
Let the number of months be x.
Cost function = Initiation fee + (cost)(x)
Cost function for gym A is

Cost function for gym B is

Cost of these two gyms are equal if f(x)=g(x).

Therefore, the required equation is
.
On solving this equation, we get



Hence, after 2 months the cost of these two gyms are same.