Answer:
The number of visit so that both plan cost same is 10 . 
Both the plan has equivalent choice of benefit
Step-by-step explanation:
Given as :
A gym has two membership plans.
For Gold plan
The charge per month = $50  
The charge per visit = $3
For Platinum plan
The charge per month = $20  
The charge per visit = $6
Let The number of visit for which each plan be same = n visits
Now, According to question
<u>∵ Each plan cost to be same</u>
So, 
The charge per month for gold plan+ The charge per visit × numbers of visit = The charge per month for platinum plan+ The charge per visit × numbers of visit 
I.e $50 + $3 × n = $20 + $6 × n 
Or, $50 - $20 =  $6 × n  -  $3 × n 
Or, $30 = ($6 - $3) × n  
Or, $30 = $3 × n  
∴ n = 
I.e n = 10
So, The number of visits = n = 10 
Now, For Gold plan
The charge per month = $50  
The charge per visit = $3 × 10 = $30
So, Total charge for gold plan = $50 + $30 = $80
Similarly For Platinum plan
The charge per month = $20  
The charge per visit = $6×10 = $60
So, For Platinum plan ,total charge = $20 + $60 = $80
Hence, The number of visit so that both plan cost same is 10 
and both the plan has equivalent benefit. Answer