after 5 moths Joe and Bill will have paid the same amount
Step-by-step explanation
Step 1
Joe paid $100 to join a health club and $50 a month to use the club
let
x represents the number of months
then
after x months joe has paid:

Now, for Bill
Bill paid nothing down to join the health club and $70 a month to use the club
after x months bill has paid:

Step 2
months will they have paid the same amount of money
it menas total 1= total 2

Step 3
solve the equation

so, the answer is
after 5 moths Joe and Bill will have paid the same amount