You would set up equations for both the member and the non-member.
The member's equation would be: 384+8x (x being the number of rounds)
The non-member's equation would be: 48x+24x
then you would set them equal to each other and then solve:
384+8x=48x+24x
384=64x
384/64=x
x=6
they would have to play 6 rounds in order to pay the same amount.