Number of people who signed up on the opening = 124
Number of people for whom registration fee is waived off = 50
Registration fee = $60
Monthly fee = $20
Part A: Money it will make from the grand opening memberships = ?
⇒ Money it will make from the grand opening memberships = Money made from registration fee + Money made from first month's fee
⇒ Money it will make from the grand opening memberships = (Number of people who were charged registration fee × Registration fee per person) + (Number of people who registered × Monthly fee per person)
⇒ Money it will make from the grand opening memberships = (124 - 50) × 60 + (124 × 20)
⇒ Money it will make from the grand opening memberships = (74 × 60) + (124 × 20)
⇒ Money it will make from the grand opening memberships = (4,440) + (2,480)
⇒ Money it will make from the grand opening memberships = $6,920
Part B: Money made in 6 months, from the original 124 people who joined at the grand opening = ?
⇒ Money made in 6 months = Money made from registration fee + Money made from 6-months monthly fee
⇒ Money made in 6 months = (Number of people who were charged registration fee × Registration fee per person) + (Number of people who registered × Monthly fee per person × 6)
⇒ Money it will make from the grand opening memberships = (124 - 50) × 60 + (124 × 20 × 6)
⇒ Money it will make from the grand opening memberships = (74 × 60) + (124 × 20 × 6)
⇒ Money it will make from the grand opening memberships = 4,440 + 14,880
⇒ Money it will make from the grand opening memberships = $19,320
Hence, by the end of 6 months, the gym would have made $19,320
=> 8+x = 15 => x = 15-8=7