4. tom decided to join platinum gym because of its new equipment. at the grand opening, the manager announced that 124 people had signed up for gym membership. as part of the grand opening event, the manager waived the registration fee for 50 random people. platinum gym charges a one-time registration fee of $60, and membership is $20 a month. (a) write an expression to represent how much money platinum gym will make from the grand opening memberships. simplify the expression and label any variables. (b) after 6 months, how much money will platinum gym have made from the original 124 people who joined at the grand opening, assuming that all 124 people are still members? show your work.

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

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