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.
(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.
(a) To represent how much money Platinum Gym will make from the grand opening memberships, we need to consider two things: the registration fee and the number of people who signed up for membership.
Let's define the registration fee as "f" (in dollars) and the number of people who signed up as "p".
Since the manager waived the registration fee for 50 random people, we only need to consider the remaining 124 - 50 = 74 people who paid the registration fee.
Therefore, the expression to represent how much money Platinum Gym will make from the grand opening memberships is:
Money made = registration fee x number of people
= f x (p - 50)
= f(p - 50)
(b) After 6 months, assuming all 124 people are still members, we need to calculate the total membership fees collected for these 124 members.
Let's define the membership fee per month as "m" (in dollars) and the number of months as "n".
To calculate the total membership fees collected after 6 months, we multiply the monthly fee by the number of months and the number of members:
Total money made after 6 months = membership fee per month x number of months x number of members
= m x n x 124