Jonathan is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The monthly fee to be a member is $25 and the total cost of membership, including the joining fee, would be $300 for 8 months. Write an equation for C, commaC, in terms of t, commat, representing the total cost of the gym membership over tt months.
The one-time fee to join the gym is a fixed cost and does not change based on the number of months. Let's denote this fee as J.
The monthly fee to remain a member is $25.
To find the equation for the total cost, we need to find the expression for the joining fee plus the monthly fees for tt months.
The joining fee is a one-time fee, so it can be written as J.
The monthly fee is $25, and there are t months, so the total monthly fees for tt months is 25t.
Therefore, the equation for the total cost of the gym membership over t months is C = J + 25t.
But, we are also given that the total cost of membership, including the joining fee, would be $300 for 8 months. We can use this information to find the value of J.
When t = 8, the total cost of membership, C, is $300.
Substituting these values into the equation, we have:
300 = J + 25(8)
Simplifying this equation, we get:
300 = J + 200
Subtracting 200 from both sides, we get:
100 = J
Therefore, the value of J is $100.
Thus, the final equation for the total cost of the gym membership over t months is:
C = 100 + 25t