how could I make this problem into two linear equations for graphing...

Question

Bob is a traveling salesman and wants to get back into shape; he decides to join a gym. Bob needs a gym that has several locations nationwide and is open all hours of the day/night. He does not know how many weeks a year he will be training. The gym has two types of membership; the first type of membership is a monthly membership that has a $360 sign up fee and a $466 monthly rate to be paid at the beginning of each month and has unlimited uses per month. The second type of membership is a weekly pass it has a $480 sign up fee and charges $118.5 a week. Both types of memberships allow nationwide access to all gyms. What would be the most cost effective membership for him per month?

Answer 1

Let the x-axis represents the number of days Bob trains, and the y-axis represents the amount of money he needs to pay.

The 2 equations will be:

y = 360 + (466/30)x
y = 480 + (118.5/7)x

Note that you can modify the equations so that the x-axis represents the number of days, weeks, or even years.

Answer 2

Thank you very much and I appreciate your help. I would like to ask at least more questions...I have altered some of the numbers to make the problem easier. The next thing i have to do is see where the two options are equal and I keep coming up with a negative number, which I don't think is right.

here are the new numbers and my linear system

480 + (119/7)x = 360 + (450/30)x

            480 + 17x = 360 + 15x

            17x = -120 + 15x

             2x = -120

             x = -60

I also have to graph this. I have confused myself throughly now because the lines don't interesct, they run parallel to each other. Also how would I graph this anyway. because the fee breaks down into 30 days and then no more money is owed. Like i said i'm so confused or am i way pover thinking this.