Your group will have 30 minutes to complete the following problem...
You are wanting to join a gym to get in better shape. You have two options to choose from.
Option 1: Joseph's Super Gym charges a $40 up front fee and $25 a month.
Option 2: Melchor's Muscle Madness charges a $30 up front fee and $30 a month.
Your group must:
1) Create a table of values for each gym, with 4 different values.
2) Make a detailed graph, with both gym's being displayed on the same grid.
3) Find the slope of each line and what the slope represents exactly.
4) Find the formula that represents each relation.
...also answer the following questions:
a) If you joined a gym for 1 month, which option would be better and why?
b) If you joined a gym for 4 months, which option would be better and why?
c) If you joined Melchor's Muscle Madness for 2 years, how much would you have paid
in membership fees?
d) What is the crossover point? What is the meaning of it? Be very specific.
3) Joeseph: Melchor:
slope = $25 slope = $30
The slope represents the monthly cost for a membership.
4) Joeseph: Melchor:
C = 25m + 40 C = 30m + 30
a) C = 25(1) + 40 C = 30(1) + 30
C = $65 C = $60
b) C = 25(4) + 40 C = 30(4) + 30
C = $140 C = $150
c) C = 30(24) + 30
C = $750
d) The crossover point is where for 2 months, the cost of each gym is $90.
C = 25(2) + 40 C = 30(2) + 30
C = $90 C = $90
...therefore making each gym a equally valid choice if you're joining for two months.