a Introduce variables for the number of visits and the total cost.
B
b Look for the intersection point of the lines.
C
c Compare the cost of the two options.
D
d There are 52 weeks in a year.
A
aOption 1: y=400 Option 2: y=5x+150
B
bGraph:
Break-even point: 50 visits.
C
c See solution.
D
d Option 1
Practice makes perfect
a To be able to write equations, we need to introduce variables based on the information in the graphic.
Description
Variable
Number of visits to the gym in a year
x
The cost of belonging to the gym
y
Let's use these variables to write equations that represent the information given in the graphic.
Information
Equation
For option 1 there is no fee for a visit, and the yearly membership costs $400.
y=400
For option 2 there is a $5 fee for each visit, and the yearly membership costs $150.
y=5x+150
b We found two equations in Part A. Both of these are linear, and the graphs are straight lines. Both of these lines can be graphed through two of their points. Let's find these points by finding the cost of belonging to the gym for x=0 and x=100 visits.
Equation
x=0
x=100
Points on Graph
y=400
y=400
y=400
(0,400) and (100,400)
y=5x+150
y=5(0)+150=150
y=5(100)+150=650
(0,150) and (100,650)
Let's use these points to draw the graphs.
The break-even point is represented by the intersection point of the lines.
We can see from the graph that this is around 50 visits.
We can confirm this by calculating the cost of 50 visits for option 2.
We can see that the two options indeed have the same cost for 50 visits.
c Comparing the graphs of Part B, we can see that the break-even point gives the number of visits where the cost-effectiveness of the options change.
For less than 50 visits, Option 2 costs less than Option 1.
For more than 50 visits, Option 1 costs less than Option 2.
d If we plan to visit the gym at least once a week, then we plan to visit at least 52 times. Since the break-even point is 50 visits, Option 1 will cost less. If we can afford to pay the higher membership fee, we should choose Option 1.
