Faster Fitness has a yearly membership fee of $90, but it costs members only $5 to take an instruction class. At Drop-In Fitness, there is no membership fee, but clients pay $35 per instruction class.
a) Write an equation for each situation.
b) Graph both equations on the same set of axes. Find the point of intersection
c) What does the point of intersection mean in this case?
d) What would you advise someone someone who is trying to choose between the two fitness clubs?

Question

Faster Fitness has a yearly membership fee of $90, but it costs members only $5 to take an instruction class. At Drop-In Fitness, there is no membership fee, but clients pay $35 per instruction class.
a) Write an equation for each situation.
b) Graph both equations on the same set of axes. Find the point of intersection
c) What does the point of intersection mean in this case?
d) What would you advise someone someone who is trying to choose between the two fitness clubs?

mathmate · Answer

The membership fee is a one-time charge, so it is a constant to be added to the number of classes one takes.
For FF, cost=y1=90+5x, where y1 is cost for FF, x=number of classes.
At DIF, cost=y2=0+35x, again, x is the number of classes.

Try to plot them (for example at Desmos.
The point where the two lines intersect represent the cross-over for the number of classes taken.  The higher curve means it is more expensive.