Question 250403
in the following equations:


y = total cost
m = cost per movie
x = number of movies per year
f = fixed cost per year


general equation is:


y = m*x + f


for members:


m = $2.00 per movie
f = $75.00 per year


member equation is:


y = 2*x + 75


for non-members:


m = $5.75


non-member equation is:


y = 5.75*x


break even point is when the 2 equations are equal to each other.


2*x + 75 = 5.75*x


subtract 2*x from both sides of the equation to get:


3.75*x = 75


x = 75/3.75 = 20


At 20 movies in a year, they break even.  above 20 movies in a year, the total cost to the member becomes less than the total cost to the non-member.


member equation is:


y = 2x + 75
when x = 20, y = 40+75 = 115


non-member equation is:


y = 5.75*x
when x = 20, y = 20*5.75 = 115


anything over 20, the member pays less.


assume x = 30


member pays 2*30 + 75 = 60 + 75 = 135
non-member pays 5.75*30 = 172.5