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Question 250403: Please help me write two equations for this word problem. One equation for members and one for non members.
To encourage customers a movie theater is offering memberships. The membership costs $75.00 per year plus $2.00 per movie. For non-members, the cost of a movie is $5.75.
Thanks sooo much! Lisa
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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
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