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Question 305372: A marketing group developing online ad space is offering two payment options:
Option 1: $210 set up fee plus $10/inch of the ad.
Option 2: No set up fee but $25/inch of the ad.
Let x = inches of the proposed ad, for example x=2 for a colum ad that is 2
a) Write a mathematical model representin the total ad cost, c, in terms of x for the following:
Option 1: C=
Option 2: C=
b) How many inches of ad space would need to be purchased for option 1 to be less than option 2? Set up an inewuality and show work algebraically usint the information in part a. Summarize the findings in a brief sentence.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Option 1: $210 set up fee plus $10/inch of the ad.
Option 2: No set up fee but $25/inch of the ad.
Let x equal number of inches of ad space.
Equation for option 1:
C = 210 + 10*x
Equation for option 2:
C = 25*x
b) How many inches of ad space would need to be purchased for option 1 to be less than option 2?
Equation you want to solve is:
210 + 10*x < 25*x
Subtract 10*x from both sides of this equation to get:
210 < 15*x
Divide both sides of this equation by 15 to get:
14 < x
This would be the same as:
x > 14
If the inches of ad space were greater than 14, then option 1 would be cheaper than option 2.
To confirm if this is true, we need to test at x = 13, 14, and 15.
When x = 13, option 1 will cost 210 + 10*13 = 210 + 130 = 340
When x = 14, option 1 will cost 210 + 10*14 = 210 + 140 = 350
When x = 15, option 1 will cost 210 + 10*15 = 210 + 150 = 360
When x = 13, option 2 will cost 25*13 = 325
When x = 14, option 2 will cost 25*14 = 350
When x = 15, option 2 will cost 25*15 = 375
The results are:
When x = 13, option 1 costs 340 and option 2 costs 325 so option 1 is more expensive than option 2.
When x = 14, option 1 costs 350 and option 2 costs 350 so option 1 and option 2 cost the same.
When x = 15, option 1 costs 360 and option 2 costs 375 so option 1 is cheaper than option 2.
Break even point is when x = 14.
When x > 14, option 1 becomes less than option 2 and stays less than option 2.
Answer to the question is that more than 14 inches of ad space would have to be purchased for option 1 to cost less than option 2.
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