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Question 326772: Please help me solve this problem. Thank you so much
3) 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 column ad that is 2” long.
a) Write a mathematical model representing 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 inequality and show your work algebraically using the information in part a. Summarize your findings in a brief sentence.
Answer:
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! For option 1, you know that the total ad cost is equal to a $210 set up fee plus $10 per inch of add. This can be written as:
C = 210 + 10x (where x = inches of the add)
For option 2, you know that the total ad cost is equal to no set up fee plus $25 per inch of add:
C = 0 + 25x
C = 25x
Now for part (b), we need to set up an inequality that will answer the question of how many inches of ad space are needed for option 1 to be less than option 2. So set option 1 less than option 2:
option 1 < option 2
210 + 10x < 25x
Now solve for x:
210 + 10x < 25x
210 + 10x - 10x < 25x - 10x
210 < 15x
210/15 < 15x/15
14 < x
So you know the ad has to be greater than 14 inches long for option 1 to cost less than option 2.
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