SOLUTION: 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.

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.

RELATED QUESTIONS
A marketing group developing online ad space is offering two payment options: Option... (answered by Deina)

Please help me solve this problem. Thank you so much 3) A marketing group developing... (answered by jessica43)

a marketing group develpoing online as space is offering two payment options: Option 1:... (answered by stanbon)

This is the problem that I have to do and I have never had algebra, could you help me... (answered by Fombitz)

I really don't know how to set this up to get my answer....Please someone Help!! A... (answered by mananth)

3) A temporary agency offers two payment options for administrative help: Option1: $25... (answered by richwmiller)

A temporary agency offers two payment options for administrative help: Option1: $25... (answered by moshiz08)

The problem is two parts: part 1: A temporary agency offers two payment options: Option (answered by swincher4391)

5) A tennis club offers two payment options: Option 1: $42 monthly fee plus $5/hour for (answered by oscargut)