Intermath | Workshop Support



Is free installation really free?

Problem Statement

SafeT Systems charges $125 for installation of their burglar alarm system and a $35 per month fee.
Uprotect Systems installs their burglar alarm system for free, but charges more money per month than SafeT. If the average burglar alarm user keeps an alarm system for 5 years, how much money should Uprotect Systems charge per month to generate a profit equal to SafeT's over that 5 year span?

Problem setup

The problem is to determine the monthly fee a burglar alarm company will have to charge a client in a five year span to match profits with another company while offering free installation of the system. The competition charges $125 for installation and $35 a month.


Plans to Solve/Investigate the Problem

The first step is to determine how much profit the competition nets within the five year time span, divide that by 60 months to find out how much Uprotect systems will have to charge per month to make the same profit.


Investigation/Exploration of the Problem

SafeT charges $35 for 60 months (5 years) and an initial $135 installation fee.


y= (35 x 60) +125

y = 2215

SafeT has a $2215 price tag for 60 months of burglar alarm service.

Expanding this equation, for any month,  y = 125 + 35 x, “x” being the month of service.

 = 36.91 which would round off to $37/month, giving the company $2200 for 5 years.


 To find out how much Uprotect will have to charge to get the same fee, I created a spreadsheet to calculate how much Uprotect has to charge to make the same profit as SafeT.


Click here for spreadsheet


Extensions of the Problem

An extension of the problem would be to determine what would happen after the 5 years passed? Which company would profit the most after time?

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