Final answer:
The cost of the installation fee is $150.
Step-by-step explanation:
To find the cost of the installation fee, we can set up a system of linear equations using the given information.
Let x be the number of weeks and y be the total cost.
From the given information, we know that the security company charges $5 per week plus an installation fee. So the total cost y can be represented as:
y = 5x + installation fee
We are also given that the total fee for 12 weeks of service is $210. So we have:
210 = 5(12) + installation fee
Simplifying the equation, we get:
210 = 60 + installation fee
Subtracting 60 from both sides, we get:
150 = installation fee
Therefore, the cost of the installation fee is $150.