Question

A home security system costs $150 to purchase, and then the services to run this system cost $7 per month .Let x represent the number of months the security system is in operation and y represent the cost of owning the system for x months. Write an equation to represent this situation.Use your equation to estimate how many months you will have owned the system by the time you've spent $200 on home security

Answer 1

• y=150+7x

,

• 8 months

Explanation:

• The purchase cost of the home security system = $150.

The monthly service cost = $7.

If the number of months the security system is in operation = x

• Then, the service cost for x months = $7x

Therefore, the cost of owning the system for x months is given by the equation:

`y=150+7x`

When the amount spent, y = $200

`200=150+7x`

We solve for x in order to estimate how many months you will have owned the system.

`\begin{gathered} \text{Subtract 150 from both sides} \\ 200-150=150-150+7x \\ 50=7x \\ \text{Divide both sides by 7} \\ (7x)/(7)=(50)/(7) \\ x=7(1)/(7) \end{gathered}`

By the time you've spent $200 on home security, you will have owned the system for 8 months.