Question

Solving linear equationsOpptimum charges new customers $50.00 for installation fees and $140 per month for premium cable service. Time Warner charges new customers $230.00 for installation fees and $120.00 per month for its premium service. Write and solve an equation to show after how many months the costs of both cable services will be the same?

Answer 1

For Opptimum, we have that the initial fee is $50 and $140 per month. If x represents the number of months and y represents the total amount, then we can write the following equation:

`y=140x+50`

Then, for Time Warner, the initial fee is $230 and charger $120 per month, then the equation is:

`y=120x+230`

to find out in how many months the costs will be the same,we can equate both expressions and solve for x to get the following:

`\begin{gathered} 140x+50=120x+230 \\ \Rightarrow140x-120x=230-50=180 \\ \Rightarrow20x=180 \\ \Rightarrow x=(180)/(20)=9 \\ x=9 \end{gathered}`

therefore, the costs of both cable services will be the same after 9 months