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:
[tex]y=140x+50[/tex]Then, for Time Warner, the initial fee is $230 and charger $120 per month, then the equation is:
[tex]y=120x+230[/tex]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:
[tex]\begin{gathered} 140x+50=120x+230 \\ \Rightarrow140x-120x=230-50=180 \\ \Rightarrow20x=180 \\ \Rightarrow x=\frac{180}{20}=9 \\ x=9 \end{gathered}[/tex]therefore, the costs of both cable services will be the same after 9 months
