Question

You are considering changing cable companies tosave on cost. With the cable channel package thatyou want, Cox charges a monthly fee of $79.95 andan initial sign up fee of $105. DirecTV is willing tolower their price to get your business. They willonly charge you $1 for signup and $102 per month.How many months would it take for the overallcost to be the same?

Answer 1

We have that with the company Cox, the relation function is:

$y=79.95x+105$

where 'y' represents the total cost paid and 'x' represents the months. For DirecTV, we have the following:

$y=102x+1$

Since we want to know how many months would it take for the overall to cost the same, we have to equal both expressions and solve for x:

$\begin{gathered} 102x+1=79.95x+105 \\ \Rightarrow102x-79.95x=105-1 \\ \Rightarrow22.05x=104 \\ \Rightarrow x=\frac{104}{22.05}=4.7 \\ x=4.7\approx5 \end{gathered}$

Therefore, it will take approximately 5 months for the overall cost to be the same