Uptown Cable, a cable TV provider, charges each customer $120 for installation, plus $25 per month for cable programming. Uptown’s competitor, Downtown Cable, charges each customer $60 for installation, plus $35 per month for cable programming. A customer who signs up with Uptown will pay the same total amount for cable TV as a customer who signs up with Downtown if each pays for installation and cable programming for how many months?

3
3

6
6

10
10

18
18

30

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xKelvin xKelvin · Answer 1 · 2021-05-02T23:55:47+02:00

Answer:

B) Six Months.

Step-by-step explanation:

We can write an equation to model each situtation.

Let m be the number of months and c be its total cost.

Uptown Cable charges $120 for the initial installation fee plus $25 per month. In other words, its total cost is:

[tex]c=120+25m[/tex]

Downtown Cable charges an initial $60 fee plus $35 per month. So:

[tex]c=60+35m[/tex]

To find after how many months will the two services remain the same, we can set the two equations equal to each other and solve for m. So:

[tex]120+25m=60+35m[/tex]

Solve for m:

[tex]60=10m\Rightarrow m=6[/tex]

The two cable companies will charge the same after six months of use.

Notes:

If the customer uses the service for less than six months, then Downtown Cable is better since its initial cost is lower.

If the customer uses the service for more than six months, then Uptown Cable is better since its rate per month is lower.