Question

A satellite company offers an introductory price of $49 for 120 basic channels plus two movie channel packages. Another option is $67 for 120 basic channels with four movie channels. What is the equation that represents the linear relationship between price and the number of movie channels? The equation is Price = _________ + _________ movies

Answer 1

Given:

120 basic channels plus 2 movie channels packages cost $49.

120 basic channels with 4 movie channels packages cost $67.

To find:

The equation represents the linear relationship between price and the number of movie channels.

Explanation:

Let u be the cost of 120 basic channels.

Let v be the cost of a movie channel.

So, the equations are,

$\begin{gathered} u+2v=49.............(1) \\ u+4v=67.............(2) \end{gathered}$

Subtracting (1) from (2), we get

$\begin{gathered} 2v=18 \\ v=9 \end{gathered}$

Substiting v = 9 in equation (1), we get

$\begin{gathered} u+2(9)=49 \\ u+18=49 \\ u=49-18 \\ u=31 \end{gathered}$

So, the equation that represents the linear relationship between price and the number of movie channels is,

$\begin{gathered} Price,\text{ }P=Price\text{ of basic channels+Price of movie channels}\times No.\text{ of movie channels} \\ Price,P=31+9n \end{gathered}$

Where n represents the number of movie channels.

Final answer: The equation is,

$Price=31+9n$

Where n is the number of movie channels.