Question

Question 5:7A cable company charges $50 to install a digital box and $5.00 per premium channel. Write a rule for thecompany's fee. Write ordered pairs for the fees for 1, 2, 3, and 4 premium channels.

Answer 1

Given:

The charge for installing a digital box, c=$50.

The charge per premium channel, m=$5.

Let x be the number of premium channels and y be the total fee charged by the company.

Hence, the expression for the total charge is,

`\begin{gathered} y=mx+c \\ y=5x+50\text{ ---(1)} \end{gathered}`

So, the the expression for the total charge is given by equation (1).

To find the total fee for 1 premium channel, put x=1 in equation (1) and solve.

`\begin{gathered} y=5*1+50 \\ y=55 \end{gathered}`

The ordered pair for the fees for the channels taken is to be expressed as (x, y).

So, the ordered pair for the fees of 1 premium channel is (1, 55).

To find the total fee for 2 premium channel, put x=2 in equation (1) and solve.

`\begin{gathered} y=5*2+50 \\ y=10+50 \\ y=60 \end{gathered}`

So, the ordered pair for the fees of 2 premium channels is (2, 60).

To find the total fee for 3 premium channels, put x=3 in equation (1) and solve.

`\begin{gathered} y=5*3+50 \\ y=15+50 \\ y=65 \end{gathered}`

So, the ordered pair for the fees of 3 premium channels is (3, 65).

To find the total fee for 4 premium channels, put x=4 in equation (1) and solve.

`\begin{gathered} y=5*4+50 \\ y=20+50 \\ y=70 \end{gathered}`

So, the ordered pair for the fees of 4 premium channels is (4, 70).