Question

The total cost, C, for running an advertisement in a local newspaper, The Free Press, is made up of an initial cost of $12 plus a charge of $5 per day. A rival newspaper, The Banner, is currently running a special on advertisements at $8 per day with no initial cost.

a) Write an equation representing the cost in The Free Press.

b) Write an equation representing the cost in The Banner.
c) For each newspaper, create a table of values.
d) Use Rapid Tables (will need to select 2 lines from the drop down - see example in relation to the Jason's Trip graph below) to graph each cost on the same set of coordinate axis. Your two lines will represent The Free Press and The Banner. You are also able to create the graph on other technology or a piece of paper.
e) Which newspaper would you use for an ad that ran 1 day?
f) Which newspaper would you use for an ad that ran 12 days?

Answer 1

(a)
`C(x) = 12 + 5x`

(b)
`C(x) = 8x`

(c) Tables

(d) See attachment for graph

(e) Banner newspaper

(f) Free press newspaper

Free Press

`\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}`

Banner

`\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}`

Explanation:

Given

Free Press

`Initial = 12`

`Rate =5`

Banner

`Initial=0`

`Rate =8`

Solving (a): Free Press Equation

This is calculated as:

`C(x) = Initial + Rate * x`

Where

`x \to` days

So, we have:

`C(x) = 12 + 5x`

Solving (b): Banner Equation

This is calculated as:

`C(x) = Initial + Rate * x`

Where

`x \to` days

So, we have:

`C(x) = 0 + 8x`

`C(x) = 8x`

Solving (c): Table of values

For free press, we have:

`\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}`

C(x) is calculated as:

`x = 1;\ C(1) = 12 + 5* 1 =17`

`x = 2;\ C(2) = 12 + 5* 2 =22`

..

`x = 5;\ C(5) = 12 + 5* 5 =37`

For banner, we have:

`\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}`

C(x) is calculated as:

`x = 1;\ C(1) = 8* 1 =8`

`x = 2;\ C(2) = 8* 2 =16`

..

`x = 5;\ C(5) = 8* 5 =40`

Solving (d): Graph of both using rapidtable

See attachment

Solving (e) Newspaper to use for 1 day

From the graph, when
`x = 1`

`Free\ press = 17`

`Banner = 8`

So, we use Banner newspaper because it is cheaper

Solving (f) Newspaper to use for 12 days

From the graph, when
`x = 12`

`Free\ press = 72`

`Banner = 96`

So, we use free press newspaper because it is cheaper