Chapter 1.2, Problem 31IP

To determine

Write and evaluate an expression to find the total cost for an ad that has 6 lines, then make a table showing the cost if there are 6, 10, 14, and 18 lines in the ad.

Answer to Problem 31IP

  $\text{cost}=8+\left(0.75\right)\left(\text{number of lines}\right)$

  $\$12.50$

Lines	Cost
6	$12.50
10	$15.5
14	$18.5
18	$21.5

Explanation of Solution

GIVEN:

To place an ad in a newspaper, it costs $8 plus $0.75 for each line.

In order to write and evaluate an expression to find the total cost for an ad that has 6 lines, first the cost is equal to 8 plus 0.75 times the number of lines and there are given first 6 lines so, the expression is as shown below:

  $\text{cost}=8+\left(0.75\right)\left(\text{number of lines}\right)$

Now, putting number of lines, that is 6 in the above expression as shown below:

  $\begin{array}{l}\text{cost}=8+\left(0.75\right)\left(\text{number of lines}\right)\\ \text{cost}=8+\left(0.75\right)\left(6\right)\\ \text{cost}=8+4.5\\ \text{cost}=12.5\end{array}$

So, the total cost for an ad that has 6 lines is $12.5 .

Now, in order to make a table showing the total cost of an ad if there are 10, 14, and 18 lines in the ad.

First for 10 lines, putting the value of number of lines in the expression $\text{cost}=8+\left(0.75\right)\left(\text{number of lines}\right)$ so total cost will be :

  $\begin{array}{l}\text{cost}=8+\left(0.75\right)\left(\text{number of lines}\right)\\ \text{cost}=8+\left(0.75\right)\left(10\right)\\ \text{cost}=8+7.5\\ \text{cost}=15.5\end{array}$

Then for 14 lines, putting the value of number of lines in the expression $\text{cost}=8+\left(0.75\right)\left(\text{number of lines}\right)$ so total cost will be :

  $\begin{array}{l}\text{cost}=8+\left(0.75\right)\left(\text{number of lines}\right)\\ \text{cost}=8+\left(0.75\right)\left(14\right)\\ \text{cost}=8+10.5\\ \text{cost}=18.5\end{array}$

And then for 18 lines, putting the value of number of lines in the expression $\text{cost}=8+\left(0.75\right)\left(\text{number of lines}\right)$ so total cost will be :

  $\begin{array}{l}\text{cost}=8+\left(0.75\right)\left(\text{number of lines}\right)\\ \text{cost}=8+\left(0.75\right)\left(18\right)\\ \text{cost}=8+13.5\\ \text{cost}=21.5\end{array}$

So, the table is as shown below:

Lines	Cost
6	$12.50
10	$15.5
14	$18.5
18	$21.5