Chapter 1.5, Problem 36E

a.

To determine

To find: the linear equation that represents the given situation.

Answer to Problem 36E

  $O=CT+S$

Explanation of Solution

Given information:

The given data is as follows:

Order No.	Number of T-shirts	Total order cost ($)
1	40	295
2	80	565

Each order included standard shipping and handling charges.

Calculation:

Let the variables be as follows:

  $\begin{array}{l}O=\text{ Total cost of order}\\ C=\text{ Cost per shirt}\\ T=\text{ Number of T-shirts}\\ S=\text{ Standard charge}\end{array}$

The total cost of an order can be evaluated as follows:

  $\text{Total cost of order}=\left[\left(\text{Cost per shirt}\right)\left(\text{Number of T-shirts}\right)\right]+\text{Standard charge}$

Therefore, the equation will be as follows:

  $O=CT+S$

b.

To determine

To find: the cost per T-shirt.

Answer to Problem 36E

$6.75

Explanation of Solution

Given information:

The given data is as follows:

Order No.	Number of T-shirts	Total order cost ($)
1	40	295
2	80	565

Each order included standard shipping and handling charges.

The equation evaluated in problem a. is as follows:

  $O=CT+S$

Here, the variables $O$ is total cost of order, $C$ is cost per shirt, $T$ is number of T-shirts, and $S$ is Standard charge.

Calculation:

Compare the given equation with the slope intercept equation as follows:

  $\begin{array}{l}y=mx+b\\ O=CT+S\\ \therefore y=O,x=T,\text{ and }m=C\end{array}$

Thus, the slope equation for the given equation can be written as follows:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ C=\frac{O_2-O_1}{T_2-T_1}\mathrm{...}\left(1\right)\end{array}$

Put the value $T_1=40,T_2=80,O_1=\$295$ and $O_2=\$565$ in equation (1) and evaluate C as follows:

  $\begin{array}{c}C=\frac{\$565-\$295}{80-40}\\ =\frac{\$270}{40}\\ =\$6.75\end{array}$

Thus, the cost per T-shirt is $\$6.75$ .

c.

To determine

To find: the standard shipping and handling charge.

Answer to Problem 36E

$25

Explanation of Solution

Given information:

The given data is as follows:

Order No.	Number of T-shirts	Total order cost ($)
1	40	295
2	80	565

Each order included standard shipping and handling charges.

The equation evaluated in problem a. is as follows:

  $O=CT+S$

Here, the variables $O$ is total cost of order, $C$ is cost per shirt, $T$ is number of T-shirts, and $S$ is Standard charge.

The value of C is $6.75.

Calculation:

Put the value of C, T and O of first order in the given equation and evaluate S as shown below.

  $\begin{array}{c}O=CT+S\\ \$295=\$6.75\left(40\right)+S\\ \$295=\$270+S\\ S=\$295-\$270\\ =\$25\end{array}$

Thus, the standard shipping and handling charge is $25.