Chapter 6, Problem 14STP

(a)

To determine

To Find :

The rate of change of the shipping charge per pound.

Answer to Problem 14STP

The rate of change is 59 cents per pound of weight.

Explanation of Solution

Given :

The amount that a retailer charges for shipping an electronics purchase is determined by the weight of the package.The charges for several different weights are given in the table.

  

Concept Used :

• Slope of a line passing through points $(x_1,y_1)\&(x_2,y_2)\text{ is given by m=}\frac{y_2-y_1}{x_2-x_1}$

Calculation:

  $\begin{array}{l}\text{To find the rate of change of the shipping chare per pound,}\\ \text{we need to find the slope:}\\ slope=\frac{change\text{ in the shipping charge}}{change\text{ in the weight }}=\frac{6.76-5.58}{3-1}=0.59=\frac{7.35-6.76}{4-3}\\ So,the\text{ rate of change is 0}\text{.59 \$ per pound of weight or}\\ \text{the rate of change is 59 cents per pound of weight}\text{.}\\ \text{Since 1\$=100 cents }\end{array}$

(b)

To determine

To Find :

Write an equation that could be used to find the shipping charge y for a package that weighs x pounds .

Answer to Problem 14STP

  $\begin{array}{l}y=0.59x+4.99\\ where\\ \text{x= weight in pound}\\ \text{y= shipping charge in \$}\end{array}$

Explanation of Solution

Given :

The amount that a retailer charges for shipping an electronics purchase is determined by the weight of the package.The charges for several different weights are given in the table.

  

From part (a) ,

The rate of change is 59 cents per pound of weight.

Concept Used :

• Slope of a line passing through points $(x_1,y_1)\&(x_2,y_2)\text{ is given by m=}\frac{y_2-y_1}{x_2-x_1}$
• Slope intercept form a linear equation:

  $\begin{array}{l}y=mx+b\\ where\\ m=slope\\ b=y-\mathrm{int}ercept\end{array}$

Calculation:

  $\begin{array}{l}Let\\ x=weight\\ y=shipping\text{ cost}\\ {\text{(x}}_1,y_1)=(1,5.58)\\ (x_2,y_2)=(3,6.76)\\ From\text{ part (a) , slope = m = }\frac{y_2-y_1}{x_2-x_1}=0.59\\ \text{Slope Intercept form of a linear equation:}\\ y=mx+b\\ b=y-\mathrm{int}ercept\\ Substitute\text{ (x,y)=(1,5}\text{.58), m= 0}\text{.59 and find b:}\\ 5.58=0.59(1)+b\\ b=5.58-0.59=4.99\\ So,the\text{ equation is given by:}\\ y=0.59x+4.99\\ where\\ \text{x= weight in pound}\\ \text{y= shipping charge in \$}\end{array}$

(c)

To determine

To Find :

The shipping charge for a package that weighs 19 pounds.

Answer to Problem 14STP

  $\text{The shipping cost for a package that weighs 19 pounds is \$16}\text{.20}\text{.}$

Explanation of Solution

Given :

From part (b), we have the equation :

  $\begin{array}{l}y=0.59x+4.99\\ where\\ \text{x= weight in pound}\\ \text{y= shipping charge in \$}\end{array}$

Calculation:

  $\begin{array}{l}\text{Given:}\\ y=0.59x+4.99\\ where\\ \text{x= weight in pound=19 pounds}\\ \text{y= shipping charge in \$}\\ \text{Substitute the value x = 19 in the equation and solve for y:}\\ y=0.59x+4.99=0.59(19)+4.99\\ y=11.21+4.99=16.2\\ So,\text{ the shipping cost for a package that weighs 19 pounds is \$16}\text{.20}\text{.}\end{array}$