Chapter 1, Problem 1.108QP

(a)

Interpretation Introduction

Interpretation:

Sally and Gertrude were comparing their weight-loss regimen.  Sally started her diet weighing $\text{193}\text{lb}$ and in one year she weighed $\text{145}\text{lb}$.  Whereas Gertrude started her diet weighing $\text{80}\text{kg}$ and at the end of the year, she weighed $\text{65}\text{kg}$.  The problem solving strategy used to determine who was more successful in the loss of weight has to be described.

Explanation of Solution

The problem solving strategy is conversion of units.

The pound can be converted into grams by a sequence of conversion by the conversion factors:

  $\begin{array}{l}\text{Conversion}\text{of}\text{pound}\text{to}\text{gram:}\\ \text{1}\text{lb}\text{=}\text{454}\text{g}\\ \text{Conversion}\text{factor:}\\ \text{=}\frac{\text{454}\text{g}}{\text{1}\text{lb}}\\ \text{Conversion}\text{of}\text{gram}\text{to}\text{kilogram:}\\ \text{1}\text{kg}\text{=}{\text{10}}^{\text{3}}\text{g}\\ \text{conversion}\text{factor:}\\ \text{=}\frac{\text{1}\text{kg}}{{\text{10}}^{\text{3}}\text{g}}\end{array}$

The overall conversion of pound to kilogram can be given as

  $\text{=}\frac{\text{454}\text{g}}{\text{1}\text{lb}}\text{×}\frac{\text{1}\text{kg}}{{\text{10}}^{\text{3}}\text{g}}$

The weight lost by Sally and Gertrude can be calculated either by converting the pounds into kilograms or by converting the kilograms into pounds.

(b)

Interpretation Introduction

Interpretation:

Sally and Gertrude were comparing their weight-loss regimen.  Sally started her diet weighing $\text{193}\text{lb}$ and in one year she weighed $\text{145}\text{lb}$.  Whereas Gertrude started her diet weighing $\text{80}\text{kg}$ and at the end of the year, she weighed $\text{65}\text{kg}$.  The weight lost by Sally and Gertrude has to be calculated in pounds and kilograms.

Explanation of Solution

The weight of Sally before started the diet is $\text{193}\text{lb}$ and in one year she weighed $\text{145}\text{lb}$.  The weights are converted into kilograms by the conversion factor.

  $\begin{array}{l}\text{Given,}\text{before}\text{weight}\text{=}\text{193}\text{lb}\\ \text{after}\text{weight}\text{=}\text{145}\text{lb}\\ \text{193}\text{lb:}\\ \text{=}\text{193}\text{lb}\text{×}\frac{\text{454}\text{g}}{\text{1}\text{lb}}\text{×}\frac{\text{1}\text{kg}}{{\text{10}}^{\text{3}}\text{g}}\\ \text{=}\text{87}\text{.6}\text{kg}\\ \text{145}\text{lb:}\\ \text{=}\text{145}\text{lb}\text{×}\frac{\text{454}\text{g}}{\text{1}\text{lb}}\text{×}\frac{\text{1}\text{kg}}{{\text{10}}^{\text{3}}\text{g}}\\ \text{=}\text{65}\text{.8}\text{kg}\\ \text{weight}\text{lost}\text{=}\text{87}\text{.6}\text{kg}\text{-}\text{65}\text{.8}\text{kg}\\ \text{=}\text{21}\text{.8}\text{kg}\end{array}$

The weight of Gertrude before started the diet is $\text{80}\text{kg}$ and in one year she weighed $\text{65}\text{kg}$.  The weights are converted into pounds by the conversion factor.

  $\begin{array}{l}\text{Given,}\text{before}\text{weight}\text{=}\text{80}\text{kg}\\ \text{after}\text{weight}\text{=}\text{65}\text{kg}\\ \text{80}\text{kg:}\\ \text{=}\text{80}\text{kg}\text{×}\frac{{\text{10}}^{\text{3}}\text{g}}{\text{1}\text{kg}}\text{×}\frac{\text{1}\text{lb}}{\text{454}\text{g}}\\ \text{=}\text{176}\text{.2}\text{lb}\\ \text{65}\text{kg:}\\ \text{=}\text{65}\text{kg}\text{×}\frac{{\text{10}}^{\text{3}}\text{g}}{\text{1}\text{kg}}\text{×}\frac{\text{1}\text{lb}}{\text{454}\text{g}}\\ \text{=}\text{143}\text{.2}\text{lb}\\ \text{weight}\text{lost}\text{=}\text{80}\text{kg}\text{-}\text{65}\text{kg}\\ \text{=}\text{15}\text{kg}\end{array}$

Sally lost more weight than Gertrude in a year.