Chapter 3.2, Problem 21E

Reminder Round all answer to two decimal places unless otherwise indicated.

Lean Body Weight in Females This is a continuation of Exercise 20. The text cited in Exercise $20$ gives a more complex method of calculating lean body weight for your adult females:

$L=19.81+0.73W+21.2R-0.88A-1.39H+2.43F.$

Here $L$ is lean body weight in pounds, $W$ is weight in pounds, $R$ is wrist diameter in inches, $A$ is abdominal circumference in inches, $H$ is hip circumference in inches, and $F$ is forearm circumference in inches. Assuming the validity of the formulas given here and in Exercise $20,$ compare the increase in lean body weight of young adult males and of young adult females if their weight increases but all others factors remain the same.

Lean Body Weight in Males Your lean body weight $L$ is the amount you would weigh if all the fat in your body were to disappear. One text gives the following estimate of lean body weight $L$ (in pounds) for young adult males:

$L=98.42+1.08W-4.14A,$

Where $W$ is total weight in pounds and $A$ is abdominal circumference in inches. ${}^7$

a. Consider a group of young adult males who have the same abdominal circumference. If their weight increases but their abdominal circumference remains the same, how does their lean body weight change?

b. Consider a group of young adult males who have the same weight. If their abdominal circumference decreases but their weight stays the same, how does their lean body weight change?

c. Suppose a young adult male has a lean body weight of $144$ pounds. Over a period of time, he gains $15$ pounds in total weight, and his abdominal circumference increases by $2$ inches. What is his lean body weight now?