College Algebra, Exercise P, Exercise P.4, Section Exercise P.4, Problem 104

The equation $\displaystyle D = 703\frac{W}{H62}$ represents the body-mass index used by medical researchers to determine whether a person is overweight, underweight or of normal weight. Where $W$ is the weight in pounds, $H$ is the height measured in inches.
A body-mass index is considered "normal" if it satisfies $19.5 \leq B \leq 24.9$, while a person with body-mass index $B \geq 30$ is considered obese.

a.) Calculate the body-mass index for each person listed in the table, then determine whether he or she is of normal weight, underweight, overweight, or obese..

$
\begin{array}{|c|c|c|}
\hline\\
\text{Person} & \text{Weight} & \text{Height}\\
\hline\\
\text{Carlo} & 295 \text{ lb} & 5 \text{ ft } 10 \text{ in}\\
\\
\text{Richard} & 105 \text{ lb} & 5 \text{ ft } 6 \text{ in}\\
\\
\text{Marlon} & 220 \text{ lb} & 6 \text{ ft } 4 \text{ in}\\
\\
\text{Angel} & 110 \text{ lb} & 5 \text{ ft } 2 \text{ in }\\
\hline
\end{array}
$


For Carlo, $W = 295$ lb and $H = $5ft 10in or 70in (Recall that 1 ft = 12in.)

$
\begin{equation}
\begin{aligned}
B &= 703 \frac{W}{H^2} && \text{Model}\\
\\
B &= 703 \frac{(295\text{lb})}{(70\text{in})^2}\\
\\
B &= 42.32 \frac{\text{lb}}{\text{in}^2}
\end{aligned}
\end{equation}
$

Based from the condition, Carlo is an obese person.

For Richard, $W$ = 105 lb and $H$ = 5ft 6in or 66in (Recall that 1ft = 12in.)

$
\begin{equation}
\begin{aligned}
B &= 703 \frac{W}{H^2} && \text{Model}\\
\\
B &= 703 \frac{(105\text{lb})}{(66\text{in})^2}\\
\\
B &= 16.95 \frac{\text{lb}}{\text{in}^2}
\end{aligned}
\end{equation}
$

Based from the condition, Richard is underweight.

For Marlon, $W$ = 220 lb and $H$ = 6ft 4in or 76in (Recall that 1ft = 12in.)

$
\begin{equation}
\begin{aligned}
B &= 703 \frac{W}{H^2} && \text{Model}\\
\\
B &= 703 \frac{(220\text{lb})}{(76\text{in})^2}\\
\\
B &= 26.78 \frac{\text{lb}}{\text{in}^2}
\end{aligned}
\end{equation}
$

Based from the condition, Marlon is overweight.

For Angel, $W$ = 110 lb and $H$ = 5ft 2in or 62in (Recall that 1ft = 12in.)

$
\begin{equation}
\begin{aligned}
B &= 703 \frac{W}{H^2} && \text{Model}\\
\\
B &= 703 \frac{(110\text{lb})}{(62\text{in})^2}\\
\\
B &= 20.12 \frac{\text{lb}}{\text{in}^2}
\end{aligned}
\end{equation}
$

Based from the condition, Angel has a normal weight.