Chapter 2, Problem 1GA

Computing Body Mass Index (BMI)

Materials: Calculator

Estimated Time: 10 minutes

Group Size: 2

Body mass index is a statistical measures of an individual's weight in relation to the person's height. It is computed by

$\text{BMI}=\frac{703W}{h^2}$ $\begin{array}{l}\text{were }W\text{ is a person's weight in }pounds\text{.}\\ h\text{ is the person's height in }inches\text{.}\end{array}$

The National Institutes of Health (NIH) categorizes body mass indices as shown in the table.

Body Mass Index (BMI)	Weight Status
$18.5\le \text{BMI}\le 24.9$	Considered ideal
$25.0\le \text{BMI}\le 29.9$	Considered overweight
$\text{BMI}\ge 30.0$	Considered obese

Compute the body mass index for a person $5^{\prime }{4}^{″}$ tall weighing 160 lb. Is this person's weight considered ideal?

To determine

To calculate: The BMI ofa person who is $5\text{'}4"$ and weighs $160\text{ lb}$.

Answer to Problem 1GA

Solution:

The BMI of the person is $27.46$.

Since the BMI falls in the range of $25.0\le 27.46\le 29.9$. Therefore, no person is considered overweight.

Explanation of Solution

Given Information:

Person is $5\text{'}4"$ and weighs $160\text{ lb}$.

Calculation:

The BMI of a person is given by the relation as follows:

$\text{BMI}=\frac{703W}{h^2}$ …… (1)

Here, $W$ is the weight in pounds and $h$ is the height in inches.

One foot contains 12 inches in total. Therefore the height of $5\text{'}4"$ in inches can be expressed as:

$\begin{array}{c}5\text{'}4"=5\times 12+4\\ =60+4\\ =64\end{array}$

So, the height of $5\text{'}4"$ in inches is $64$.

Substitute $160\text{ lb}$ for $W$ and $64$ for $h$ in equation (1).

$\begin{array}{c}\text{BMI}=\frac{703\left(160\right)}{{\left(64\right)}^2}\\ =\frac{703\times 160}{4096}\\ =\frac{112480}{4096}\\ =27.46\end{array}$

Therefore, the BMI of the person is $27.46$.

Since the BMI falls in the range of $25.0\le 27.46\le 29.9$, therefore the person is considered overweight.