Question

body - mass index, or bmi, takes both weight and height into account when assessing whether an individual is underweight or overweight. bmi varies directly as ones weight, in pounds, and inversely as the square of ones height, in inches. in adults, normal values for the bmi are between 20 and 25. a person who weighs 183 pounds and is 70 inches tall has a bmi of 26.25. what is the bmi, to the nearest tenth, for a person who weighs 119 pounds and who is 63 inches tall?

a. 21.4
b. 20.7
c. 21.1
d. 20.4

Explanation:

Step1: Find the proportionality constant

The formula for BMI is $BMI = k\frac{W}{H^{2}}$, where $W$ is weight, $H$ is height and $k$ is the constant. Given $BMI = 26.25$, $W = 183$ and $H=70$, we can solve for $k$.
$26.25=k\frac{183}{70^{2}}$
$k = 26.25\times\frac{70^{2}}{183}$
$k = 26.25\times\frac{4900}{183}$
$k=\frac{26.25\times4900}{183}=\frac{128625}{183}\approx 692$

Step2: Calculate the new BMI

Now we use the value of $k$ to find the BMI for $W = 119$ and $H = 63$.
$BMI=k\frac{W}{H^{2}}$
$BMI = 692\times\frac{119}{63^{2}}$
$BMI=692\times\frac{119}{3969}$
$BMI=\frac{692\times119}{3969}=\frac{82348}{3969}\approx 20.7$

Answer:

B. 20.7