Question

The federal government has developed the body mass index​ (bmi) to determine ideal weights. a​ person's bmi is directly proportional to his or her weight in pounds and inversely proportional to the square of his or her height in inches.​ (a bmi of 19 to 25 corresponds to a healthy​ weight.) a​ 6-foot-tall person weighing 177 lb has bmi 24. find the bmi​ (to the nearest whole​ number) of a person whose weight is 180180 lb and whose height is 7575 in.

Answer 1

The BMI of a person whose weight is 180 lb and whose height is 75 inches is 22.

Step-by-step explanation:

According to question , BMI is directly proportional to weight in pounds and inversely proportional to the square of height inches.

`BMI\propto (w)/(h^2)`

`BMI=k* (w)/(h^2)`

BMI = body mass index

w = weight of person in pounds

h = height of the person inches.

BMI of a​ 6-foot-tall person weighing 177 lb = 24

w = 177 lb , h = 6 feet = 72 inches

1 feet = 12 inches

`24=k* (177 lb)/((72 inches)^2)`

`k=(24* (72 inches)^2)/(177 lb)`

BMI of a​ 75 inhces person weighing 180 lb = BMI'

w = 180 lb , h = 75 inches

`BMI'=k* (180 lb)/((75 inches)^2)`

Substitute value 'k' calculated above:

`BMI'=(24* (72 inches)^2)/(177 lb)* (180 lb)/((75 inches)^2)`

`BMI'=22.493\approx 2`

The BMI of a person whose weight is 180 lb and whose height is 75 inches is 22.