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.

From what you said, BMI = kw/h²
where k is a proportionality constant, w is weight and h is height.

Take the data given and solve for k
24 = kw/h² = k177/72² = 0.0341k
k = 703

thus the equation is BMI = 703w/h²

BMI = 703•162 / 66² = 26

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Tringa0 Tringa0 · Answer 2 · 2019-09-24T10:52:03+02:00

Answer:

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

Explanation:

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

[tex]BMI\propto \frac{w}{h^2}[/tex]

[tex]BMI=k\times \frac{w}{h^2}[/tex]

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

[tex]24=k\times \frac{177 lb}{(72 inches)^2}[/tex]

[tex]k=\frac{24\times (72 inches)^2}{177 lb}[/tex]

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

w = 180 lb , h = 75 inches

[tex]BMI'=k\times \frac{180 lb}{(75 inches)^2}[/tex]

Substitute value 'k' calculated above:

[tex]BMI'=\frac{24\times (72 inches)^2}{177 lb}\times \frac{180 lb}{(75 inches)^2}[/tex]

[tex]BMI'=22.493\approx 2[/tex]

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