Find a model for the Body Mass Index (BMI) of a person, given that BMI varies directly as a person's weight in pounds and inversely as the square of the person's height in inches.

If a 6 ft tall person weighing 143 lb has a BMI of 19.39, how much weight would a 5 ft, 4 in. tall person weighing 119 lb need to gain or lose to have a BMI of 20?

Write your answer as a positive value for weight gain or a negative value for weight loss. Round your answer to one decimal place.

Answer:

The Body Mass Index (BMI) of a person varies directly with weight and inversely with height squared. Using the given information, we can find the weight needed for a person to have a specific BMI.

Explanation:

The Body Mass Index (BMI) of a person can be modeled using the equation:

BMI = k * (weight / height^2)

In this equation, BMI varies directly with a person's weight in pounds and inversely with the square of their height in inches. To find the value of k, we can use the provided information:

For a 6 ft tall person weighing 143 lb, BMI is given as 19.39:

19.39 = k * (143 / (6*12)^2)

Solving for k gives us: k = 19.39 / (143 / (6*12)^2)

Now we can find the weight needed for a 5 ft 4 in. tall person to have a BMI of 20:

BMI = 20, height = (5*12 + 4) inches

20 = k * (weight / ((5*12 + 4)^2)

Solving for weight:

weight = 20 * ((5*12 + 4)^2) / k

Plugging in the value of k we found earlier, we can calculate the weight needed.

Learn more about Body Mass Index (BMI) here:

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