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 157 lb has a BMI of 21.29, how much weight would a 6 ft, 11 in tall person weighing 207 lb need to gain or lose to have a BMI of 22?

To find the weight change required for a 6ft 11in tall person to reach a BMI of 22, we first calculate the BMI constant using a known BMI case. Then we use this constant in the algebraic BMI formula to solve for the new weight, and subtract the current weight to find the required weight gain or loss.

Explanation:

To determine the weight a 6ft, 11in tall person would need to gain or lose to reach a BMI of 22, we can start by utilizing the given BMI formula:

BMI = [weight (lb) x 703] / [height (in)]2

First, let's calculate the BMI for the provided 6ft tall, 157lb individual:

BMI = [157 lb x 703] / [72 in]2

BMI = 21.29 (as given)

Let's use this information to find the proportionality constant. Rearranging the formula and substituting in the provided values, we get:

k = BMI x height2 / weight

k = 21.29 x 722 / 157

Now, using the height in inches for a person who is 6ft 11in tall (83 inches) and the desired BMI of 22, we will solve for the new weight (W):

22 = k / 832

W = 22 x 832 / k

After solving for W, we can subtract the current weight (207lb) to determine the weight change required.

Here's the step-by-step calculation:

Find the constant k using the known BMI, weight, and height of the first person.
Calculate the new weight (W) using the constant k, the height of the second person, and the desired BMI.
Determine the difference between W and the current weight to find out how much weight the second person needs to gain or lose.