Questions: 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 158 lb has a BMI of 21.43, how much weight would a 6 ft, 4 in. tall person weighing 170 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.

Solution Steps

The Body Mass Index (BMI) is given by the formula: \[ \text{BMI} = \frac{703 \times \text{weight (lb)}}{\text{height (in)}^2} \]

Convert the height of the person from feet and inches to inches.

• 6 feet = 72 inches
• 4 inches = 4 inches
• Total height = 72 + 4 = 76 inches

We need to find the weight \( W \) that gives a BMI of 20 for a person who is 76 inches tall. \[ 20 = \frac{703 \times W}{76^2} \]

Rearrange the equation to solve for \( W \): \[ W = \frac{20 \times 76^2}{703} \] \[ W = \frac{20 \times 5776}{703} \] \[ W = \frac{115520}{703} \] \[ W \approx 164.3 \text{ lb} \]

The current weight of the person is 170 lb. To find the weight change: \[ \text{Weight change} = 170 \text{ lb} - 164.3 \text{ lb} \] \[ \text{Weight change} = 5.7 \text{ lb} \]

Final Answer