A portly biochemistry professor weighs 260 lb (118 kg) and is 5 feet 8 inches (173 cm) tall. What is his body mass index? How much weight would he have to lose to bring his body mass index down to 25 (normal)?
The correct answer and explanation is :
To calculate the Body Mass Index (BMI), we use the following formula:
[
\text{BMI} = \frac{\text{weight in kilograms}}{(\text{height in meters})^2}
]
Step 1: Convert the weight and height to appropriate units
The professor’s weight is 260 lbs, which is equivalent to 118 kg (since 1 lb = 0.453592 kg).
The professor’s height is 5 feet 8 inches, which is 68 inches. To convert inches to meters, we multiply by 0.0254 (since 1 inch = 0.0254 meters):
[
68 \, \text{inches} \times 0.0254 = 1.7272 \, \text{meters}
]
Step 2: Calculate the BMI
Now, we can calculate the BMI:
[
\text{BMI} = \frac{118}{(1.7272)^2} = \frac{118}{2.981} \approx 39.6
]
So, the professor’s current BMI is approximately 39.6, which falls in the obese category (BMI > 30).
Step 3: Determine the weight needed for a BMI of 25
To achieve a BMI of 25, we rearrange the formula to solve for weight:
[
\text{weight} = 25 \times (\text{height in meters})^2
]
Substitute the professor’s height (1.7272 meters):
[
\text{weight} = 25 \times (1.7272)^2 = 25 \times 2.981 \approx 74.5 \, \text{kg}
]
To convert this weight back to pounds, multiply by 2.20462 (since 1 kg = 2.20462 lbs):
[
74.5 \, \text{kg} \times 2.20462 \approx 164.2 \, \text{lbs}
]
Step 4: Calculate the weight loss needed
The professor currently weighs 260 lbs. To bring his BMI down to 25, he would need to weigh around 164.2 lbs. Thus, the weight he needs to lose is:
[
260 – 164.2 \approx 95.8 \, \text{lbs}
]
Conclusion:
To reduce his BMI to 25, the professor would need to lose approximately 95.8 lbs (43.4 kg). This would bring his weight within the normal BMI range (18.5 to 24.9).