The revised Harris-Benedict equation for a woman’s BMR is given by BMR =9.247w+3.098 h-4.330a+447.593, where w is the woman’s weight in kilograms, h is her height in centimetres, a is her age in years, and the BMR is measured in kilocalories per day. For men, the revised Harris-Benedict equation is given by BMR=13.397w+4.799 h-5.677a+88.362. The Mifflin-St. Jeer equation states the new BMR formula as BMR =10.0w+6.25 h-5.0a+s, where s=+5 for men and s=-161 for women. A person cannot control their age and height, but they can control their weight. Suppose a man wanted to reduce the BMR reading by 200kcal per day. If the man’s BMR is 1700kcal per day, his age is 27 , and height is 173 cm, then substitute into both formulas and solve the resulting equations to determine how much weight he would have to lose to achieve this reduction. According to the revised Harris-Benedict formula, a man has to lose approximately kg to reduce the BMR reading by 200kcal per day. (Simplify your answer. Round to the nearest whole number as needed.) According to the Mifflin-St. Jeer BMR formula, a man has to lose approximately kg to reduce the BMR reading by 200kcal per day. (Simplify your answer. Round to the nearest whole number as needed.)
The Correct Answer and Explanation is :
To achieve a 200 kcal reduction in BMR per day, let’s break down the calculations for both formulas:
1. Revised Harris-Benedict Formula:
Given that the man’s initial BMR is 1700 kcal per day, and his age is 27, height 173 cm, we can substitute these values into the formula:
[
\text{BMR} = 13.397w + 4.799h – 5.677a + 88.362
]
To reduce the BMR by 200 kcal, we set the equation:
[
1700 – 200 = 13.397w + 4.799(173) – 5.677(27) + 88.362
]
Solving for ( w ) (weight), the result is approximately 54.84 kg of weight loss needed.
2. Mifflin-St. Jeer Formula:
Using the Mifflin-St. Jeer equation, we substitute the same values into the following formula for men (with ( s = +5 )):
[
\text{BMR} = 10.0w + 6.25h – 5.0a + 5
]
To reduce the BMR by 200 kcal:
[
1700 – 200 = 10.0w + 6.25(173) – 5.0(27) + 5
]
Solving for ( w ), the result is approximately 54.88 kg of weight loss needed.
Conclusion:
- According to the Revised Harris-Benedict formula, the man needs to lose 55 kg (rounding to the nearest whole number).
- According to the Mifflin-St. Jeer formula, the man needs to lose 55 kg as well.
This weight loss will reduce his BMR by 200 kcal per day.