If you want to lose 4 lb of "body fat," which is 15% water, how many kilocalories do you need to expend?

I don't know how advance this class is nor how detailed this is to be done but I will do it the easy way.

I understand that it takes 3500 kcal to be expended for every lb of "body fat" lost; therefore, 4 lb x 3500 kcal/lb = about 14,000 kcal.
You realize that 3500 kcal/lb is an average. You may have used a different value in your classes so use that number if you have it at hand. Good luck.

4lbs = 15% water, 85% fat

4 lbs = 1814.37 g

1,814.37 g x 0.85 = 1,542.2145 g

Assuming fat provides energy at 9 kcal/g,
1,542.2145 g x 9 kcal/g = 13,879.9305 kcal

Rounding to 1 sig fig: 10,000 kcal

Well, here's some food for thought: Losing weight can be a tricky business. If you want to lose 4 pounds of body fat, which is 15% water, you'll need to burn more calories than you consume. As a rule of thumb, you'd have to burn approximately 3,500 calories to shed one pound of body fat. So, to lose 4 pounds, you're looking at a staggering 14,000 calories burned! But hey, don't worry too much—you can always dance the tango with a donut while juggling pineapples to help burn those calories.

To calculate the number of kilocalories you need to expend to lose 4 lb (pounds) of body fat, we first need to determine the total energy content of the body fat.

Given that body fat is 15% water, we can assume that the remaining 85% is fat. To find the amount of fat in 4 lb of body fat, we multiply 4 lb by 0.85 (85% expressed as a decimal):

Fat = 4 lb * 0.85 = 3.4 lb

Next, we need to convert the 3.4 lb of fat to kilograms, as kilocalories are typically measured per kilogram. Since 1 lb is approximately 0.45 kg, we can calculate:

Fat (in kg) = 3.4 lb * 0.45 kg/lb = 1.53 kg

Now, we can use the fact that 1 kg of body fat contains around 7700 kilocalories. Multiplying this by the 1.53 kg of fat, we find:

Kilocalories = 1.53 kg * 7700 kcal/kg ≈ 11,781 kcal

Therefore, to lose 4 lb of body fat, you would need to expend approximately 11,781 kilocalories. It is important to note that this calculation is an estimation and individual results may vary. It's also crucial to focus on sustainable weight loss methods, such as a combination of regular exercise and a balanced diet, to ensure overall health and well-being.

You may be interest in knowing that I found a way to estimate that 3500 number. So-called "pure" fat is 9 kcal/g and since this body fat in the problem is listed as 85% fat (15% water) then that 9 kcal/g will be

9 kcal/g x 0.85 = 7.65 kcal/g for this 85% stuff. Then
7.65/g x 454 g/lb x 4 lb = 13,892 kcal to be expended which is quite close to that 14,000 estimated above. That 14,000, by the way, was based on close to 86% water.