Body composition scale results

Question

Problem: 

Hi I have a body composition test result question to ask, it’s quite basic but because of a lot of head trouble I’m unable to work it out so I need your help please...

Basically here is the the first reading:

(Beginning weight)

Week one: 

Total weight: 175.8kg

Percentage of body fat: 42% 

Percentage of muscle: 28% 

(Final weight)

Week 3:

Total weight: 179.9kg = 4.1 kg 

Percentage of body fat: 39% 

Percentage of muscle: 30%

Questions:

How much body fat was lost total ? = 

How much muscle was gained total ?= 

Does your end calculation tally up to the final body weight of 179.9kg? =

Things to consider:  According to the composition results 3% fat was lost And 2% muscle gained All summing up to final weight 🙃 in week 3

Remember the final weight is 179.9kg after losing 3% body fat...

It’s not as easy as it seems

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Debated solutions 

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Here are the 2 major solutions, all producing different results:

Introduction:

Start weight = 175.80kgs

End weight = 179.90kgs

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Only look at this section if simplification needed else work it out yourselves please:

Start Fat weight =73.836kg

End Fat weight =70.161kg

Start muscle weight=49.222kg

End muscle weight = 53.97kg 

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Solution 1:

FAT:

Fat = 42% of 175.80(0.42 * 175.80) = 73.836kg 

ANS : Lost 3% of fat (73.836kg) =  0.03 * 73.836 = 2.21kg fat lost 

Basically 3 percent of 73.836 is 2.21kg

Rough estimation: We know this because 3% of 100 is 3 yes? And 73 is not far off from 100

Muscle:

Muscle = 28% of 175.80 (0.28 * 175.80) = 49.222kg 

ANS: Gained 2% of muscle = 0.02 * 49.222 = 0.98kg muscle gained 

Solution 2: 

 

Starting Fat (73.836kg) - end fat (70.161) = 3.702kg fat lost 

End muscle  (53.97) - Starting Muscle (49.224kg) = 4.746kg muscle gained

Answer 1

Hi Jah-Femi T.,

Set the problem up as:

Beginning weight:

Total weight: 175.8kg

Percentage of body fat: 42% 

Percentage of muscle: 28%

Other: 30%, (organ mass, blood, water, etc.)

Final weight:

Total weight: 179.9kg = 4.1 kg 

Percentage of body fat: 39% 

Percentage of muscle: 30%

Other: 31%

Then muscle gain + other gain - fat loss = 4.1 kg

I hope this helps, Joe.