Need some help with percentages
I'm really struggling with a percentage problem for a new spreadsheet I'm developing to support me achieving my fitness and weight goals. I'm hoping to develop something which will help others to lose weight as I think I have a really good system for losing and maintaining weight. Here goes:
I'm trying to calculate how many weeks it will take me to achieve my body fat goals following the nutrition programme I've just designed. The measure I'm struggling with is called 'Lean Body Mass' which is essentially your weight minus you Body Fat Mass; here's an example:
Weight in kg: 71kg
Body Fat Percentage (BFP): 12%
Body Fat Mass = Weight – (Weight*BFP), or in my example Body Fat Mass = 71-(71*0.12) = 8.5kg, therefore,
Lean Body Mass = Weight – Body Fat Mass, i.e., Lean Body Mass = 71-8.5 = 62.5kg
The complexity comes in when I try to calculate what my target Body Fat Mass is should my BFP be 7%. It sounds easy because we know what my Lean Body Mass is, but you can't just add 7% to BFP as it gives an incorrect figure. For example, if we try to reverse engineer the first problem it works out like this:
Weight = Lean Body Mass * BFP, or in our example, Weight = 62.5*1.12 = 70kg. The unknown factor is the total new weight so this causes the problem.
In summary, I need to know how to calculate my 71kg starting weight from my Lean Body Mass of 62.5kg and my known BFP of 12%.
Can someone please help as this is driving me crazy?