Calculate weight based on body fat percentage

Question

This is the YMCA method for determining body fat percentage for a female based on weight and waist size:

$${-76.76+(4.5A)-(0.082B)\over B}=C$$

Where: A = Waist size in inches, B = Weight in lbs, C = Ratio of body fat.

I would like to re-arrange this formula to solve for B.

ie: determine target weight based on waist and body fat ratio.

Source: http://web.archive.org/web/20150312220209/http://strengthunbound.com/measure-body-fat-easily-accurately-home/

Thanks in advance! :-)

Answer 1

Cross multiply:

$$-76.76 + 4.5 A - 0.082B = BC$$

Rearrange:

$$-76.76 + 4.5 A = 0.082 B + BC$$

$$-76.76 + 4.5 A = (0.082 + C)B$$

So:

$$B = \frac{-76.76 + 4.5 A }{0.082 + C}$$