Final answer:
Jane's target body weight to achieve 25% body fat, calculated based on her lean body mass and desired fat percentage, is approximately 182.24 pounds. The closest available answer is 180 pounds.
Step-by-step explanation:
Jane is a 55-year-old woman who wants to reduce her body fat from 32% to 25%. To calculate her target body weight, we first need to determine her lean body mass (LBM), which is the portion of her weight that is not fat. We then use the desired body fat percentage to find the target total body weight.
Jane's current body fat in pounds is 32% of her body weight:
201 lbs * 0.32 = 64.32 lbs of fat.
To find her LBM, we subtract her fat weight from her total weight:
201 lbs - 64.32 lbs = 136.68 lbs LBM.
Now we can calculate her target weight by adding the desired amount of fat to her LBM. The desired body fat is 25%, so we want her total weight to be comprised of 75% LBM and 25% body fat. We can set up the equation where 75% of target weight equals her LBM, which is 136.68 lbs:
0.75 * Target Weight = 136.68 lbs.
Solving for Target Weight yields:
Target Weight = 136.68 lbs / 0.75
Target Weight = 182.24 lbs.
Looking at the options given, the closest answer to our calculation is (b) 180 pounds.