Final answer:
To find the goal weight with 20% body fat, we calculate the lean body mass (LBM) first and then adjust the body weight to reflect the desired body fat percentage. Starting with a current body weight of 180 pounds and 25% body fat, the LBM is 135 pounds. The goal weight, for this case, is closest to 168 pounds.
Step-by-step explanation:
To determine the goal weight of a client who currently has 25% body fat and wants to decrease this to 20% body fat, we need to calculate the lean body mass and then find what the total body weight would be with only 20% body fat.
First, we calculate the lean body mass (LBM):
(100% - current body fat percentage) x current body weight = LBM
(100% - 25%) x 180 pounds = 75% x 180 pounds = 135 pounds.
Now, we calculate the goal weight:
The LBM should now represent 80% of the total body weight, because 100% - 20% body fat = 80%.
So if 135 pounds is 80% of the total body weight, we use the following equation:
135 pounds / 80% = goal weight
135 pounds / 0.8 = 168.75 pounds.
Since we are looking for the closest estimate, we can round this figure to the nearest whole number, giving us an answer of 169 pounds, which is not listed in the options provided. However, the closest option is 168 pounds, so the most accurate answer from the choices given is option b. 168 pounds.